Supplemental Material A: Other data collection across Experiments 1-4

Experiment 1 was the first of the series focusing upon mechanisms such as reward uncertainty that might promote co-consumption of supernormal rewards (Goodwin et al., 2015). As part of this, and in addition to the collection of basic demographic information, the protocol included questionnaires to explore, in a preliminary way, associations between consumption of supernormal rewards, eating and money attitudes, and food preferences in the Bangor University student population. Questionnaires included:

(i) broader consumption behaviours (Goodwin et al., 2015)(ii) Three-Factor Eating Scale-18 (de Lauzon et al., 2004) (iii) Food Craving Questionnaire-Trait (Moreno et al., 2008)(iv) Eating Disorder Examination-Q (Fairburn & Beglin, 1994)(v) Fagerstrom Test for Nicotine Dependence (Heatherton et al., 1991)(vi) Money Attitudes Scale (Furnham et al., 2012)(vii) Perceived childhood socioeconomic status (Griskevicius et al., 2011)(viii) Beck's Depression Inventory – II (BDI_II) (Beck et al., 1996)

In laboratory-based Experiment 3, we retained (i) survey of consumption behaviours (Goodwin et al., 2015); (ii) perceived childhood socioeconomic status (Griskevicius et al., 2011); (iii) Food Cravings Questionnaire (FCQ-T) (Moreno et al., 2008); and (iv) Beck's Depression Inventory – II (BDI_II) (Beck et al., 1996). In Experiment 4, we retained (i) perceived childhood socioeconomic status (Griskevicius et al., 2011) and (ii) Beck's Depression Inventory – II (BDI_II) (Beck et al., 1996). All questionnaires were completed after the reward-uncertainty induction (or its control procedure) and once the collection of our principal outcome measures had been completed. The observed associations (as bivariate correlations) were broadly in line with what might be expected on the basis of the available literature. However, they are not relevant to the questions addressed in Experiment 1, 3 and 4, and are not detailed further.

In Experiment 2 involving MTurk (https://www.mturk.com/), we included (i) the 5-item WHO well-being scale (Topp et al., 2015); (ii) perceived childhood socioeconomic status (Griskevicius et al., 2011) and (iii) 4 items from the Quick Inventory of Depressive Symptomatology (QIDS)(Rush et al., 2003). (The four items were selected on the basis of the most discriminating items; its properties were unreliable.) Given the outcomes of Experiment 2a and Experiment 2b, we do not report any moderation by these variables in respect of the (null) effects of reward uncertainty on delay or probability discounting rates (Cox & Dallery, 2016). Neither the WHO-5 nor SES showed any marked associations with ED50 or EP50 discounting rates and are not reported here but are available, along with all other data at https://datadryad.org/stash/

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Supplemental Material B: Die-rolling device for Experiments 1, 3 and 4 and the JavaScript 6-sided (and fair) die for online Experiments 2a and 2b

Figure S1 Picture of the die-rolling apparatus used in Experiment 1, 3, and 4.

Figure S1 depicts the die-rolling device used for Experiments 1, 3 and 4. Participants rolled the die by pressing a button on the bottom of the device. Participant rolled the die repeatedly until sure that the die was fair. In the reward-uncertainty induction, the opaque cover was placed over the device to hide the outcome of the die-roll until the end of the protocol.

Figure S2 The JavaScript generated die used online in Experiments 2a and 2b.

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Figure S3 A picture of the online simulated (fair) die-rolling device. The result of the 6-sided die roll was hidden with a question mark and is only revealed at the end of the experiment.

In Experiment 2a and 2b, participants were MTurk workers (https://www.mturk.com/). The die-rolling device, written in JavaScript, was delivered with the Qualtrics platform (https://www.qualtrics.com/). Participants practiced rolling the die freely to satisfy themselves that the die was fair (Figure S2). Once happy that the die was fair, participants rolled it once more but the outcome was hidden by a question mark until the end of the protocol (Figure S3).

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Supplementary Material C: Positively vs negatively-frame reward-uncertain groups

Experiment 1Figure S4 depicts the amount of alcohol consumed (ml) for each of the three participant groups in Experiment 1. A linear regression of the form: Alcohol = Gender + Audit + Reward Uncertainty was run with the positively-framed group as the referent. The model was boot-strapped and run 1,000 times. The positively-framed participants and negatively-framed participants drank similar amounts (β=-4.51; 95% CI [-45.49, 37.87]). Participants in the positively-framed group consumed more alcohol than those in the control group (β=42.56; 95% CI [-0.03, 83.62]). When the control group was used as the reference, the negative frame participants tended to drink more than the controls (β=38.01; 95% CI [-2.10, 76.99]).

Figure S4 Violin plot of alcohol consumed by condition (ml). Black dots represent the groups’ mean consumption. Error bars represent 95% confidence intervals. The outline of each figure represents the distribution of the groups’ consumption.

Figure S5 Violin plot of snacks consumed by condition, normalized as described in the main text. Black dots represent the groups’ mean consumption. Error bars represent 95% confidence intervals. The outline of each figure represents the distribution of the groups’ consumption.

