Chapter 93

STRUCTURE INDUCED EQUILIBRIUM IN SPATIAL COMMITTEEGAMES

RICK K. WILSON

Rice University

Political economists have long recognized that collective choice processes are inher-ently unstable. Work by Arrow (1963), Plott (1967) and McKelvey (1976) illustrate justhow sensitive collective choices are to the structure of preference. Absent distinct dis-tributions of preferences for decision makers, outcomes are predicted to be unpatterned.These findings led at least one social scientist to declare that political science, ratherthan economics, ought to assume the mantle of the “dismal science” because if politi-cal scientists cannot predict outcomes from common forms of democratic practice, thenpolitical science has little to offer (Riker, 1980).

This view first was challenged by Shepsle (1979) who claimed that while disequi-librium was the logical outcome of much social choice theorizing, disequilibrium inempirical settings was surprisingly rare. Decisions are often made in predictable ways.Shepsle argued that collective choices are seldom made under the minimal institutionalmechanisms proposed by social choice theory, but instead take place within a richerinstitutional structure. Institutional rules are viewed as producing a “structure inducedequilibrium” (SIE) in which preferences combined with institutions yield predictable,equilibrium outcomes.

The experimental results discussed here illustrate two examples of SIE. The firstdevelops a point raised by McKelvey (1976) in which a single individual is grantedmonopoly agenda power. This simple change to the ordinary rules leads to a uniqueequilibrium prediction where previously none existed. The second example reopensagenda setting to all members of the committee. However, instead of a forward movingagenda, in which any proposal can be brought against the current status quo, a backwardagenda process is used. In this process the status quo is voted last, with the sequenceof votes fully specified, the last proposal voted on first, and the first proposal is votednext-to-last. Some variant of this mechanism is common in many collective choice in-stitutions, including many legislatures.

1. Theoretical Basics

The basic notation for this discussion is in a previous entry (see the article entitled “En-dogenous Properties of Equilibrium and Disequilibrium in Spatial Committee Games”).It is important to note that sets of individually preferred alternatives can be charac-terized as Pi(x

o), which are those x ∈ X that the ith actor prefers to the status quo

Handbook of Experimental Economics Results, Volume 1Copyright © 2008 Elsevier B.V. All rights reservedDOI: 10.1016/S1574-0722(07)00093-5

Ch. 93: Structure Induced Equilibrium in Spatial Committee Games 881

under binary comparisons. Likewise, for a particular coalition Sj that is able to im-plement a choice, the set of preferred elements from the alternative space is given asP(xo) = ⋂

i∈SjPi(x

o). Those alternatives preferred to the status quo by all winningcoalitions is given as W(xo) = ⋃

Sj ∈S PSj(xo).

There are two distinct settings investigated here. The first is a social choice settingin which W(xo) �= ∅, ∀x ∈ X. This is the standard social choice problem in whichthere is no preference-induced equilibrium under a standard open agenda procedure.Suppose this procedure is changed such that a single individual, given by � ∈ N , whoseideal point is located at x� and who is the only actor allowed to bring amendments toa vote. Such a case implies that no alternative is called to a vote unless � prefers theamendment. This fundamentally changes the set of alternatives preferred by a coalition,requiring P(xo) = ⋂

i∈SjPi(x

o)⋂

P�(xo) such that the agenda setter is always a piv-

otal member of any winning coalition. With this qualification in mind at a minimumthis yields W(x�) = ∅ such that there exists a unique equilibrium at the agenda set-ter’s ideal point. In other words a simple, albeit important, change in the structural rulesyields stability where none previously existed.

In the second case suppose that an agenda must be announced and is voted backwards.First consider the usual case under a forward moving agenda with two steps. Supposethe agenda begins from the status quo, xo. At the first step it must be that x1 ∈ W(xo)

for the amendment to succeed. Depending on the specific x1, then the only constrainton the second element of the agenda is that x2 ∈ W(x1). Conceivably this could cover avery large portion of the alternative space. It may well be the case that xo ∈ W(x2). Insuch a case there is an intransitive social choice in which x1 defeats xo, x2 defeats x1,and finally xo defeats x2. Now consider the case where specific amendments must bechosen and the agenda is ordered backward (x2, x1, x

o), with x2 and x1 first paired andthe winner of that pairing voted against xo. At a minimum for x2 to win it must be thatx2 ∈ W(x1) ∪ W(xo) (see Shepsle and Weingast, 1984).

This places a powerful constraint on the choice of amendments – especially if theyare expected to win. Of course the strategic problems of what to select are compoundedby “sophisticated” choices and voting by actors (see McKelvey and Niemi, 1978). Re-gardless of the case this change in the agenda process results in a structure inducedequilibrium.

2. Experimental Design

The experimental design uses a computer-controlled setting in which 5 subjects arebrought together as a committee to make a decision. Each subject is assigned a differentideal point in a two-dimensional alternative space. That space is quite dense, made upof either 300 × 300 or 350 × 350 points, depending on the experimental design. Payoffsto subjects, for any point, are a non-linear decreasing function of distance from theirideal point. Sample indifference contours are provided for a subject and by moving apointer in the alternative space the computer provides an exact dollar value for any point

882 R.K. Wilson

in the space. The location of other subject’s ideal points are common knowledge, whileother’s payoffs are not.

