do sympathy biases induce charitable giving? the effects of advertising content · 2019-12-04 ·...

Vol. 35, No. 6, November–December 2016, pp. 849–869ISSN 0732-2399 (print) � ISSN 1526-548X (online) https://doi.org/10.1287/mksc.2016.0989

© 2016 INFORMS

Do Sympathy Biases Induce Charitable Giving?The Effects of Advertising Content

K. SudhirSchool of Management, Yale University, New Haven, Connecticut 06520, [email protected]

Subroto RoyCollege of Business, University of New Haven, Orange Campus, Connecticut 06477, [email protected]

Mathew CherianHelpAge India, New Delhi, India 110016, [email protected]

We randomize advertising content motivated by the psychology literature on sympathy generation andframing effects in mailings to about 185,000 prospective new donors in India. We find a significant impact

on the number of donors and amounts donated consistent with sympathy biases such as the “identifiablevictim,” “in-group,” and “reference dependence.” A monthly reframing of the ask amount increases donors andthe amount donated relative to daily reframing. A second field experiment targeted to past donors, finds thatthe effect of sympathy bias on giving is smaller in percentage terms but statistically and economically highlysignificant in terms of the magnitude of additional dollars raised. Methodologically, the paper complements thework of behavioral scholars by adopting an empirical researchers’ lens of measuring relative effect sizes andeconomic relevance of multiple behavioral theoretical constructs in the sympathy bias and charity domain withinone field setting. Beyond the benefit of conceptual replications, the effect sizes provide guidance to managerson which behavioral theories are most managerially and economically relevant when developing advertisingcontent.

Data, as supplemental material, are available at https://doi.org/10.1287/mksc.2016.0989.

Keywords : charitable giving; sympathy biases; identified victim effect; in-group effect; reference dependence;nonprofit marketing; persuasive advertising; informative advertising; direct mail; behavioral economics;conceptual replications

History : Received: November 30, 2013; accepted: December 5, 2015; Preyas Desai served as the editor-in-chiefand Avi Goldfarb served as associate editor for this article. Published online in Articles in AdvanceOctober 11, 2016.

1. IntroductionAs charities face increasingly competitive fundraisingenvironments, they have begun to employ marketingactivities to encourage donations. This has led to anexplosive growth of research in recent years on the“demand side” of charitable giving. These papers havefocused on various dimensions of charitable givingappeals such as incentives, seed money, and match rates(e.g., List and Lucking-Reiley 2002, Karlan and List2007), social comparison (e.g., Shang and Croson 2009),and social pressure (Della Vigna et al. 2012) on donorbehavior. Although there is a large volume of behav-ioral research in the laboratory on how advertising con-tentaffectsoutcomesof interest, there is littlefield-basedempirical research in general on the effects of advertis-ingcontentonconsumerpurchases ingeneralanddona-tion behavior in particular. Our goal in this paper is todocument and quantify the relative magnitudes of var-ious types of advertising appeals on donation behaviormotivated by the psychology theories through large-scale field experiments.

Academic research by empirical scholars on advertis-ing effects using field data typically focus on estimat-ing the relationship between the volume, frequency,and timing of advertising on market outcomes suchas sales and market shares;1 but field research onhow different elements of advertising content affectsmarket outcomes is rare.2 Some exceptions includeBertrand et al. (2010), who vary advertising contentin combination with interest rates and offer dead-lines to study its impact on loan take-up in a directmail field experiment in South Africa and Liaukonyte

1 See Kaul and Wittink (1995), Wind and Sharp (2009), Della Vignaand Gentzkow (2010), and Sethuraman et al. (2011) for reviews ofthe empirical evidence on advertising.2 Otherwise, research on advertising content has focused primarilyon laboratory experiments. To be sure, advertising agencies anddirect marketing firms routinely do copy testing before launchingadvertisements or sending mailers, but these studies are seldomdesigned to enable generalizable learning because they are builton context specific intuition; few results have been reported in theliterature (e.g., Stone and Jacobs 2008).

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https://doi.org/10.1287/mksc.2016.0989

Sudhir, Roy, and Cherian: Do Sympathy Biases Induce Charitable Giving?850 Marketing Science 35(6), pp. 849–869, © 2016 INFORMS

(2012) who codes the video content of TV ads for com-parative and self-promotional advertising and studiesthe differential effect of demand for over the counter(OTC) analgesics in the United States. The paucityof research on advertising content effects is partlybecause unlike the data on the level of spend, fre-quency, and timing, which are easily quantifiable andamenable to empirical testing, content of ads vary ona large number of dimensions, and it is difficult to iso-late dimensions of interest systematically from adver-tisements used in the field.

Psychologists have found that emotions sometimeswork better to motivate people to action than cog-nition; hence, treatments that generate an emotionalresponse can be more effective in generating dona-tions. Sympathy is the particular emotional responsetriggered by another person’s misfortune; laboratoryexperiments consistently show that evoking sympa-thy leads to prosocial behavior and charitable giv-ing (e.g., Bagozzi and Moore 1994, Batson et al. 1997,Coke et al. 1978).

Researchers have demonstrated framing effectscalled “sympathy biases” that can generate dispro-portionately greater sympathy relative to the actualneeds of the victims. We believe this should trans-late to greater giving. Hence, we consider three suchsympathy biases to generate three advertising contenttreatments in our experiment. They are (1) the identi-fied victim effect, (2) the in-group effect, and (3) thereference dependent sympathy effect. Sympathy canbe increased by reducing the perceived social distancefrom the victim (Small 2011). The identified victimeffect reduces the perceived social distance betweenthe donor and the victim by identifying an individ-ual victim to a potential donor; whereas the in-groupeffect reduces social distance because the victim isfrom the same in-group as the target donor. Thereference dependent sympathy effect arises becausesympathy is greater if one framed a victim’s cur-rent condition as a decline from a reference conditionrather than simply presenting the actual condition(Small 2010).

Our additional experimental treatment for adver-tising content involves a temporal reframing of thedonation. Charities often reframe an aggregate annualdonation into a smaller monthly or daily amount,even though the donation itself is annual. For exam-ple, a $365 donation can be made to appear moreaffordable by reframing it as $1 a day or $30 amonth. Such strategies are also used in other market-ing contexts, ranging from insurance, magazine sub-scriptions, durable goods, and charitable donations.Gourville (1998) dubbed such temporal reframing intoa small daily amount as “a pennies a day” (PAD)strategy. However, the pennies a day framing violatesan alternative prescription based on prospect theory

that one should “integrate” losses by combining theminto a larger amount (e.g., Thaler 1985). Thus far, therehas been little research on the bounds of the PADstrategy and whether alternative temporal framingcould lead to superior outcomes. We therefore com-pare donations from monthly and daily reframing.

We test these hypotheses using two field experi-ments in an entirely natural setting in partnershipwith HelpAge India, one of India’s leading chari-ties in the aid of seniors. In the first and primaryexperiment, we tagged onto an annual new donoracquisition campaign, where the organization sendsout mailers to a cold list of around 200,000 high networth individuals all over India. We added an addi-tional flyer to the regular ask used in this campaign.This flyer randomized the contents of the ask mes-sage in line with the hypotheses we sought to test.The magnitude of donations solicited and obtained issignificant relative to incomes in India.3 We find eco-nomically large and statistically significant effects onboth the intensive and extensive margin for the vari-ous sympathy generation and framing effects that wetested. For the various effects we test, the number ofdonations per mailer increases by 43%–155%, and thedonation amount per mailer increases by 33%–110%.

It is likely that the impact of framing on sym-pathy and donation is very high for a cold list ofdonors, because their baseline level of sympathy forthe cause is likely lower. Would such effects of fram-ing vanish among past donors, where the baselinesympathy level for the cause is already high? To testthis, our second experiment targeted a warm list ofabout 100,000 donors, who have previously donatedto HelpAge. As HelpAge was reluctant to conduct thefull battery of treatments, many of which had beenshown to be ineffective in the first experiment, weonly experimented with a few treatments to test ourconjecture that the effect vanishes for past donors.As expected, the percentage impact on donations forour previously largest effect falls; the effect falls from110% to 15%. However the effects remain both statisti-cally and economically significant. In particular, sincethe baseline amount of donations from past donorsis significantly higher, even the 15% increase due tothe sympathy bias generates more in dollars than the110% treatment effect on the cold list. We concludethat whereas framing effects of advertising contenthave a much larger proportional impact in new donoracquisition, the economic impact in incremental abso-lute amounts is very significant among both new andexisting donors.

3 According to the mail list provider, the average annual incomeof the households in the mailed list is about |600,000 (about$10,000). The donation requested is |9,000, about 1.5% of the annualincome. The median amount donated is |3,000, about 0.5% of theannual income.

Sudhir, Roy, and Cherian: Do Sympathy Biases Induce Charitable Giving?Marketing Science 35(6), pp. 849–869, © 2016 INFORMS 851

Methodologically, this paper is part of a small butgrowing empirical literature in marketing using fieldexperiments to measure advertising effects (e.g., East-lack and Rao 1989, Lodish et al. 1995, and Sahni 2015).More broadly, this paper contributes to a researchparadigm bridging empirical work in behavioral andquantitative marketing. Behavioral marketing schol-ars test and provide evidence for particular psy-chological theories in controlled laboratory settings.Because the focus is often on isolating and under-standing the mechanism underlying the novel psycho-logical theories, there is limited interest on whetherthese effects replicate in field settings and whether themagnitude of the effects are managerially important.Lynch et al. (2015) describe the value of conceptualreplications and replications with extensions (moder-ators) in behavioral work in generating marketingknowledge. Furthermore, from a managerial perspec-tive, there is value in knowing the relative magnitudesof the behavioral levers suggested by different theo-ries, so that a firm can prioritize on which behaviorallever to use. Quantitative scholars routinely focus onrelative elasticities of alternative marketing actionson an outcome of interest using field data to aidmanagers in choosing the most effective marketingactions. In a similar vein, this paper complements andbuilds on the behavioral literature to measure the rel-ative magnitudes of alternative behavioral levers onoutcomes of managerial interest—in this case dona-tion behavior.