Figure S5 illustrates the amount of snacks consumed in Experiment 1 by participant group. A linear regression of the form: Snack Consumption = Gender + Reward Uncertainty was boot-strapped 1,000 times with positively-framed participants as the baseline. There were no marked differences in consumption between the participants in the positively-framed group compared to the negatively-framed group (β =-0.014; 95% CI [-0.40, 0.39]). The positively-framed participants consumed more than the control participants (β = 0.39; 95% CI [0.10, 0.69]). When the control group was used as the reference, the negatively-framed group tended to consume marginally more than controls (β=0.17; 95% CI [-0.13, 0.55]).

Experiment 4Figure S6 depicts the average sensory ratings for each of the three participant groups in Experiment 4. Sensory ratings were calculated by taking the average of a participant's salty rating for Hula Hoops, salty popcorn, and salty & sweet popcorn along with the average sweetness rating for sweet popcorn, salty & sweet popcorn, Coke, 7-up, and Capri-Sun. We ran a linear regression of the form: Sensory ratings = Gender + Reward Uncertainty with the positively-framed participant group as the referent. The model was boot-strapped and run 1,000 times. Participants in the negatively-framed and the positively-framed group reported comparable sensory responses to the foods (β=0.0087; 95% CI [-0.23, 0.24]). Those in the positively-framed group reported stronger ratings of sweet and saltiness compared with those in 4

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the control group (β=0.27; 95% CI [0.033, 0.51]). Finally, when the control group was used as the referent, participants in the negatively-framed group also reported significantly higher sensory ratings compared with participants in the control group (β=0.29; 95% CI [0.03, 0.50]).

Figure S6 Mean sensory rating in Experiment 4 by each group. Black dots represent the groups’ mean sensory rating. Error bars represent 95% confidence intervals. The outline of each figure represents the distribution of the participants’ ratings.

Figure S7 Mean amount consumed by each participant group. Black dots represent the groups’ mean consumption. Error bars represent 95% confidence intervals. The outline of each figure represents the distribution of the participants’ ratings.

Figure S7 illustrates the amounts of snacks consumed in Experiment 4 by the participant groups. As above, we ran a model of the form: Snack Consumption = Gender + Reward Uncertainty, boot-strapped 1,000 times with the negatively-framed participant group as the baseline. There was no difference between the participants of the positively- and negatively-framed groups in the amount consumed (β = 0.14; 95% CI [-0.09, 0.40]). The negatively-framed group tended to consume marginally more snacks than the controls (β=0.21; 95% CI [-0.008, 0.44]), as did the positively-framed group, albeit to a lesser extent (β=0.07; 95% CI [-0.18, 0.28]).

To analyse the amount drank, we ran a linear model of the form: Drink Consumption = Gender + Group, boot-strapped 1,000 times, with the positively-framed participant group as the baseline. There was no difference in the amount consumed between the participants of the positively-framed group and the control group (β = 0.004; 95% CI [-0.20, 0.23]). The negatively-framed participants consumed slightly more than the positively-framed (β = 0.14; 95% CI [-0.1, 0.38]). Finally, when the negative-framed participants was used as the referent, the controls drank slightly less than the negatively-framed participants (β=-0.13; 95% CI [-0.36, 0.1]).

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Supplemental Material D: Group characteristics and matching for Experiments 1, 3 and 4

  Positive(n=30)

Negative(n=30)

Reward-uncertain

Control(n==30)

Gender (M:F) 13:17 13:17 26:34 13:17

Age 22.6 ± .63 22.4 ± .55 22.5 ± .41 23.6 ± .59

AUDIT 6.7 ± .55 6.6 ± .57 6.6 ± .39 5.4 ± .39

Baseline Hunger 3.87 ± .51 3.23 ± .45 3.55 ± .34 3.66 ± .41

Baseline Thirst 4.37 ± .5 5.65 ± 1.87 4.16 ± .37 4.43 ± .43

Baseline PANAS - Negative

11.5 ± .55 12.2 ± .45 11.87 ± .36 12.7 ± .55

Baseline PANAS - Positive

30.5 ± 1.53 29.6 ± 1.35 30.1 ± 1.01 28.17 ± 1.77

Post consumption PANAS N

10.5 ± .17 11.6 ± .39 11.07 ± .22 12.2 ± .51

Post consumption PANAS P

30.5 ± 1.95 30.6 ± 1.61 30.5 ± 1.25 28.4 ± 2.8

Post Exp. PANAS - Negative

11.6 ± .66 11.6 ± .47 11.6 ± .40 11.8 ± .48

Post Exp. PANAS - Positive

29.6 ± 2.82 30.4 ± 1.70 30.0 ± 1.61 28.8 ± 2.60

Table S1 Demographic information, alcohol drinking patterns and self-report state variables for the participant samples of Experiment 1. Mean, standard errors (mean±SE) and linear tests for the positively-framed participants, negatively-framed participants and control participants. The reward-uncertain column contains the mean and standard error when both the positively- and negatively-framed groups are combined; as used in the main analysis of the text. Note. Alcohol Use Disorders Identification Test (AUDIT)(Saunders et al., 1993); Positive and Negative Affect Scale – State (PANAS-S) (Watson et al., 1988). *p< .05.

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  Positive(n=37)

Negative(n=34)

Reward-uncertain

Control(n=36)

Gender (M:F) 18:19 18:16 36:35 18:18

Age 20.8 ± .40 20.9 ± .73 20.8 ± .40 21.8 ± 1.06

AUDIT 7.9 ± .92 10.3 ± 1.27 8.4 ± .72 9.3 ± .97

Baseline Hunger 3.8 ± .41 4.7 ± .50 4.3 ± .33 2.9 ± .33

Baseline Thirst 5.6 ± .33 6.5 ± .37 6.0 ± .26 5.5 ± .32

PANAS - Negative 12.4 ± .42 12.1 ± .39 12.3 ± .31 12.4 ± .90

PANAS - Positive 29.4 ± 1.06 28.0 ± .91 28.7 ± .74 27.9 ± .93

Table S2 Demographic information, alcohol drinking patterns and self-report state variables for Experiment 3. Only the sweet-likers (see main text) were included in this table as the main analysis was conducted on that subset. Mean, standard errors (mean±SE) and linear tests for the positively-framed participants, negatively-framed participants and control participants. The reward-uncertain column contains the mean and standard error when both experimental groups are combined. Note. Alcohol Use Disorders Identification Test (AUDIT)(Saunders et al., 1993); Positive and Negative Affect Scale – State (PANAS-S) (Watson et al., 1988).

  Positive(n=44)

Negative(n=44)

Reward-uncertain

Control(n=44)

Gender (M:F) 21:23 21:23 42:46 21:23

Age 21.0 ± .39 21.6 ± .70 21.3 ± .40 20.7 ± .41

Mean BDI 9.9 ± 1.00 14.8 ± 1.69 12.4 ± 1.01 13.4 ± 1.29

Mean AUDIT 7.45 ± .77 8.02 ± .96 7.74 ± .61 8.56 ± .92

Mean FTND .50 ± .23 .80 ± .25 .65 ± .17 .93 ± .24

Mean PSECDI .48 ± .37 .45 ± .26 .47 ±.23 .34 ± .32

Baseline Hunger 3.38 ± .33 3.98 ± .36 3.68 ± .25 3.55± .44

Baseline Thirst 4.91 ± .27 4.80 ± .33 4.85 ± .21 4.98 ± .33

Last eaten (hours ago) 3.4 ± .58 4.7 ± 1.0 4.0 ± .57 3.9 ± .74

Baseline Happiness 6.63 ± .20 5.98 ± .31 6.31 ± .19 6.29 ± .20

Table S3 Demographic information, recent depression symptoms, alcohol drinking patterns, nicotine dependence and use, and state variables for Experiment 4. Mean, standard errors and linear tests for the positively-framed, negatively-framed participants and control participants. The reward-uncertain column contains the mean and standard error of the combined experimental groups. Note. Beck's Depression Inventory – II (BDI_II)(Beck et al., 1996), Fagerstrom Test for Nicotine Dependence (Heatherton et al., 1991), Penn State Electronic Cigarette Dependence Index (PSECDI)(Foulds et al., 2014), Alcohol Use Disorders Identification Test (AUDIT)(Saunders et al., 1993) and Positive and Negative Affect Scale – State (PANAS-S)(Watson et al., 1988). *p< .05.

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Supplemental Material E: Choice of rewards and elicitation in Experiments 2a and 2b

Testing the effects of reward uncertainty on temporal and probabilistic discounting involved several challenging design decisions. First, in Experiment 1 (and all the experiments in this series), the reward-uncertainty induction used receivable money – payable at the end of the protocol – as its incentive; and its effects were tested against consumable rewards in the bogus taste test. In Experiments 2a and 2b, it would have been preferable to test the effects of reward uncertainty on the delay and probability discounting of comparable (and incentive-compatible) rewards of equivalent value (£1.20 or less). However, the measurement of discounting rates for small edible rewards, while possible – for example, 16ml or less of orange juice in thirsty subjects (Jimura et al., 2009) – is technically challenging. Our own pilots with both 'adjusting delay' and 'adjusting amount' procedures showed that, without restriction on prior food and liquid intake, healthy adults are quite able to delay (over periods of 1 to 2 min) consumption of larger over smaller servings of the pub snacks used Experiment 1 (even blocking convergence of elicitations in some participants). Second, offering actual monetary rewards in the discounting elicitations of Experiment 2a and 2b, as alternative rewards, might have encouraged participants to combine the monetary outcomes of the induction's die-roll (delivered at known probabilities) with the delay or probability-discounted monetary outcomes of the elicitations as a single complex prospect value, complicating interpretation of the reward-uncertainty induction's effects.

Given the above, it seemed sensible to test first whether reward uncertainty induces any general perturbation of delay discounting and risk-attitudes (measured as probability discounting rates) with hypothetical rewards. Numerous studies show no systematic differences between discounting rates when rewards are real or hypothetical (Johnson & Bickel, 2002; Lagorio & Madden, 2005; Madden et al., 2003) and statistical equivalence of real and hypothetical rewards in delay and probability discounting elicitations (Matusiewicz et al., 2013).