The rest of the article is organized as follows: Sec-tion 2 provides an industry background and overviewsof the literature. Section 3 describes the hypotheses,and Section 4 describes the experimental setting andtreatments. Section 5 describes the results and Section 6concludes.

2. Background2.1. AdvertisingThe advertising industry is a major sector in theworld economy. In 2011, advertising spending wasabout $147 billion in the United States and $490 bil-lion worldwide. These numbers are likely to growrapidly as advertising is growing rapidly at double-digit rates in emerging markets such as China andIndia, and now accounts for a significant and growingfraction of the economy.4 Even though a large fractionof that cost is incurred on media spending to deliverthe message, the effort and cost on the development

4 China’s advertising spend in 2011 is estimated to be $54 billion andforecast to be $64 billion, an annual growth of 16.9%. Overall, theAsia Pacific region had an advertising spend of $175 billion with anannual growth of 10.2%. See the Group M report (http://www.aaaa.org/120511_groupm_forecast/).

of the advertising “creative” to maximize advertis-ing effectiveness is substantial.5 The industry alsospends considerable effort in evaluating and recog-nizing the effectiveness of creative advertising ideasthrough high profile annual awards such as the CLIOand Effie awards.

Despite the recognition that advertising contentand creativity are critical to advertising effective-ness, econometric research has mostly been aboutthe link between advertising spending on sales (seereviews of the literature in Kaul and Wittink 1995and Chandy et al. 2001). There have also been stud-ies in the direct marketing literature about how vary-ing the number of advertisements or frequency ofmailings impact consumer purchases (e.g., Andersonand Simester 2004, Gönül and Shi 1998). This focuson spend, timing, and frequency of advertising onsales in econometric modeling perhaps arises fromthe easy quantifiability of such variables. Liaukonyte(2012) is an exception in that she codes the video con-tent of over 4,000 TV advertisements to distinguishbetween comparative and self-promotional advertis-ing and studies the impact on demand in the UnitedStates OTC analgesics market.

Research related to advertising content has gener-ally been done by consumer psychologists who haveshown systematic effects of advertising content oncognition, affect, and purchase intentions in the labo-ratory. However there has been little effort on replicat-ing these effects in field settings (Chandy et al. 2001);furthermore, we do not know whether the effectsare large enough to be economically important.6 Wenote that many advertising agencies do test alterna-tive advertising concepts for effectiveness in on-fieldtesting but the insights from such concept tests arehard to generalize because they do not vary contentsystematically in a theoretically grounded manner.7

Bertrand et al. (2010) test the effectiveness of a num-ber of noninformative advertising cues and priceson loan uptake from a credit card lender using adirect mailer-based randomized field experiment. Ourwork is similar in its focus on understanding relativemagnitudes of different advertising content effects. Interms of contrasts (apart from the obvious differencein empirical contexts), their focus is on testing theeconomic magnitudes of ad content relative to priceeffects, whereas we test the relative magnitudes of a

5 The industry had traditionally bundled its creative and media ser-vices and hence share of spend on creative is not available (see Silkand Berndt 2003).6 Levitt and List (2007) provide many reasons for why the labora-tory findings need to be validated on the field.7 Goldfarb and Tucker (2011) recently studied how matching adver-tising to Web content and the level of obtrusiveness impact pur-chase intent through data from a large-scale field experiment.

http://www.aaaa.org/120511_groupm_forecast/

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set of well-recognized sympathy biases documentedin the psychology literature to measure the relativeeconomic importance of these theories for managersin inducing sympathy and charitable giving.

Our paper is also related to the literature on fieldexperiments in advertising. In a landmark set offield experiments, Eastlack and Rao (1989) report theeffects of a number of treatments: marketing budgets,media type and mix, creative copy, and target audi-ence on factory shipments of various products at theCampbell Soup Company. Lodish et al. (1995) reporta meta-analysis of advertising experiments using splitcable, where the only difference between the exper-imental and treatment group was on the TV adver-tisements they saw. Sahni (2015) uses an online fieldexperiment to test for alternative mechanisms bywhich the temporal spacing of advertising impactssales; whereas Bart et al. (2014) use field experimentsto study for which types of products mobile displayadvertising favorably impacted attitudes and pur-chase intentions.

2.2. Charitable GivingCharitable giving constitutes a significant portion ofthe gross domestic product (GDP) of countries. Amer-icans gave more than $306 billion to charity in 2007,or approximately 2.2% of GDP (Sargeant and Shang2008). Despite the recession, Americans gave morethan $290 billion to charity in 2010, a growth of3.8% from 2009 (AAFRC Trust for Philanthropy 2010).Individual giving accounted for 73% of this total,whereas foundations accounted for 14%, bequests for8%, and corporations for 5%. Almost 70% of U.S.households report giving to charity. Even though thevolume of giving is large, intercharity competition fordonations is substantial with over 800,000 charitableorganizations in the United States alone. Increasingly,nonprofit organizations are adopting marketing andtargeted advertising techniques used by the for-profitsector to obtain funds for their causes. Watson (2006)estimated marketing spend at large U.S. nonprofits at$7.6 billion based on IRS exemption data.

Despite the larger need for charitable giving indeveloping countries, individual giving constitutes aninsignificant share in these countries. For example,even though India’s giving totaled close to $5 billionin 2006 (about 0.6% of India’s GDP),8 individual andcorporate donations constitute only 10% of charitablegiving, with over 90% of the sector funded by govern-ment and foreign organizations. In fact, nearly 65% ofthe sector funds come from India’s central and stategovernments with a focus on disaster relief. Given the

8 Countries like Brazil and China have smaller nonprofit sectorsat 0.3% and 0.1%, but are growing. Yet this is cold comfort giventhe enormous needs of the poor and disadvantaged in India.

massive inequalities and the enormous needs of thepoor and disadvantaged in emerging economies, theability to understand the persuasive impact of com-munication to increase individual giving is of greatsocial importance.

Relative to research focused on demand for goodsthat improve one’s own welfare, there is limitedresearch on “demand” for spending on others’ wel-fare (Bendapudi et al. 1996, Andreoni 2006). The fieldof charitable giving in economics has recently seen asurge in the use of randomized field experiments (seeList 2011 for a survey), but most studies are focusedon price and incentive effects on charitable giving(e.g., List and Lucking-Reiley 2002). In the context ofblood donations, Lacetera et al. (2014) show that eco-nomic rewards increase blood donations and changetheir timing of donations; but they also find that asurprise reward for donations reduces future dona-tions, relative to giving no reward. Academics haverarely used randomized field experiments to studythe persuasive effects of advertising content in naturalsettings. Other behavioral work on charitable givingincludes Soetevent (2005), who shows that revealingthe identity of givers increasing donations suggestingsocial effects. Landry et al. (2006) find that lotteriesincrease giving, but surprisingly the attractiveness ofthe fundraiser is at least as important as the economicincentive in persuading people to give. Shang andCroson (2009) show that providing social comparisonsof giving impacts donation behavior. Della Vigna et al.(2012) test the role of altruism relative to social pres-sure in charitable giving.

Research in laboratory settings have tested howthe framing of asks impacts fundraising (e.g., Ferraroand Bettman 2005, Gourville 1998). Fishbein’s (1967)behavioral intentions model has been frequently usedto model donation behavior (see LaTour and Manrai1989). Recently Small and colleagues (e.g. Small andLoewenstein 2003, 2005; Small 2010), among othershave focused on developing psychological theoriesthat inform how a generation of sympathy for otherpeople and worthy causes affect donation behavior.We leverage on these theories for our hypotheses.

3. HypothesesOur first four hypotheses are based on framing effectsfrom the literature on sympathy biases, and the fifth isbased on temporal reframing of monthly versus dailyask for an annual donation. Of the four sympathy biashypotheses, the first three are related to how socialdistance impacts sympathy; the fourth addresses thesympathy bias due to reference dependence. We dis-cuss each of the hypotheses in turn.


(A) Identified Victim Effect

The death of one Russian soldier is a tragedy; the deathof millions is a statistic. —Joseph Stalin

If I look at the mass I will never act, if I look at theone I will. —Mother Teresa

Schelling (1968) first proposed and demonstratedthat an identified victim evokes greater emotion anddonations than a statistical victim. As Slovic (2007)notes, people seem to care deeply about individuals,whereas they seem to be numb to the sufferings ofmany. As the quotes above suggest, Mother Teresaand Joseph Stalin both seemed to have an intuitivegrasp of this—perhaps the only area in which theyagreed on!

There are a number of anecdotal examples relatedto the identified victim hypothesis. An often-citedexample is that of the child, “Baby Jessica,” whoreceived over $700,000 in donations from the public,when she fell in a well near her home in Texas in 1987and received access to a trust fund of $800,000 whenshe turned 25 (CBS News 2011). Donors contributedover $48,000 to save a dog stranded on a ship adrifton the Pacific Ocean near Hawaii (Song 2002). Yet,charities struggle to raise money to feed the famished,ill, and homeless—in both developed and developingcountries. In essence, when an identifiable victim ismade into a cause, people appear to be more compas-sionate and generous; yet they give relatively little toso-called statistical victims facing enormous needs.