In addition, since we could not be certain about how long the effects of our reward uncertainty induction might last, we used the brief 5-item elicitations of delayed (ED50; Experiment 2a) and probabilistic (EP50; Experiment 2b) reward discounting rates as hyperbolic values k and h, respectively (Cox & Dallery, 2016; Koffarnus & Bickel, 2014). The ED50 and EP50 elicitations attempt to find the delay (or probability) at which preferences switch from the immediate (or more probable) small reward to the delayed (or less probable) large reward (Yoon & Higgins, 2008). These procedures can be completed in 2min and their validity is evidenced by replicated demonstrations of the dependence of k values on the reward magnitude, and the differences between k values of money and other rewards (Koffarnus & Bickel, 2014). Using the ED50 and EP50 procedures allowed the delivery of the reward-uncertainty induction and fast measurements of k and h values before the effects of the induction had dissipated because, for example, participants had forgotten about the (simulated) die-roll and its outcomes.

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Supplemental Material F: Experiment 2 & 4: Changes in state positive affect

Experiment 2a and 2b; pre- vs post-inductionIn Experiment 2a and 2b, momentary happiness and alertness were taken at three time points with 15-point Likert scales with anchor points of 'Not at all' and 'Extremely'. These were taken at the start of the experiment (pre-induction), right after the experimental induction (post-induction), and after the participants had witnessed the outcome of the die roll (post-outcome). The two experimental protocols of Experiment 2a and 2b were identical up to and including the post-induction ratings. So, we combined the datasets of Experiments 2a and 2b (N=399). Table S4 depicts the mean and standard errors of the pre- and post-induction happiness and alertness ratings for the reward-uncertain participants and the control participants. (The ratings for Experiment 2a and Experiment 2b are shown separately for completeness.)

For momentary happiness, we ran a repeated measures 2x2 analysis of variance with the between-subjects factor of Group (reward-uncertain vs control) and the within-subjects factor of Time (pre- vs post-induction). This demonstrated that, post-induction, happiness increased more in the control participants (11.30±0.22 to 12.94±0.17) compared with the reward-uncertain participants (10.87±0.21 to 10.74±0.22), as reflected in the significant 2-way interaction between Group and Time (Table S4; F(1)=67.21, p=3.41x10-15). Analysis of simple main effects showed that, while the reward-uncertain and control participants were well matched for their pre-induction happiness ratings (10.87±0.21 vs 11.30±0.22; F(1)=1.944, p=0.164), happiness ratings were greater in the control participants after the induction (10.74±0.22 vs 12.94±0.17; F(1)=60.76, p=5.71x10-14).

For momentary alertness, the 2x2 analysis as above demonstrated larger increases in post-induction alertness in the control participants (12.38±0.18 to 13.35±0.13) compared with the reward-uncertain participants (12.26±0.18 to 12.64±0.17), reflected in the significant two-way interaction between Group and Time (F(1)=11.88, p=6.29x10-4). Analysis of the simple main showed that, while the two groups were well-matched for their pre-induction alertness happiness ratings (12.26±0.18 vs 12.38±0.18; F(1)=0.21, p=0.647), the control participants were more alert immediately following the induction than the reward-uncertain participants, (F(1)=9.96, p=0.001). Overall, these data show that, at least with the online platform MTurk, the reward-uncertain participants, waiting on a die-roll outcome of an extra $4 or the baseline payment of $1 reported weaker momentary happiness and alertness ratings compared with the controls who had been told of their windfall of the die-roll's expected value to take their payment to $2.33.

Happiness AlertnessExperiment Group Time 1 Time 2 Time 1 Time 2

2a&b Control 11.30 ± 0.22 12.94 ± 0.17 12.38 ± 0.18 13.35 ± 0.132a&b R’ uncertain 10.87 ± 0.21 10.74 ± 0.22 12.26 ± 0.18 12.64 ± 0.17

2a Control 11.14 ± 0.34 12.85 ± 0.26 12.28 ± 0.26 13.36 ± 0.172a R' uncertain 10.92 ± 0.30 10.79 ± 0.33 12.48 ± 0.24 13.05 ± 0.222b Control 11.45 ± 0.29 13.03 ± 0.22 12.47 ± 0.25 13.33 ± 0.212b R' uncertain 10.82 ± 0.31 10.68 ± 0.31 12.04 ± 0.27 12.20 ± 0.27

Table S4 Mean 15-point Likert ratings of state happiness and alertness at the start of the experiment (Time 1: baseline), once the risk-induction had been administered (Time 2) for the risk-uncertain participants and control participants. At Time 2, the reward-uncertain group had rolled a fair 6-sided die for an additional $4 payment, but did not know the result while the control participants had been informed that they would be given an additional $1.33 as a 'gift'.

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Experiment 2a and 2b; post-induction vs post-outcomeOther evidence suggests that uncertainty (as ambiguity) can increase and prolong the happiness elicited by positive events (Bar-Anan et al., 2009; Wilson et al., 2005). Therefore, for completeness, we provide information about the comparison between the post-induction measurements of happiness compared with the post-outcome measurements, when participants discovered the outcomes of the die-roll in the reward-uncertainty induction.