Based on a dual deliberative (cognitive) and affec-tive (emotional) process model of cognition (e.g.,Chaiken and Trope 1999, Kahneman and Frederick2002, Small and Loewenstein 2005, Small et al. 2007)argue that identifiable victims reduce social distanceand thereby generate more sympathy because theyinvoke the affective (emotional) system (e.g., Smalland Loewenstein 2005), whereas statistical victimsinvoke the deliberative (cognitive) system. The affec-tive mode also dominates when the target of thoughtis specific, personal, and vivid as happens when weidentify victims (Sherman et al. 1999), but the delib-erative mode is evoked by abstract and impersonaltargets.

Some scholars have argued that the identified vic-tim effect is plausibly because of human sensitivityto proportions rather than absolute numbers (e.g.,Friedrich et al. 1999, Jenni and Loewenstein 1997).Ten deaths concentrated in a small neighborhood ofa 100 people will evoke much greater consternationthan 10 deaths across a large city of a million people.The identified victim is an extreme example where bymaking the individual the cause, the reference groupsize is reduced to the victim. With a victim propor-tion of 100%, maximum sympathy is evoked. Yet oth-ers have shown that identification is critical, in thatindividuals gave more to help an identifiable victim

than a statistical victim, even when controlling forthe reference group (e.g., Small and Loewenstein 2003and Kogut and Ritov 2005a). Kogut and Ritov (2005b)found that a single, identified victim (identified by aname and face) elicited greater emotional distress andmore donations than a group of identified victims andmore than both a single and group of unidentifiedvictims.

In this paper, we specifically test the hypothesis thata single identified victim generates more donors anddonations, relative to a group of unidentified victims.

(B) The In-Group vs. Out-Group Effect. Thein-group effect suggests that potential donors arelikely more sympathetic and give more to victims whoshare similarities with them because of reduced per-ceived social distance. The literature on social iden-tity provides the foundation for the argument. Socialidentity is commonly defined as a person’s senseof self derived from perceived membership in socialgroups. Tajfel and Turner (1979) developed the con-cept to understand the psychological basis for inter-group discrimination. Social identity has three majorcomponents: categorization, identification, and com-parison. Categorization is the process of putting peo-ple, including ourselves, into categories; for example,labeling a person as Chinese, black, female, or a lawyerare all different ways of categorization. Categoriza-tion also defines our self-image. Identification is theprocess by which we associate or identify ourselveswith certain groups. We identify with in-groups, andwe do not identify with out-groups. Finally, compar-ison is the process by which we compare in-groupswith out-groups, creating a favorable bias toward thein-group.

Overall, categorization of others as belonging toan in-group arouses feelings of greater closeness andresponsibility and augments emotional response totheir misfortune through greater sympathy (Brewerand Gardner 1996, Dovidio et al. 1997) and willing-ness to help (Dovidio 1984, Dovidio et al. 1997). Forexample, a bystander is more likely to offer help inan emergency situation (including natural disasters)if the victim is perceived as a member of the samesocial category as herself (Levine et al. 2002, Levineand Thompson 2004). Cuddy et al. (2006) find that inthe aftermath of the Katrina hurricane in the UnitedStates where a majority of black victims were affected,blacks/Latinos felt more sympathy for the victimscompared to whites, and vice versa. Sturmer et al.(2005) found that homosexual volunteers were morelikely to help homosexuals with AIDS than hetero-sexual volunteers. Kogut and Ritov (2007) find in lab-oratory experiments that Israeli students felt moreempathy for a single Israeli victim of the tsunami. Yet,they also report a higher willingness of white Jew-ish students to contribute to a black Jewish child of


Ethiopian descent compared to a white Jewish child.The students were white and the authors argue thatthe higher empathy for black Jews is probably a senseof responsibility for in-group people who are suffer-ing. Chen and Li (2009) also find in laboratory exper-iments that participants are more altruistic toward anin-group match.

We wish to note that the in-group effect does notoccur only with respect to sympathy generation andcharitable giving. It is also applicable in commercialadvertising situations, where the goal is to persuadethe target to buy a product or service for oneself.Evans (1963) showed that customers are more likelyto buy insurance from a salesperson similar in age,religion, politics, and even cigarette smoking habits!

In this paper, we test the hypothesis that anin-group victim generates more donors and dona-tions, relative to an out-group victim.

(C) Out-Group “Identified Victim” vs. “Uniden-tified” Group. As discussed above, research hasdemonstrated that sympathy would be greater (1) foran in-group individual relative to an out-group indi-vidual; and (2) an identified individual victim thana group of victims. Yet how does an identifiedout-group individual fare relative to the group? Toour knowledge, there is no research on the strengthof the identified victim effect relative to the in-groupout-group effect. Although we have no a priorihypothesis on which effect is stronger, we test the rel-ative magnitudes of the effects in this paper.

(D) Reference Dependent Sympathy. Our finalsympathy bias hypothesis is based on the “referencedependence sympathy” effect. When a major disasterhappens, there is a large outpouring of sympathyand substantial donations are made. Private dona-tions averaged USD $1,839 per person for HurricaneKatrina, and as much as USD $37 per person forthe 2005 Kashmir earthquake, which was not as sig-nificantly covered by the mass media (Spence 2006).Donations for AIDS victims amount to about USD$10 per victim. Yet the magnitude of the problemof AIDS, malaria, famine, and unsafe water is farmore substantial. Over 660,000 people die from AIDS,malaria, famine, and unsafe water per month; andthat monthly number is close to double the number oflives lost as a result of the Asian Tsunami, HurricaneKatrina, and the earthquake in Kashmir.

What explains the differences in sympathy and giv-ing behavior? Why do we feel more sympathy forthose who lost their homes because of the housingbust than for the chronically homeless? The literatureon reference dependence based on prospect theorysuggests a possible explanation. Victims of chronicconditions maintain a constant state of welfare butvictims of events have suffered a loss in welfare. Peo-ple value not an absolute amount, but rather gains

and losses relative to a reference point (Kahnemanand Tversky 1979). Small (2010) shows that referencedependence is not only supported in the context ofone’s own utility but also applicable to sympathy gen-erated for others. She finds that reference-dependentjudgments and decisions are a function of emotionalresponses to changes in others welfare. When judg-ments are made toward a pallid target, the emotionalmechanism ceases to exert influence; therefore, others’losses hurt more than their chronic conditions.

(E) Temporal Reframing: Monthly vs. Daily Ask.Marketers temporally reframe the amount of anannual donation into smaller monthly or dailyamounts, even though the donation itself is annual.Such strategies are used in a variety of contexts, rang-ing from insurance, magazine subscriptions, durablegoods, and charitable donations. A $360 annual insur-ance premium or donation to National Public Radioseems more affordable when framed as less than $1 aday. Gourville (1998) dubbed such temporal refram-ing into a small daily amount as “a pennies a day”strategy.

Standard economic theory would suggest thatmere temporal reframing should not affect behav-ior. Different presentations of the same stimuli—in this case, the same physical cash flows, shouldnot alter donor behavior (e.g., Tversky et al. 1988).Gourville (1998) therefore proposes a two-step con-sumer decision-making process of (1) comparisonretrieval and (2) transaction evaluation to explain whyPAD strategies may be effective. He demonstrates inlaboratory experiments that the PAD framing of atarget transaction systematically fosters the retrievaland consideration of small ongoing expenses as thestandard of comparison, whereas an aggregate fram-ing of that same transaction fosters the retrieval andconsideration of large infrequent expenses. Since mostindividuals indeed perform many small transactionsroutinely, this difference in retrieval makes it morelikely that the individual will more favorably evaluateand comply with the smaller transaction.

However, prospect theory (Kahneman and Tversky1979) and its derivative mental accounting (Thaler1985) would predict that the PAD strategy wouldbackfire by magnifying the perceived cost of the dona-tion or spend. Their recommendation to “integratesmall losses” is based on the idea that an individualwould, rather than experience many small costs witheach cost assessed at the steepest and most painfulpart of the prospect theory value function, prefer toexperience one larger loss taking advantage of theflattening value function for increasingly larger losses.

Hence, would the $360 transaction be perceivedmore favorably if temporally reframed as $30 permonth or less than $1 per day? This would depend onwhat type of small transaction would be considered


more normal or less painful: ongoing monthly pay-ments such as utility bills or rentals or daily spendssuch as for a cup of coffee or tea? If compliance is eas-ier for a monthly payment, where people do not havemuch discretion, as opposed to daily spend wherethere is discretion, it is possible that a monthly fram-ing might be more effective. Such a framing has notbeen subject to empirical testing. We therefore do nothave a strong a priori hypothesis about which fram-ing will lead to more donors and donations; we treatthis as an empirical question.

4. The Primary Experiment:New Donor Acquisition

4.1. The SettingThe aged are a growing population worldwide as lifeexpectancy increases. Whereas there are safety netslike social security and Medicare in the developedworld to support the elderly in their old age, thesemechanisms are not developed in countries like India,where the primary source of support for the elderlyis the support from the savings of the elderly andsupport from the joint family. With growing economicopportunities, the young migrate from their tradi-tional homes in villages or set up nuclear households,leaving the elderly increasingly abandoned. Worse,the aged are abused with children taking control overthe aged parents’ property and financial resourcesand then abandoning them. Given the magnitude ofthe problem, the Indian Government recently passeda law providing for imprisonment of children neglect-ing elderly parents.9 Nevertheless, there is a greatneed for societal support of the elderly, especiallywhen the children do not have the means to sup-port even themselves. India has currently 90 millionelderly, of whom about over 7 million (7.8%) requiresome form of societal support (Rajan 2006).

HelpAge India was founded in 1978 as a secular,not-for-profit organization registered under the Soci-eties’ Registration Act of 1860 to provide relief toIndia’s elderly through various activities. Focus areasinclude advocacy for elders’ rights, healthcare, socialprotection, shelters, and disaster mitigation.10 Ourinvestigation is around one HelpAge social protectionprogram called “Support a Gran.” In this program,elderly destitutes are adopted by HelpAge and pro-vided with basic food, minimal clothing and necessi-ties, and a small amount of discretionary cash on amonthly basis. The Support a Gran donations are con-sidered “restricted gifts” in that funds raised for thisprogram can only be used for this program.

9 The laws are similar in spirit to laws in the developed world de-signed to prevent neglect of children.10 HelpAge India Website–About Us, https://www.helpageindia.org/aboutus.html.

Our experiment on behalf of Support a Gran wasdone around an annual fundraising campaign ofHelpAge in March 2011. This fundraising campaigncoincides with the Hindu festival of Holi in March, aperiod of celebration of the triumph of good over evil,and considered a time for doing good and giving. It isalso fortuitously close to the annual tax filing deadlineof March 31, which perhaps serves as another incen-tive to “give.” The appeals are targeted to a “cold”mailing list of 184,396 high net worth individuals inIndia to acquire new donors.

Appeals to cold mailing lists tend to have verylow response rates; typical response rates at Help-Age have been around 0.1%. With giving per donoraveraging around |3,000,11 the low response rates ofabout 0.1% implies that actual money raised per mail-ing is only around |3. With costs of the campaignaveraging around |6 per mailing, the campaign isconsidered a loss leader to acquire new donors withpropensity to donate, who can be more efficientlyreached in subsequent mailings to “active” (hot) donorlists or “dormant” (warm) donor lists. In standardmarketing parlance, this campaign is part of the acqui-sition cost of new donors. The expense is worthwhileonly because there is a lifetime value for each acquireddonor through subsequent donations. Our experimentimposed little incremental cost to HelpAge, exceptthe insignificant cost of printing a small color flyerand including it in addition to the standard one pageappeal sheet.

4.2. Experimental TreatmentsAs described earlier, we test hypotheses related to thefollowing four psychological effects: (1) identified vic-tim, (2) in-group versus out-group victim, (3) referencedependence sympathy, and (4) temporal reframing—daily versus monthly ask. We provide the copy of theflyer we used in one condition (Individual-In-Group-Loss-Monthly) in Figure 1.

We explain how the flyer was modified for the other11 treatment conditions (see Figure 2). We operational-ize the test of the identified victim effect using two dif-ferent types of treatments: an individual (I) and group(G) condition. See stylized examples of the individ-ual and group condition below. The areas marked initalics are the text, which change for different condi-tions (apart from appropriate change of pronouns andnames in the rest of the text).

In the individual condition, we describe an identi-fied individual (see Figure 1) along with her photo-graph, whereas in the group condition we describethe victims as a group of four women (who areshown in a picture collage in the actual treatment)

11 The exchange rate in May 2011 averaged |44.93 (Indian rupees)for $1 (U.S. dollar), http://www.xrate.com.

https://www.helpageindia.org/aboutus.html

https://www.helpageindia.org/aboutus.html

http://www.xrate.com


Figure 1 (Color online) Experiment Treatment: Individual-In-group-Loss-Monthly

Figure 2 Flyer Modifications from Figure 1 for Other Treatments

Individual conditionPhoto of Sushila Sushila worked as a school teacher and retired comfortably. But she became destitute when her husband passed

away and other family members refused to support her.Support a Gran has helped Sushila meet her basic needs of food, clothing and shelter in her time of need.

Today in her old age, she leads a dignified life.Your tax deductible donation of |9,000 a year (that is just |750 a month) helps Sushila and people like her

live a life of dignity in their golden years.Group condition

Photo collage of fourunnamed ladies

These ladies share a common story. They worked as school teachers and retired comfortably. But then they becamedestitute when their husbands passed away and other family members refused to support them.

Support a Gran has helped them all meet their basic needs of food, clothing and shelter in their time ofneed. Today in their old age, they lead a dignified life.

Your tax deductible donation of |9,000 a year (that is just |750 a month) helps these and other people likethem live a life of dignity in their golden years.

and describe the group.12 We implement the in-groupand out-group treatment as subtreatments within theindividual condition: because Hindus are the over-whelmingly majority community in India and Chris-tians form a very small minority, we use a Hinduwoman (Sushila) for the in-group treatment. Forthe out-group treatment, we use a Christian womanbelonging to the Anglo-Indian community (ShirleyBarrett). The individuals pictured had to be real ben-eficiaries with real stories of the nonprofit as per theethical guidelines of the organization. We could nottherefore merely change the names of the beneficia-ries with the same image. We discuss a subsequent

12 Whereas the individual treatment uses a Hindu and Christianwoman as a victim (the religion is not mentioned, but can beinferred from their names), the group treatment simply describes agroup of four women, without mentioning religion. Although wecould have mentioned they were Hindu or Christian even in thegroup condition and obtained a fully crossed design, HelpAge didnot consider it appropriate to mention religion in the flyer. Fur-thermore, not mentioning religion in the group condition made itin some ways more comparable to the individual treatment wherereligion is not mentioned, but only (potentially) inferred by thereader from the name.

robustness check using an M-Turk experiment to ruleout if the attitude to the charity changed because ofdifferences in the images in the in-group–out-groupcondition among Hindu respondents.

We implement the reference dependent sympathytreatment as follows. For the loss condition, we high-light the fact that the individual concerned had livedan independent life earlier as a school teacher andretired, before she became destitute. In a laboratoryexperiment, to create the contrasting chronic treat-ment, we could have stated that “Sushila has led a lifeof deprivation all her life.” However, because this wasa natural field experiment, HelpAge policy wouldnot allow for any kind of deception or falsehood inmessaging. Hence we chose an “uncertain” referencetreatment, where we omit mentioning about her pastlife. So we dropped the first line, “Sushila workedas a school teacher and retired comfortably.” Theuncertain treatment started with the following sen-tence: “Sushila became destitute when her husbandpassed away 0 0 0 0” Similarly, the group treatment alsodropped the reference to the past and simply said,“These ladies share a common story. They becamedestitute, when their husbands passed away 0 0 0 0”


Table 1 New Donor Experiment: Experimental Treatments

Individual/ In-group/ Reference Monthly/Treatment Mnemonic Group Out-group loss/Uncertain Daily

1 IHLM Individual Hindu Loss Monthly2 IHUM Individual Hindu Uncertain Monthly3 IHLD Individual Hindu Loss Daily4 IHUD Individual Hindu Uncertain Daily5 ICLM Individual Christian Loss Monthly6 ICUM Individual Christian Uncertain Monthly7 ICLD Individual Christian Loss Daily8 ICUD Individual Christian Uncertain Daily9 G_LM Group NA Loss Monthly

10 G_UM Group NA Uncertain Monthly11 G_LD Group NA Loss Daily12 G_UD Group NA Uncertain Daily13 Control NA NA NA NA

We implement the monthly/daily temporal refram-ing treatment as follows. Although everyone is givenan amount of |9,000 to anchor as the amount neededto support one person over a year, that same amountis framed as |750 a month for the monthly conditionand |25 a day for the daily condition.13

In the control condition, HelpAge sends its routineflyer—a one-page sheet requesting for donations. Ineach of the treatment conditions, in addition to theroutine flyer, an additional one-page flyer (describedabove) was sent. All of the flyers are presented in theonline appendix (available as supplemental materialat https://doi.org/10.1287/mksc.2016.0989).

4.3. Experimental DesignWithin the individual treatment, we follow a full fac-torial design on the in-group–out-group, referencedependence (loss/uncertain) and temporal reframing(monthly/daily) ask conditions. Thus we have 2 ×

2 × 2 = 8 conditions in the individual treatments. Aswe explained earlier, within the group treatment, wedo not provide any identifying characteristics includ-ing religion—hence we do not have an in-group andout-group condition in the group treatment. So weonly have the remaining 2 × 2 = 4 conditions withinthe group treatment. Finally, we have a control condi-tion, where we do not send the additional flyer at all;this is what HelpAge would have done in the absenceof our experiment. Thus, in all, we have 8+4+1 = 13treatment conditions.

The full set of treatments is listed in Table 1. Themnemonics provided will serve to identify treatmentsin a meaningful manner.

We randomly assign names on the mailing listroughly equally to 12 treatments and leave a slightlylarger number of names for the control treatment. The

13 As a price reference, a regular cup of coffee at India’s largestcoffee chain Café Coffee Day costs |40. In that sense, it satisfies thepennies a day logic of a routine and ongoing daily expense.