Following the completion of the ED50 delay discounting elicitation (Experiment 2a) and the EP50

probability discounting elicitations (Experiment 2b), the outcomes of the die-roll were revealed. Given the similarity of the protocols - the only difference being the use of the ED50 and EP50 elicitations - we combined the datasets and divided the reward-uncertain participants into those who won the extra payment of $4 through the die-roll and those participants who lost. Table S5 shows the average happiness and alertness ratings of the three participant groups following the die-roll 'reveal'. For happiness ratings, we ran a 3x2 repeated-measures analysis of variance with the between-subjects factor of Group (reward-uncertain winners, reward-uncertain losers vs controls) and the within-subject factor of Time (post-induction vs post-outcome).

Relative to their post-induction ratings, the outcome of the die-roll affected the groups differently, reflected in the 2-way interaction between Group and Time (Table S5; F(2)=31.83, p=1.52x10-13). Analysis of the simple effects revealed differences in post-outcome happiness ratings of the three groups (F(2)= 24.67; p= 8.11x10-11). Participants who lost the die-roll were less happy than those who won (μ diff= -2.41; 95% CI [-3.444, -1.388]) and less happy than the control participants (μ diff= -2.11; 95% CI [-2.88, -1.323]). There was no substantive differences in the post-outcome momentary happiness ratings of the die-roll winners and the control participants (μ diff= 0.311; 95% CI [-0.668, 1.289]). Finally, an equivalently-structured repeated measures analysis of variance with the post-outcome alertness ratings showed increased alertness relative to the post-induction ratings (F(1)=8.357, p=0.004) but only a trending interaction between Group and Time (F(2)=2.44, p=0.088). Exploratory TukeyHSD post-hoc tests revealed that, post-outcome, the reward-uncertain losers were less alert than the controls (μ diff=-0.773; 95% CI [-1.415, -0.135]).

Experiment Group Happiness Alertness2a & 2b Control 12.46 ± 0.18 13.06 ± 0.152a & 2b Uncertain: winners 12.77 ± 0.33 12.87 ± 0.222a & 2b Uncertain: losers 10.36 ± 0.31 12.29 ± 0.22

2a Control 12.36 ± 0.28 13.03 ± 0.212a Uncertain: winners 13.00 ± 0.39 13.30 ± 0.322a Uncertain: losers 10.66 ± 0.43 12.58 ± 0.322b Control 12.56 ± 0.23 13.09 ± 0.212b Uncertain: winners 12.56 ± 0.51 12.48 ± 0.612b Uncertain: losers 10.00 ± 0.44 11.95 ± 0.31

Table S5 Mean (and standard error) post-outcome 15-point Likert ratings of momentary happiness and alertness (Time 3) once the gamble provided to the reward-uncertain participants had been resolved. The reward uncertain group was divided into those participants who won the die-roll and the extra payment of $4 and those participants who had lost the die-roll.

Experiment 4In Experiment 4, happiness levels were measured on a 10cm VAS. They were measured at three different time points. Initial happiness ratings were taken on arrival at the experiment. Pre-induction happiness was measured after the completing the Observe-or-Bet, STOP-IT and ED50

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and EP50 discounting assessments, but before the experimental induction. Post-induction happiness was measured immediately following the induction, but before the consumer taste test. Table S6 depicts the means and standard errors of the happiness ratings for both the reward-uncertain and control groups. Detailed statistical analysis is provided in the main text.

Happiness

Experiment Group Initial Pre-induction Post-induction

4 Control 6.29 ± 0.20 5.84 ± 0.25 6.79 ± 0.314 R' uncertain 6.30 ± 0.19 5.53 ± 0.19 6.21 ± 0.21

Table S6 Mean (and standard error) of 10cm VAS happiness rating in Experiment 4.

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Supplementary material G: Power/sample size calculations for Experiments 3 and 4

We calculated the sample sizes required to reach 80% power for the subsequent experiments on the basis of each of the alcohol and snacks consumed in Experiment 1.

Experiment 1: Alcoholic drink consumedWe began by calculating the variance in volume drunk explained with only the intercept and gender included in the model but without the reward uncertainty manipulation:

Model 1: Amount drunk = Gender.

In this model, R2 = 0.1621

Next, we added the reward uncertainty as the categorical predictor 'Frame' with 3 levels: positive frame; negative frame and control (as the referent):

Model 2: Amount Drunk = Gender + Frame.In this model, R2 = 0.2233.

Consequently, the variance explained by the 'Frame' = 0.0612 (i.e .2233 - .1621).

We then used G*Power to calculate the sample sizes required to have 80% power to find statistically significant treatment differences in Experiments 3 and 4 at p< .05. We used the test family 'F-Test' and the statistical test 'Linear Multiple Regression: Fixed Model, R2 increase'. Using this, we found that 80% power to detect required sample sizes of 126.