Table 2(a) New Donor Experiment: Summary of ExperimentOutcomes

No. ofTreatment Mnemonic mailed Donate (%) |/mailing |/donor

1 IHLM 13,826 0.36 16028 4,5012 IHUM 13,832 0.27 9029 3,4743 IHLD 13,823 0.34 11096 3,5164 IHUD 13,669 0.14 7063 5,5615 ICLM 13,832 0.34 12024 3,6036 ICUM 13,805 0.22 6045 2,9677 ICLD 13,820 0.14 2093 2,1348 ICUD 13,690 0.08 3088 4,8869 G_LM 13,859 0.11 3077 3,480

10 G_UM 13,682 0.12 6059 5,34111 G_LD 13,876 0.06 2059 3,99612 G_UD 13,682 0.07 3085 5,33913 Control 15,506 0.11 4030 3,958Overall 184,396 0.17 6098 3,993Average for 12 treatments 165,982 0.19 7029 3,889

Table 2(b) New Donor Experiment: Logistic Regression on DonationChoice

Logistic regression Tobit regression onon donation choice donation amounts

Coefficient Odds Coefficient(std. err) ratio Z (std. err) t-stat

Individual 00743∗∗∗ 2.10 4037 31095∗∗∗ 40084001705 47595

In-group 00358∗∗∗ 1.41 2084 11756∗∗∗ 20974001265 45915

Loss 00411∗∗∗ 1.51 3055 11786∗∗∗ 30344001165 45355

Month 00535∗∗∗ 1.71 4055 21438∗∗∗ 40464001185 45465

Intercept −7052∗∗∗ −43042 −471312∗∗∗ −180504001735 4215575

N 165,982

Note. Base treatment is Group-Uncertain-Daily Condition.∗∗∗p < 0001.

exact number of mailings for each treatment is reportedin Table 2(a) along with the descriptive statistics.14

5. Results5.1. Summary StatisticsWe report summary statistics associated with each ofthe treatment cells in Table 2(b). Roughly 14,000 peo-ple were assigned to each treatment condition, andabout 15,500 were assigned to the control condition.We report three outcome metrics for each treatment:(1) donation rate, i.e., % of mailings that generated adonation; (2) donation amount per mailing (|/mail);

14 To assess the effectiveness of the randomization, we checkwhether the number of mailings is roughly equal across the mainobservable we have in the mailing list: the different states of India.The assignments are roughly equal for all treatments, not only forthe whole sample but also at the level of each state, suggesting thatthe randomization was effective.



and (3) donation amount per donor (|/donor), i.e.,donation amount, conditional on giving.

The highest donation rate and |/mail is for theIndividual-In-group (Hindu)-Loss-Monthly (IHLM)condition. This condition generated 3.3 (0.36/0.11)times the donation rate as the control condition.Furthermore, the |/mail in this condition is 3.78(16.28/4.30) times the amount generated in the controlcondition. By contrast, the worst performing Group-Loss-Daily (G_LD) condition produced only 59% ofdonors and raised only 60% of |/mail relative to thecontrol. In general, the group mailer is not only inef-fective, but in combination with the daily ask framingperforms substantially worse than the control con-dition. Overall, these results suggest that relativelyminor variations in advertising content significantlyaffect persuasion and charitable giving.

5.2. Tests of HypothesesWe test our hypotheses about the persuasive effects ofalternative treatments by comparing (1) the donationrate and (2) |/mail across the relevant treatments. Anadditional question is when there is an increase in|/mail, whether it is only due to a higher donationrate or whether individuals who donate also feel moresympathy and give more. For this, one cannot simplycompare |/donor, i.e., donation, conditional on giv-ing, because when the more effective treatment gen-erates more donors, the marginal donors are innatelyless interested in the cause and are therefore likely togive less. To make an apples-to-apples comparison,we can rank the donors in descending order of theirdonations within each treatment and do a paired testof donation amounts for a donor of given rank.15 Thelogic is that if treatment A generates more sympathy,a donor of a given rank subject to treatment A shouldgive more relative to an identically ranked donor sub-ject to treatment B.16

(A) Identified Victim Effect. Figure 3 shows theresults for the identified victim effect. Figure 3(a) com-pares the donation rates across the individual andgroup conditions. The average donation rate in theindividual condition is 0.24%, whereas it is only 0.09%

15 Comparing donations of persons of identical rank is valid onlyif we have an identical number of mailings in the different com-parison treatments. Otherwise, one will have to compare donors ofidentical percentiles rather than ranks.16 However there may be other possibilities for the donation deci-sion process. As an example, the additional donors for the moreeffective treatment may be systematically wealthier and thereforegive more, unrelated to their level of sympathy. Because we do nothave demographic information on the donors, we are unable to ruleout this explanation by checking whether there are any systematicdifferences in donor demographics for the different treatments. Wehope future research can address this issue. We thank a reviewerfor raising this possibility.

Figure 3 (Color online) Identified Victim: Individual vs. Group Effect

for the group condition and the difference is signif-icant 4p < 00055. Thus the donation rate for the indi-vidual treatment is 2.55 times the donation rate in thegroup treatments.

Figure 3(b) compares the |/mail. Not only is thedonation rate higher in the individual condition, thedonations raised per mailing is also higher. Whereasthe average donation per mailing is |8.83 in theindividual condition, it is only |4.20 in the groupcondition. This ratio of 2.1 shows that a charity more


than doubles donation dollars by recognizing theidentified victim sympathy bias in making its appeals.

Figure 3(c) graphs the ratio of individual to groupdonations of identically ranked pair of donors. Thereare 51 donations in the group condition and 260 dona-tions in the individual condition. However the num-ber of mailers in the individual condition is (roughly)double the number of mailers in the group condi-tion. Given the percentile discussion in Footnote 14,this translates to comparing the 51 ranked donationsin the group condition against the top 51 odd rankeddonations in the individual condition. All of the 51ratios are at or above 1, suggesting that the identifiedvictim effect not only causes more donors to give butalso increases the giving among those that give. Theeffect is statistically significant; the mean of the ratiois 3.6 and the 95% confidence interval of 43005140165clearly excludes 1.

(B) In-Group vs. Out-Group Identified Victim.Figure 4 shows the results of the tests for in-groupversus out-group. From Figure 4(a), we see that thedonation rate in the in-group condition is higher at0.28%, relative to the out-group condition at 0.19%.Thus, the number of donors increase by 42% withan in-group individual relative to the out-group indi-vidual. The difference is statistically significant atthe 95% level. Note that, the average individual effectof 0.24% reported in Figure 4 is the average of thein-group and out-group effect.

From Figure 4(b), we see that the |/mail is alsohigher at |11.29 for the in-group condition, relativeto |6.38 for the out-group condition, thus generating77% more donations. Comparing the increase in dona-tion rate of 43%, and the increase in donations of 77%,we can conclude that not only does an in-group leadmore donors to give, those donors also give substan-tially more to in-group victims.

Figure 4(c) shows that conditional on giving, iden-tically ranked individuals in the in-group conditiongive more than the donors in the out-group condi-tion. Because roughly an identical number of mailerswere sent in the in-group and out-group conditions,we directly compare the donations of the same rank.There are 153 in-group donations and 107 out-groupdonations. We therefore compare the top 107 ranksin both conditions. Only two of the 107 pairs haveratios less than 1. The effect is statistically significant;the mean of the ratio is 2.61 and the 95% confidenceinterval of 42040120825 clearly excludes 1.

One concern here is that even though our poten-tial donor base is predominantly Hindu, there are alsoChristian and Muslim potential donors in the sam-ple. Even though we do not have access to the reli-gion information of the potential donor database, theemail list provider indicates that Hindus consisted of

Figure 4 (Color online) In-Group vs. Out-Group Effect

about 90% of the sample, Muslims about 7%, Chris-tians about 2%, and others about 1%. This implies thatour estimates of the in-group and out-group dona-tion and giving rates and the differences are poten-tially biased. In the appendix we show mathemat-ically that the difference in giving rates when theexact identity of the potential donor is known will belarger relative to the estimates we obtain where someof the potential donors are also from the out-group.Thus the current estimates of the difference between


in-group and out-group giving are an underestimate.We report robustness and mechanism checks aroundthe in-group result using a survey-based experimentin Section 6.

(C) Out-Group “Identified Victim” vs. “Unidenti-fied” Group. Figure 5 compares the out-group identi-fied victim effect against the unidentified group. FromFigure 5(a), we see that the average rate of dona-tions in the identified out-group condition is higherat 0.19%, relative to the group condition at 0.09%,Overall, the number of donors can be increased by110% with an out-group identified individual relativeto an unidentified group, suggesting that the identi-fied victim effect is stronger than the in-group effectin inducing sympathy and giving. The difference isclearly statistically significant 4p < 00055.

In addition to the donation rate being higher, inFigure 5(b) we also see that the identified out-groupcondition generates 52% more donations; |/mail is|6.38 for the out-group condition, relative to |4.29 forthe group condition.

Roughly, an equal number of mailers was sent tothe out-group and group conditions. So we directlycompare donations of a given rank. Given 107 dona-tions from the out-group condition, and 51 donationsfrom the group condition, we compare the top 51pairs of donations from each condition. Only one of51 pairs has a ratio lower than 1. The effect is statisti-cally significant; the mean of the ratio is 2.04 and the95% confidence interval is 41080120285, excludes 1.

(D) Reference Dependent Sympathy. Figure 6shows the tests for reference dependence sympathyby comparing the loss condition against the uncertaincondition. From Figure 6(a), we see the donation ratefor the loss condition is higher at 0.23%, relative tothe uncertain condition at 0.15% 4p < 00055. Overall,the number of donors was higher by 51% in the losscondition.

Figure 6(b) shows that the |/mail is also higher at|8.37 for the loss condition, relative to |6.28 for theuncertain condition. Thus the loss condition generates33% more in terms of funds raised.