Experiment 1: Snacks consumedTo calculate the sample size required to have 80% power to find the effect of snacks consumed, we used a similar method:

Model 1: FoodConsumed = Gender; R2 = 0.03185

Model 2: FoodConsumed = Gender + Frame; R2 = .09783

So, the variance explained by Frame = 0.06598 (.09783 - .03185)

Running through G*Power, a sample size of 135, offered an 80% power to detect statistically significant treatment effects at p< .05 in Experiments 3 and 4.

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Supplemental Material H: Participant selection as sweet-likers; analytic models

Analysis of the complete datasetAs described in the main text, we used a mixed effect model to consider the effect of reward uncertainty on sweetness and liking for the complete dataset of 121 participants. This included the 107 participants whose maximal liking aligned to the 0.42 and 0.83M concentration and the 14 participants whose maximal liking aligned with the lower concentrations. The models showed effects trending in the hypothesized direction, with reward uncertainty predicting a sharper increase in both sweetness ratings, χ2(1)=1.9504; p=0.1625, and liking ratings, χ2(1)=2.3593; p=0.1245. Figure S8 illustrates these effects. Just as with the sub-sample of sweet-liking participants (see Figure 3 in the main text), the graphs illustrate that, as molarity increases, the reward uncertain participants rate both sweetness and liking higher than the controls.

Figure S8 Average sweetness (left) and liking (right) ratings by molarity and group, normalized against the least sweet mixture. For each individual, the rating for a given molarity was calculated by taking their average rating across all five blocks and subtracting it against the average rating at 0.05M. Error bars represent standard errors. The dataset included all participants (N=121).

Participant exclusionsSweet-liking shows significant inter-individual variation. Following previous investigations, we confined our data analysis to those participants who liked the highest concentrations of sucrose solution. Sweet-likers have been identified in various ways (Asao et al., 2015; Kim et al., 2014; Mennella et al., 2005; Moskowitz et al., 1985; Pangborn, 1970). Some studies have identified variable and sometimes small numbers of sweet-likers in healthy control or comparison samples as individuals whose maximal liking rating aligned with the highest concentration of 0.83M sucrose: n= 5/37 (Kampov-Polevoy et al., 1997); 2/25 (Kampov-Polevoy et al., 2001); 2/16 (Janowsky et al., 2003); n= 34/95 (Weafer et al., 2014). Given our a priori intention to test the 2-way interaction between reward uncertainty and molarity of sucrose concentration, we allowed our sweet-likers to be identified as those whose maximal liking ratings included the 0.83M and 0.42M concentrations. This identified 71 participants in the pooled reward-uncertain group (51 preferring 0.83M; 20 preferring 0.42M) and 26 participants in the control group (23 preferring 0.83M; 13 preferring 0.42M). The proportion of excluded sweet-haters in the reward-uncertain and control participant groups was comparable (9/80 (11%) and 5/41 (12%). Consistent with previous findings (Asao et al., 2015; Cherek, 1982; Kim et al., 2014; Mennella et al., 2005; Moskowitz et al., 1985; Pangborn, 1970), our sweet-likers showed monotonically higher liking across increasing concentrations of sucrose solution whereas the 14 remaining participants who showed reduced liking ratings at higher concentrations (Figure S9).

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Figure S9 Average sweetness liking ratings by molarity for the 87 included 'sweet-liker' participants and the 14 excluded sweet-hater participants. For each participant, the rating for a given molarity was calculated by taking their average rating across all five blocks and subtracting it against the average rating at 0.05M. Error bars represent confidence intervals.

Statistical approachSince the experimental design was repeated measures with each participant being asked to rate five molarities on five separate occasions, we used a random-slope mixed-effect model to assess the between-subject effect of reward uncertainty on sensory experience. When using mixed-effect models to assess the dependency of one variable on another, it is best to use two hierarchical models: a baseline model without the independent variable of interest, and the same model with the variable (Barr, 2013). A likelihood-ratio test can then be run against the two models to evaluate whether including the additional variable explains significantly more variance. In addition, models with the maximum random effects (justified by the experimental design) are preferred as random-intercept-only models are prone to Type 1 errors (Barr, 2013). As such, our models included group and molarity as fixed effects with block nested by participant as random effects, and concentration included as a random slope.

Controlling for thirst ratingsThere was little evidence that reward uncertainty’s effects on both sweetness and liking ratings across increasing concentrations of sucrose solutions are an artefact of uncontrolled variation in participants' thirst. First, we tested whether including participants' pre-induction thirst ratings in the statistical model explained more variance in their sweetness ratings. So, we compared a mixed-effect baseline model without pre-induction thirst ratings to another model that included them. An ANOVA between the two models showed no marked or significant change in the amount of variance explained by adding pre-induction thirst; the p-value shown here in red:

Model 1: sweetness Reward Uncertainty + Molar + (1 + Molar | PID/Block)Model 2: sweetness Reward Uncertainty + Molar + ThirstPre + (1 + Molar | PID/Block)

Df AIC BIC logLik deviance Chisq Df Pr(>Chisq)Model1 10 11337 11396 -5658.6 11317 Model2 11 11339 11404 -5658.3 11317 0.4557 1 0.4996

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The same was true with participants' ratings of how much they liked the sucrose solutions:

Model 1: liking ~ Reward Uncertainty + Molar + (1 + Molar | PID/Block)Model 2: liking ~ Reward Uncertainty + Molar + ThirstPre + (1 + Molar | PID/Block)

Df AIC BIC logLik deviance Chisq Df Pr(>Chisq)Model1 10 11332 11390 -5655.8 11312 Model2 11 11331 11396 -5654.7 11309 2.2552 1 0.1332

Second, since adding pre-induction thirst ratings does not explain more variance in the model, we would not usually check whether the two-way interaction between reward uncertainty and molarity hold when controlling for thirst ratings. However, to be absolutely sure, we tested this too; i.e. whether adding the interaction explained significantly more variance between when controlling for pre-induction thirst across nested models.

The result holds for sweetness and – at threshold level – for liking ratings; p-values in red:

Model 1: sweetness ~ Reward Uncertainty + Molar + ThirstPre + (1 + Molar | PID/Block)Model 2: sweetness ~ Reward Uncertainty + Molar + Reward Uncertainty * Molar + ThirstPre + (1 + Molar | PID/Block)

Df AIC BIC logLik deviance Chisq Df Pr(>Chisq) Model 1 11 11339 11404 -5658.3 11317 Model 2 12 11336 11407 -5656.2 11312 4.1946 1 0.04055 *

Model 1: liking ~ Reward Uncertainty + Molar + ThirstPre + (1 + Molar | PID/Block)Model 2: liking ~ Reward Uncertainty * Molar + Reward Uncertainty * Molar + ThirstPre + (1 + Molar | PID/Block)

Df AIC BIC logLik deviance Chisq Df Pr(>Chisq) Model 1 11 11331 11396 -5654.7 11309 Model 2 12 11330 11400 -5652.8 11306 3.7336 1 0.05333 .

Controlling for hunger ratingsGiven that the reward uncertain and control Reward Uncertainty differed in pre-induction hunger levels, we tested whether hunger moderated the effect of reward uncertainty on sweetness and liking ratings. There was little evidence of this. First, we tested whether including participants' pre-induction hunger ratings in the statistical model explained more variance in their sweetness ratings. So, we compared a mixed-effect baseline model without pre-induction hunger ratings to another model that included them. An ANOVA between the two models showed no marked or significant change in the amount of variance explained by adding pre-induction hunger; the p-value shown here in red:

Model 1: sweetness ~ Reward Uncertainty + Molar + (1 + Molar | PID/Block)Model 2: sweetness ~ Reward Uncertainty + Molar + HungerPre + (1 + Molar | PID/Block)

Df AIC BIC logLik deviance Chisq Df Pr(>Chisq)Model 1 10 11337 11396 -5658.6 11317 Model2 11 11339 11404 -5658.5 11317 0.0622 1 0.8031

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The same was true with participants' ratings of how much they liked the sucrose solutions:

Model 1: liking ~ Reward Uncertainty + Molar + (1 + Molar | PID/Block)Model 2: liking ~ Reward Uncertainty + Molar + HungerPre + (1 + Molar | PID/Block)

Df AIC BIC logLik deviance Chisq Df Pr(>Chisq)Model 1: 10 11332 11390 -5655.8 11312 Model 2: 11 11332 11397 -5655.1 11310 1.4251 1 0.2326

Second, since adding pre-induction hunger ratings do not explain more variance in the model, we would not usually check whether the two-way interaction between reward uncertainty and molarity hold when controlling for hunger ratings. However, to be absolutely sure, we tested this too; i.e. whether adding the interaction explained significantly more variance between when controlling for pre-induction hunger across nested models.

The result holds for sweetness and – at threshold level – for liking ratings; p-values in red:

Model 1: sweetness ~ Reward Uncertainty + Molar + HungerPre + (1 + Molar | PID/Block)Model 2: sweetness ~ Reward Uncertainty + Molar + Reward Uncertainty * Molar + HungerPre + (1 + Molar | PID/Block)

Df AIC BIC logLik deviance Chisq Df Pr(>Chisq) Model 1 11 11339 11404 -5658.5 11317 Model 2 12 11337 11408 -5656.4 11312 4.1946 1 0.04055 *

Model 1: liking ~ Reward Uncertainty + Molar + HungerPre + (1 + Molar | PID/Block)Model 2: liking ~ Reward Uncertainty + Molar + Reward Uncertainty * Molar + HungerPre + (1 + Molar | PID/Block)

Df AIC BIC logLik deviance Chisq Df Pr(>Chisq) Model 1 11 11332 11397 -5655.1 11310 Model 2 12 11330 11401 -5653.2 11306 3.7336 1 0.05333

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Supplementary material I: Recent depressive symptoms in Experiments 3 and 4

Figure S10 Effect of reward uncertainty on normalized sweetness ratings as a function of BDI scores (Beck et al., 1996) in Experiment 3. A linear regression of the form 'Sensory Rating = BDI' was run for both conditions. Each line represents the best fit line within a participant group. Grey areas = 95% confidence bands for the regression. Red circles: Control group. Blue triangles: Reward-uncertain group.