Figure 6(c) also shows that conditional on giving,identically ranked individuals in the loss conditiongive more than the donors in the uncertain condition.We had 187 donations in the loss condition and 124donations in the uncertain condition. Only 4 out of 124pairs have a ratio less than 1. The effect is statisticallysignificant; the mean of the ratio is 1.97 and the 95%confidence interval is 41081120145, clearly excludes 1.

A potential alternative explanation for the greatergiving in the loss condition could be that schoolteachers may be an in-group with respect to thedonors. We note that the socioeconomic status of thepotential donors is much higher than those of schoolteachers, and therefore school teachers are an unlikely

Figure 5 (Color online) Out-Group vs. Group Effect

in-group for these potential donors, and possibly anout-group in terms of socioeconomic status. Never-theless, the issue needs further exploration in futurefield research.

(E) Temporal Reframing: Monthly vs. Daily Ask.Figure 7 compares outcomes for the monthly versusdaily asks. From Figure 7(a), we find that that thedonation rate is higher in the monthly condition at0.24%, relative to the daily condition at 0.14%. Thus,the monthly condition increases the donation rate by71%. The effect is statistically significant 4p < 00055.


Figure 6 (Color online) Reference Dependence: Loss vs. UncertainReference Effect

(a) Donations per mailing

Ratio (loss/uncertain) = 1.51Loss 95% CI: (0.193%, 0.257%)

Uncertain 95% CI: (0.123%, 0.176%)

Ratio (loss/uncertain) = 1.32Loss CI: (6.41, 10.17)

Uncertain CI: (4.09, 8.48)

(c) Ratio of loss/uncertain donation(for given rank)

Average ratio (95% CI): 1.97 (1.81, 2.14)

0.25

0.20

0.15

0.10

Perc

ent g

iven

Loss UncertainTreatment

4

6

8

10

Don

atio

n

Loss UncertainTreatment

0

2

4

6

8

10

12

1 51 101 151

Rank

0.225%

0.149%

8.29

6.28

(b) Donation( )/mail

From Figure 7(b), we see that the |/mail is alsohigher at |9.10 for the monthly condition, relative to|5.47 for the daily condition. Thus the monthly con-dition also leads to 66% more funds raised. Overall,in contrast to recent support for the PAD framingeffect, we find that monthly temporal reframing actu-ally leads to better persuasive outcomes.

Figure 7(c) demonstrates that conditional on giv-ing, donors on average do give more in the monthlycondition. We had 216 donations in the monthly

Figure 7 (Color online) Temporal Framing: Monthly vs. Daily Ask

condition and 115 donations in the daily condition.None of the 115 pairs have a ratio less than 1, suggest-ing that the monthly reframing leads to more robustand higher donations compared to daily reframing.The mean of the ratio is 3.69 and the 95% confidenceinterval is 4301714025, which excludes 1.

5.3. Multivariate Regression AnalysisThus far, we analyzed the data—one pair of treat-ments at a time. We now analyze the experimen-tal data through two multivariate regressions that


control for simultaneous variations in multiple treat-ments: a logistic regression on donation choice anda Tobit regression on donation amounts. We use aTobit regression, because donations are left censoredat zero. The results are reported in Table 3(a)–3(c).

The logistic regression results report both the coef-ficient estimates and the odds ratios. The individualcoefficient is positive and significant 4p < 00015. Thisrepresents the individual-out-group condition in theregression, and shows that the individual-out-groupcondition more than doubles the odds of donation(odds ratio = 2.1), over the group condition. Thein-group condition further increases the effectivenessof the out-group condition relative to the group con-dition by about 40% (odds ratio = 1041). We notethat in combination, the individual-in-group condi-tion increases the odds of donations three times rela-tive to the group condition. This can also be directlychecked by replacing the individual variable without-group variable in the logistic regression. Thus theidentified victim effect is substantial; even an identi-fied out-group victim overwhelms giving for a groupof victims.

Furthermore, the results show significant effectsof reference dependence, with the loss condition in-creasing the odds of donations by 51% relative tothe uncertain condition. Finally, temporal reframingaffects donations, with monthly ask increasing theodds of donations by 71%.

The Tobit regression results show that our treat-ments significantly affect the donation amounts.Specifically, we find that the in-group identified vic-tim treatment (captured by the Individual + In-groupcoefficient) raises |4,851 per donor more than thegroup treatment. Even the out-group identified victimraises |3,095 more than the group treatment. Refer-ence dependence in the form of the loss conditionsgenerates |1,786 more than the uncertain condition.Finally, the monthly temporal framing leads to greatergiving of |2,438 relative to a daily temporal frame.Overall these results show strong statistical and eco-nomic significance of advertising content effects.17

6. Robustness ChecksWe conduct two robustness checks. The first seeksto assess the robustness of the in-group–out-grouphypothesis. The second addresses the question of

17 Because the group condition did not have in-group and out-group subconditions, we cannot identify an interaction effect ofin-group–out-group with the individual condition beyond the maineffects of individual and in-group from the experimental data.Other interactions with respect to loss or monthly conditions werenot significant. We therefore report only the main effects. In general,logistic regressions have some level of interactions built in becauseof their intrinsic nonlinearity, and this may explain why the loss ormonthly interactions were not significant.

Table 3(a) Survey-Based Experiment: Descriptive Statistics

Likelihood to Std. PastN give (1–10) dev give Education Income

Hindu–Sushila 139 7.50 2.48 0.24 4.14 4.14Hindu–Shirley 155 6.97 2.53 0.27 4.12 4.08Christian–Sushila 57 5.98 2.99 0.26 4.35 5.54Christian–Shirley 41 6.98 2.74 0.17 4.20 4.15

Table 3(b) Survey-Based Experiment-1: Likelihood of Giving

Coefficient Coefficient(std. err) t-stat (std. err) t-stat

Hindu–Sushila 00527∗ 1073 00503∗ 10734003055 4002915

Christian–Shirley 10002∗∗ 1088 10063∗∗ 20074005335 4005155

Hindu 00991∗∗∗ 20720 10053∗∗∗ 20724004035 4003885

Past giving 10566∗∗∗ 50364002925

Diplomaa 10731∗∗ 20044008505

Bachelor’s degree 20047∗∗∗ 30234006345

Graduate degree 20078∗∗∗ 30204006495

Intercept 50979∗∗∗ 17031 20807∗∗∗ 30944003455 4007125

N 392 392

Notes. Base treatment is Christian–Sushila. Base level of education is lessthan 12th grade.

aA diploma is a three year vocational degree from a technical training insti-tution that is entered after 10th grade. It is lower in prestige than a three orfour year Bachelor’s degree that is entered after 12th grade.

∗p < 001; ∗∗p < 0005; ∗∗∗p < 0001.

Table 3(c) Survey-Based Experiment-2: HelpAge Evaluations

Good cause Well-managed Positive image

Coeff (t-stat) Coeff (t-stat) Coeff (t-stat)

Sushila 00093 00035 00062400465 400175 400315

Past giving 00691∗∗∗ 00683∗∗∗ 00364430135 420995 410645

Intercept 70792∗∗∗ 70531∗∗∗ 70966∗∗∗

4350825 4330535 4360285N 252 252 252

Notes. Education is not statistically significant, but increases standard errors,so they are not included. The coefficients on Sushila remain qualitatively sim-ilar without past giving as covariate.

∗∗∗p < 0001.

whether the large effects of advertising content on giv-ing among cold list recipients, are likely to replicate fora warm list. The replication is important because it ispossible that cold list recipients, who have never givenbefore to the cause may be more sensitive to the sym-pathy biases, compared to warm list recipients thathave already shown an interest through past giving.


6.1. The In-Group–Out-Group Effect ReplicationUsing Survey-Based Experiments

We demonstrated in the field experiment that anask highlighting an in-group person (Hindu womanwhere the cold list is about 90% Hindu) leads tohigher donation rates and donation amounts thanan out-group person (Christian woman). Neverthe-less, our result is open to other alternative interpreta-tions. For example, it might be the case that Christianwomen may be considered to be wealthier on aver-age and may be seen to have less “needs” and there-fore may generate less donations. If indeed it is theout-group effect driving the lower donations, it mustbe the case that potential Christian donors are morelikely to donate to the Christian subject and less tothe Hindu subject. However, given the low number ofpotential Christian donors this is hard to test withinour field sample.

We therefore conducted a survey-based experimentto assess this question. First, we conducted a sur-vey through M-Turk on Indian respondents wherewe showed the same flyer as in our cold list ex-periment (with individual condition, loss condition,and monthly condition) but one group receiving theflyer with the Hindu woman (Sushila) and the othergroup receiving the flyer with the Christian woman(Shirley). After reading the flyer, the respondentswere asked about their likelihood of giving (1–10scale), whether they had given in the past, theirreligion, education, and income. Unfortunately, therespondents through M-Turk were disproportionatelyHindu. Given our interest in getting additional Chris-tian respondents, we augmented our sample throughan email mailing list of Christian respondents from anIndian direct marketing company (Yellow Umbrella)and did the identical survey with these respondents,randomizing for in-group and out-group treatments.

The results from the survey are reported inTables 3(a) and 3(b). Table 3(a) provides the descrip-tive statistics across the four groups: (1) Hindus askedto donate for Sushila (in-group); (2) Hindus asked todonate for Shirley (out-group); (3) Christians asked todonate for Sushila (out-group); (4) Christians askedto donate for Shirley (in-group). Hindus say theywould give more overall in the sample, though theirincome and educational conditions are not higher. Pastgiving is roughly similar across all treatments, exceptfor Christians asked to give to Shirley. What is clear isthe base rates of giving are higher for in-groups rela-tive to out-groups for both Hindus and Christians. Thisis particularly interesting given that the past giving ismuch lower for Christians facing the Shirley treatment(in-group) compared to Christians facing the Sushilatreatment (out-group).