Figure S11 Effect of reward uncertainty on normalized sweetness ratings as a function of BDI scores (Beck et al., 1996) in Experiments 3 and 4. A linear regression of the form 'Sensory Rating = BDI' was run for both conditions. Each line represents the best fit line within a participant group. Grey areas represent 95% confidence bands for the regression. Red circles: Control group. Blue triangles: Reward-uncertain group.

Experiment 3In Experiment 3, we tested whether the effects of reward uncertainty on sweetness ratings were modulated recent depressive symptoms (measured with BDI-II (Beck et al., 1996)). We calculated each participants' average sweetness rating across all Kool-aid concentrations and all blocks of samples and normalized them to a mean of zero and a standard deviation of one. Figure S10 illustrates how average sweetness ratings relate to BDI-II in each participant group. Average sweetness ratings decrease with BDI-II scores in the control participants. However, this trend is eliminated in the reward uncertain participants. We boot-strapped a regression of the form: 'Sweetness = Reward Uncertainty + BDI + Reward Uncertainty * BDI' 1,000 runs to show an interaction between reward uncertainty and BDI scores (β=0.0718; 95% CI [0.0029, 0.1541]).

Experiment 3 and 4To show the combined effect of depressive symptoms in Experiment 3 and 4, we normalized the sensory ratings to a mean of one and a standard deviation of zero. We then combined the sensory ratings and BDI-II scores for participants in both Experiment 3 and 4. Figure S11 illustrates the results. Again, the sweetness ratings of the control participants decrease as their BDI-II scores increase (β = 0.3722; 95% CI [-1.0097, -0.1518]). However, the interaction between reward uncertainty and BDI-II demonstrates that this trend is reversed in the reward uncertain group (β = 0.07339; 95% CI [0.0445, 0.1018]).

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Supplementary material J: Experiment 4's cognitive assessments

STOP-IT TaskExperiment 4 used the stop-signal 'STOP-IT' task to assess motor control/cancellation (Verbruggen et al., 2008). STOP-IT is a computer program that uses the stop-signal paradigm to assess response inhibition in a controlled laboratory setting (Logan et al., 1997; Verbruggen & Logan, 2008). Numerous experimental manipulations, such as the use of auditory (Osman et al., 1986) and tactile signals (Åkerfelt et al., 2006) have presented convergent results, supporting the validity of stop-signal as an empirical measure of self-control (Band et al., 2003; Boucher et al., 2007). In Experiment 4, the STOP-IT task consisted of a practice phase of 32 trials and an experimental phase of three blocks of 64 trials.

Participants were presented with a series of 'go' trials as white left and right arrows on a standard computer screen. Participants were instructed to respond as quickly as possible by pressing the arrow key that corresponded to the direction of the arrow that appeared on the screen. The stimulus remained on the screen until the participant had responded or until maximum duration of 1250ms. Inter-trial intervals were set at 2000ms. On 'stop-signal' trials, the stop-signal — a white arrow turning blue — appeared after a variable stop-signal duration (SSD); initially set at 250ms. The SSD was changed based on a staircase tracking procedure. When inhibition was successful, i.e. participants did not press the arrow key, the delay between the primary-task stimulus and the stop signal (SS) increased by 50msec; when inhibition was unsuccessful, SSD decreased by 50msec. Participants received feedback on their performance during 10s intervals between blocks as the number of incorrect responses on no-signal trials, the number of missed responses on go-signal trials, the mean reaction time on no-signal trials and the percentage of correctly suppressed responses. All results were written in a data file and analysed using a supporting program, ANALYSE-IT (Verbruggen et al., 2008). Stop-signal-RTs (SSRTs) were calculated as the mean SSD minus the mean no-signal reaction time (Logan et al., 1997).

Observe or bet Task:In Experiment 4, we used the 'Observe or Bet' task to assess participants' reflection impulsivity in the context of an information-sampling explore/exploit paradigm (Navarro, Newell, & Schulze, 2016; Tversky & Edwards, 1966). The game involved a 'blox machine', one red and one blue. On each of 50 trials, one light was illuminated. Participants were informed that the blox machine was biased toward illuminating one coloured light (red or blue) but that this bias may change. On each trial, participants select between three actions: 'Observe', 'Guess Red' or 'Guess Blue'. If participants selected 'Observe', they saw which light was illuminated on that trial. However, they did not receive any points. If participants selected 'Guess Red' or 'Guess Blue', they received one point if correct and lost one point if incorrect, but were not informed of the point and errors until the end of the 50 trials. All participants played the same five games (250 trials), taken from version 3 of Navarro et al.’s (2016) task. Responses on each trial were recorded and used to compute measures of information or reward-generating behaviour.

The 'decision-threshold' used in the main-text was tested as a proxy for the amount of information each participant required before making a guess as to the bias of the blox machine. As per Navarro et al. (2016), the decision-threshold was calculated by taking the absolute-value difference between the number of blue and red lights the participant witnessed prior to making their first guess. For example, if the participants started by observing six trials before guessing on the seventh, and witnessed 4 blues and 2 reds, then their decision-threshold would be 2 (|4-2|).

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