Table 3(b) reports results of an ordinary least squaresregression on the likelihood of giving (a 10-point scale)

with controls for past giving and education to testthe in-group–out-group effect. These results show thatthe in-group effects are indeed statistically significantfor both Hindus 4p < 0015 and Christians 4p < 00055.Not surprisingly, past giving is overall very signifi-cant and higher levels of education lead to higher giv-ing. Income was highly correlated with education andcreated multicollinearity issues, hence we droppedincome from the final regression we report (educationhad better explanatory power). This survey-basedexperiment result not only replicates the in-groupeffect for Hindus from the field experiment but alsosupports the in-group effect for Christians, giving usgreater confidence in our in-group–out-group com-parison result.

Next, we explore whether the difference in giv-ing for in-group and out-group is caused by dif-ferences in attitudes toward the charity rather thandifferences in sympathy.18 We ran a second M-Turkexperiment randomizing the in-group and out-groupcondition across Hindu respondents and asked themto rate the charity on a 10-point disagree-agree scaleon three statements adapted from Webb et al. (2000).The three statements are, (1) HelpAge India servesa good cause; (2) HelpAge India is a well-managedcharity; (3) I have a positive image of HelpAge India.

The regression results are reported in Table 3(c).For all three questions, the Sushila (in-group) vari-able is insignificant, indicating no statistical differ-ence in donor’s perceptions of the charity based onthe in-group or out-group treatments. Thus the differ-ence in likelihood of giving does not appear to risebecause of differences in how the charity is perceivedbased on the target recipient featured in the charity.

6.2. Raising Donations from Past DonorsThus far, we have demonstrated that advertising con-tent has large effects on both donation rates andamounts raised. The odds of giving increased from aslow as 51% between the loss and uncertain conditiontests for the reference dependence sympathy effect toas high as 300% for the in-group relative to the groupcondition for the identified victim effect.

We conjectured that sympathy biases may have arelatively strong impact in the context of new dona-tions, because the baseline levels of sympathy mightbe lower. Yet the effects of sympathy bias on dona-tions may be more muted when the base levels ofsympathy are higher. To test this, we decided to test ifthe effects of sympathy bias may be replicated amongpast donors, for whom the baseline sympathy for thecause must be higher.19

18 We thank a reviewer for the suggestion.19 Another possibility is that past experience with HelpAge hasreduced the uncertainty (lower variance) about the charity; hence


Figure 8 Group Photo–Individual Text Condition

Photo collage offour unnamedladies

These ladies share a common story. Forexample, Sushila worked as a school teacherand retired comfortably. But then shebecame destitute when her husbandpassed away and other family membersrefused to support her.

Support a Gran has helped people likeSushila meet their basic needs of food,clothing and shelter in their time ofneed. Today in their seventies, they leada dignified life.

Your tax deductible donation of |9,000 ayear (that is just |750 a month) helpsSushila and people like her live a life ofdignity in their golden years.

6.2.1. Experimental Treatments. HelpAge con-ducted multiple mailings to their warm list of pastdonors. One such mailing was in November 2011around the festival of Diwali—the festival of lights—which is celebrated almost all over India. Diwali hasreligious legends associated with the ascendancy ofgood over evil, and it also coincides with the end ofthe Indian harvest season, and again has been associ-ated with gift giving and charitable giving.

HelpAge was reluctant to test the entire set of pre-vious experimental treatments on their warm list ofpast donors, given that the results appear to favormonthly ask and loss condition for reference depen-dence. However, they were curious about under-standing the boundaries around the identified vic-tim effect. We therefore tested the individual andgroup treatments from the earlier experiment (withloss framing and monthly ask), where the photos andtext communicated either the suffering of the individ-ual or group. To this, we add a third treatment, wherewe showed a group photo, but in the text we used astory that used the example of a particular individual.The goal was to test whether the text associated withthe individual evoked the identified victim sympa-thy bias, while the group picture communicated thatthis is a problem for a larger group. We show thetreatment associated with the Group Photo-IndividualText condition in Figure 8.

6.2.2. Experimental Design. The three treatments(as described above) and the number of mailingsfor the three treatments and descriptive statistics arelisted in Tables 4(a) and 4(b). We also report on thepast giving of donors, which are standard in the directmarketing literature, such as recency (number of yearssince past donation), frequency (no. of times donated

the framing effects may have a limited impact on the warm list.Whether learning on selection accounts for the differences in ratesof giving across the warm and cold list would be an interestingpossibility for future research. We thank an anonymous reviewerfor suggesting the learning explanation as a possibility.

in last five years), and monetary value of donationsin the past (average value of previous donations) ineach treatment; we will use them as controls in addi-tion to the treatments in analyzing the donations. Themnemonics provided serve to identify treatments ina meaningful manner. We randomly assign names onthe mailing list to the three treatments, but giventhat we expected the group condition to be the leasteffective, we sent only half the number of mailingsto this condition. The exact number of mailings foreach treatment is reported in Table 4(b) along withthe descriptive statistics. As expected, the giving withthis warm list average about 1.2%, about four timeshigher than with the cold list. The | per mailing alsowas higher at |45. This validates the use of cold liststo generate donors (even at a loss) to be able to moreefficiently raise funds in subsequent fundraisers tar-geted to past donors.

6.2.3. Results. Figure 9 reports the results interms of donation rates and |/mail under the threeconditions. As before, we replicate the result that theindividual condition (with both individual photo andtext) generated more donors and higher amounts ofdonations relative to the group condition (with bothgroup photo and group text). The difference in donorrates (1.33% vs. 1.14%) however is smaller than withthe cold list of new donors and is significantly differ-ent only at p < 0001. |/mail is also higher at |53.10for the individual condition, relative to |50.70 for thegroup condition, an increase of 4.7%. To our surprise,we found the group photo-individual text conditiongenerated worse outcomes than the pure group con-dition. Donor rates were only 0.95%, and the |/mailis also substantially lower at |37.40. We speculate thathaving the individual text as an example where other-wise the photo and initial introduction are about thegroup potentially destroys the fluency of the message,by mixing up a group story with an individual exam-ple, rather than generating a bump up in donationrates relative to the group message.

The results of the logistic and Tobit regressions fordonation choice and donation amounts are reportedin Tables 4(b) and 4(c), respectively. Indeed the resultsreported under Model 1 in Tables 4(b) and 4(c) areboth qualitatively and quantitatively identical to thepaired treatment comparison results discussed in theprevious paragraph. In Model 2, we report the resultsof the logistic and Tobit regressions, controlling fordonor heterogeneity exhibited through past donationchoices described earlier. The effects of the exper-imental treatments continue to be virtually identi-cal in magnitude relative to the regressions withoutthe controls, reflecting the fact that our assignmentto treatments was random; at the very least, thisshould give faith in the quality of our random assign-ment. In terms of substantive insights from the con-trol variables, we find that recent and more frequent


Table 4(a) Past Donor Experiment: Descriptive Statistics on Past Behavior and Experiment Outcomes

Treatment Description (mnemonic) No. of mail Recency Past freq | past amt Donate (%) |/mail |/donor

1 Individual Photo-IndividualText (IPIT)

44,000 0.63 0.927 2,979 1.325 53.10 4,007

2 Group Photo-IndividualText (GPIT)

43,999 0.63 0.923 2,939 0.954 37.40 3,918

3 Group Photo-GroupText (GPGT)

22,000 0.62 0.920 3,067 1.136 50.74 4,465

Overall 109,999 0.63 0.92 2,981 1.14 45.03 4,069

Table 4(b) Past Donor Experiment: Logistic Regression on Donation Choice

Model 1 Model 2

Estimate (std. err) Odds ratio Z Estimate (std. err) Odds ratio Z

Individual Photo-Individual Text (IPIT) 0016∗ 1016 2004 0015∗ 1016 10994000845 400085

Group Photo-Individual Text (GPIT) −0018∗∗ 0083 −2019 −0018∗∗ 0083 −20224000795 4000825

Donation in past year? (recency) 0061∗∗∗ 1084 40994001235

No. of donations in five years 0074∗∗∗ 2009 38041(frequency) 400025

Total donations in five years −4011e−6∗ 0099 −1085(monetary value in thousands) 42051e−65

Intercept −4046∗∗∗ 00011 −70021 −6015 00002 −500464000635 4001215

N 109,999 109,999

Note. Base treatment is Group Photo-Group Text (GPGT) condition.∗p < 001; ∗∗p < 0005; ∗∗∗p < 0001.

Table 4(c) Past Donor Experiment: Tobit Regression on Donation Amount

Model 1 Model 2

Estimate (std. err) t-stat Estimate (std. err) t-stat

Individual Photo-Individual Text (IPIT) 800∗ 1085 739∗ 106844315 44405

Group Photo-Individual Text (GPIT) −11042∗∗ −2032 −11084∗∗ −203644505 44595

Donation in past year? (recency) 11354∗∗∗ 203945675

No. of donations in five years 41274∗∗∗ 27086(frequency) 41535

Total donations in five years 0.02∗∗∗ 3029(monetary value) (0.006)

Intercept −341178∗∗∗ −37049 −391429∗∗∗ −3506349145 4111065

Sigma 141961∗∗∗ 131850∗∗∗

43615 43295N 1091999 1091999N (left censored at 0) 1081746 1081746N (uncensored) 11253 11253

Note. Base treatment is Group Photo-Group Text (GPGT) condition.∗p < 001; ∗∗p < 0005; ∗∗∗p < 0001.

donors are not only more likely to donate but alsodonate more. We see that higher monetary value ofpast donations has a negative impact, but is onlysignificant at p < 001. Although we cannot explainthe negative impact, we note that even if consideredsignificant, the economic magnitude is small. A |1,000increase in total past giving reduces the odds by only

about 1% (odds ratio of 0.99), which is much smallerthan the impact of other variables. However, largermonetary amounts do predict greater current dollarvalue of donations as expected.20

20 We tested for interactions between past giving and treatment.We did not find significant interactions for donation rates. In the


Figure 9 (Color online) Past Donor Experiment

(a) Donation rate

IPIT 95% CI: (1.22%, 1.43%)GPIT 95% CI: (0.87%, 1.05%)

GPGT 95% CI: (1.00%, 1.28%)

(b) Donation( )/mail

IPIT 95% CI: (40.97, 65.23)GPIT 95% CI: (31.66, 43.15)

GPGT 95% CI: (39.72, 61.77)

0.8

1.0

1.2

1.4

Perc

ent g

iven

IPIT GPIT GPGT IPIT GPIT GPGT

30

40

50

60

70

Don

atio

n

1.33%

0.94%

1.14%53.10

37.40

50.74

TreatmentTreatment

Thus, we conclude that the effects of sympathy biasaffect donation behavior even among past donors,who are already sympathetic to the cause, but theframing effects are attenuated relative to the cold listsetting. Given that the number of donors and theamount of money raised with the warm list is about10 times greater, the 16% increase in donors and the4.7% increase in the amount of money raised is com-parable in economic magnitude in terms of incre-mental donors and money raised with new donoracquisition. Hence, we conclude that effects of sympa-thy biases continue to remain economically significanteven among warm donors.

7. ConclusionThis paper investigated the persuasive effects ofadvertising content on target outcomes, in the con-text of fundraising through the use of large-scalefield experiments. Our experimental treatments wereguided by the psychological literature on sympathybiases and framing effects. Broadly, we find that evenminor variations in the persuasive message have largeand dramatic impacts on donor behavior, both interms of the donation rates and amounts raised. Theresults are particularly dramatic and stark, given thatthere are no differences in incentives, match rates, orsocial pressure, which have been the focus of muchprevious research. Minor differences in language leadto fairly large differences in outcomes. More specifi-cally, our key findings are as follows:

1. Framing has large effects on donor response bothin terms of donation rates and donation amounts(|/mail). Among potential new donors, donationrates increase from as low as 51% between the two

Tobit regression on donation amount, we found negative interac-tions with recency and positive interactions with monetary valuefor the treatments.

reference dependence conditions to as high as 300%for the in-group relative to the group condition. Thesympathy bias and framing effects are much largeramong new donors relative to past donors in percent-age terms, but as the giving rates are much higheramong past donors, the incremental money raised indollar terms is larger with the warm list.

2. We find significant evidence of the identified vic-tim effect; an individually identified victim is likely togenerate over two and a half times more donors andover twice the donations relative to an unidentifiedgroup of four victims.

3. When the identified victim is from an in-group(Hindu majority in India), the treatment generatessubstantially more donors and donations than whenthe identified victim is from an out-group (Chris-tian minority). An in-group victim increases donationrates by almost 50% and nearly doubles funds raised.Even an identified out-group victim does better rela-tive to the unidentified group of victims.

4. We find support for reference dependent sym-pathy. When victims are described as currently des-titute, but previously well-off, they are likely togenerate 50% more donors and 33% more averagedonations than someone who is destitute, but the pastwas left undescribed. This supports the hypothesesthat the chronic poor are less likely to elicit sympathythan someone who suffered a change—i.e., fell intopoverty in old age.

5. We find no support of the pennies a day hypoth-esis. The monthly temporal framing generated 71%more donors and 66% more donations than the dailyframing, even when the daily frame was in terms ofan amount that is smaller than the price of a coffee inurban India.

6. The ratio graphs of the amount donated acrossconditions for the corresponding rank of the give(Figures 3–7) show that the strength of each effect


tested is extremely powerful—to our knowledge, sucha result has never been presented in the behavioralliterature. This representation based on a paired testis more convincing that a mere means and propor-tion test that is typically presented in the behavioralliterature.

Empirical research using field data on advertisinghas focused primarily on how advertising spend andtiming affect market outcomes; there has been littlesystematic research on how advertising content affectsoutcomes. Our results show that varying advertisingcontent through theoretical results identified in psy-chology has an economically significant impact on themarket outcomes in real world settings. This is par-ticularly important because these treatments add littleincremental cost, yet have a dramatic impact on mar-ket outcomes.

There are of course a few caveats that we shouldhighlight. First, as with all experimental research,the effect sizes are likely a function of the particu-lar treatments. For example, the loss treatment canbe made stronger by making the losses of the vic-tim more vivid; or we could make the in-group effectstronger by priming religion more explicitly, and/oremphasizing geography (state or city) or linguisticconnections. Similarly the effect sizes can vary acrosscontexts. For example, our donation request is in thecontext of a chronic poverty condition, but if theask is around a disastrous event (e.g., earthquake,tsunami, etc.) to help destitute seniors, the effect sizeswill likely be larger. Furthermore, the cold list dona-tion was done during tax time and the Holi holi-days. The overall giving may be more muted duringother seasons. As we show in the paper, the effectsizes are different for cold lists versus warm lists—amanagerially important distinction. The differences inframing effect sizes by treatment and context is sim-ilar to variations in price and advertising elasticitiesdocumented in empirical work across categories andin different shopping and media contexts, that typ-ically gets summarized through meta-analysis overtime (e.g., Tellis 1988, Kaul and Wittink 1995). Finally,one issue in the managerial use of these results iswhether the effects of sympathy biases might waneover time with repeated use in competitive settings, ifall fundraisers apply such ideas. As with much psy-chological research on framing effects such as lossaversion, endowment effects, etc., we believe theseeffects are unlikely to fade because of repeated useor use by competitors, but these issues are worthy oftesting in future work.

We hope our research continues to bridge thegap between behavioral and quantitative market-ing research not just in the area of advertising butalso more broadly by triggering research agendasaround field validation and conceptual replications

for various behavioral theories by quantitative empir-ical scholars. Whereas behavioral research focuseson identifying new theories and exploring the the-oretical mechanisms underlying the psychologicaleffects, empirical research by quantitative marketersand economists is more focused on measuring themagnitude of effects and the relative effect size ofalternative marketing levers in naturally occurringdata. In practice, naturally occurring empirical datado not have the variations to measure psychologi-cal effects and therefore there is often the questionof whether behavioral effects identified in the lab-oratory can be observed in real world settings andhow economically meaningful the effect sizes are.This study demonstrates that experimental treatmentsbased on well-documented theories in psychology canbe implemented in the form of experimental treat-ments in practical and natural field settings with avery light touch and still produce large economicallyrelevant effects. Such research focused on measuringrelative effect sizes of previously identified behavioraleffects in natural settings should be valuable for notonly quantitative marketers and economists interestedin whether psychological theories matter in the fieldbut also for managers interested in choosing amongthe recommendations from behavioral theories as mar-keting levers.

Supplemental MaterialSupplemental material to this paper is available at https://doi.org/10.1287/mksc.2016.0989.

AcknowledgmentsThe authors thank Leif Brandes, Daylian Cain, Ray Fisman,Shane Frederick, Mushfiq Mobarak, Vithala Rao, JiwoongShin, and Deborah Small for their helpful comments. Theauthors also thank participants in the 2012 China IndiaInsights Conference in New Haven, the 2012 Economics ofAdvertising and Marketing Conference in Beijing, the Che-ung Kong Graduate School of Business Marketing ResearchForum Conference in Beijing, the marketing seminars atthe University of Connecticut, University of Massachusetts,Texas A&M, and Fudan University for their comments. Theauthors thank the HelpAge India team for their support andacknowledge the help of Bijay Mishra and Ashima Saini.

Appendix

Proposition. The difference in giving rates for in-group andout-group victims when the potential donor list consists only ofin-group members will be greater than or equal to the difference ingiving rates for in-group and out-group victims when the donorlist has a mix of in-group and out-group members with in-groupmembers being a majority in the mailing list.

Let � and 1 − � be the proportion of in-group and out-group potential donors, respectively, in the mailing list. Letthe giving rate toward in-group and out-group victims be xand �x, respectively, where � ≤ 1 by the logic that the




out-group donation rate would be at most as large as thein-group donation rate. The table clarifies the giving ratesfor in-group and out-group victims among potential donorsfrom the in-group and out-group.

Potential Giving rate to Giving rate toSize donor base in-group victims out-group victims

� In-group x �x1 −� Out-group �x x

If the donor sample only had the in-group (i.e., � = 1),then the difference in the giving rate between the in-groupand out-group victims would be x−�x = 41 −�5x.

When the donor list has a mix of in-group and out-groupmembers whose group membership cannot be identified,the estimated giving rate for in-group victims will be �x+

41 −�5�x. The estimated giving rate for the out-group vic-tims will be ��x+ 41−�5x. The difference in estimated giv-ing rate between the in-group and out-group victims willbe �x+ 41−�5�x− 4��x+ 41−�5x5= 41−�5x42�−15. Whenthe in-group members are in the majority, i.e., � ≥ 005, 0 ≤

2�− 1 ≤ 1. Q.E.D.

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