In the baseline condition subjects are able to place a motion on the floor at any time.No motion is brought to a vote unless “seconded” by another. At that time the statusquo and the amendment are highlighted and subjects notified that a vote is forthcoming.After a 20 second delay subjects are transferred to a voting screen in which the statusquo and its value are posted against the same information for the amendment. Subjectsare then asked to vote for one or the other and their vote is cast privately. Once votingends the results are revealed. If the amendment gains at least three of five votes, it be-comes the new status quo, otherwise the status quo is retained. The committee processcontinues leaving all previous proposals on the floor and inviting subjects to make ad-ditional proposals. The committee ends its deliberations when a motion to adjourn isbrought to the floor and a majority votes to end the experiment. At that point subjectsearn the value of the current status quo (for detailed discussion of this procedure, seeHaney, Herzberg, and Wilson, 1992).

Two distinct manipulations are introduced to the baseline condition. Under the first,an Agenda Setter manipulation, any subject can put a proposal on the floor. The agendasetter, who is randomly assigned to that position, is granted exclusive power to bring analternative to a vote. The agenda setter is also given sole power to call a vote to adjourn.A simple majority is needed to either change the status quo or end the trial.

In the second manipulation, a Backward Voting Agenda, any subject may place pro-posals on the floor. Subjects are required to build a list of proposals over which they willvote in reverse order. A proposal requires a “second” to be added to the list and subjectsare given a fixed period of time to add proposals to the list. When the agenda build-ing period ends subjects vote, in reverse order, over pairs of alternatives. The winningalternative is that proposal receiving a majority at the last pairing.

3. Monopoly Agenda Setting

Outcomes from an open agenda baseline experiment and from a monopoly agenda setterexperiment are displayed in Figure 1. Actors’ ideal points are given in red. Under theagenda setting manipulation the subject at member 5’s position was always assigned tobe the agenda setter. Outcomes under this manipulation are given in blue. Outcomesunder the baseline condition are green. Two points are clear from the figure. First, eventhough the structure of preference remains the same for both experiments, the pattern ofoutcomes is quite different. Under the baseline condition outcomes are more scatteredin the alternative space and more centrally located. Outcomes under the agenda settercondition are more compact and they are anchored to the agenda setter’s ideal point.

Second, outcomes under the agenda setting manipulation do not all fall at the equilib-rium. Instead, outcomes range from the agenda setter’s ideal point to the central portionof the alternative space. At one level this might call into question the predictive capac-ity of this SIE concept. However, only focusing on a point prediction is misleading.

Ch. 93: Structure Induced Equilibrium in Spatial Committee Games 883

Figure 1. Outcomes from a 5-person spatial committee game under a baseline and an agenda setter condition.

Given the alternatives placed on the floor, 13 of the 21 final outcomes under the agendasetting manipulation were Condorcet winners; that is the outcome could have defeatedany other proposal that was placed on the floor in the trial. Moreover, the power to setthe agenda is extremely important.

Both points are illustrated by the agenda plotted in Figure 2. The figure details theideal points of the players, all of the proposals that were on the floor at the end of the trialand the agenda path chosen by the agenda setter. Interestingly, even though the agendasetter’s very first proposal was at the equilibrium (and made within 8 seconds of begin-ning the round), the agenda setter chose alternative (145, 73) as the first amendment tothe status quo. It handily defeated the status quo, (280, 280), via the coalition {1, 4, 5}and constituted the first agenda step. The second vote was over amendment (43, 152)

which won via the coalition {1, 2, 5}. By this point the agenda setter had enjoyed com-plete success and steadily moved the status quo closer to the equilibrium. The agendasetter misjudged with the third vote that she called. The proposed amendment, (49, 97),left members 4 and 5 better off, while 1, 2 and 3 were left worse off. That proposalwas defeated so the agenda setter brought the fourth vote on alternative (92, 62) whichimproved member 3 who joined with 4 and 5 to effect passage. Finally, on the fifth vote,alternative (50, 88) was brought forward and voted for by the coalition {1, 2, 5}. As isclear from the figure the agenda setter chose amendments that played off members 1

884 R.K. Wilson

Figure 2. Representative agenda path for an agenda setter experiment.

and 2 against members 3 and 4. In building the agenda the agenda setter did not have torely on her own proposals, but rather used alternatives placed on the floor by others.

Following the successful 5th vote the agenda setter called for adjournment. That votefailed 1-4, with only the agenda setter voting in favor. The agenda setter paused fora considerable amount of time studying the proposals on the floor. Building an agendaleading to her ideal point would have involved a series of minute steps. Instead of takingsuch action the agenda setter amended (50, 88) with itself and in this way signaled hercommitment to the status quo. Immediately afterward she proposed that the trial endand that vote was successful under a 4-1 vote.

4. Backward Voting Agenda

This experiment changes the form of the agenda. Figure 3 displays the outcomes forboth a forward moving agenda and a backward constructed agenda. Under the formerthere exists no equilibrium. Under the later there exist several equilibrium. If subjectsare assumed to be myopic (and the evidence supports this point) then the initial statusquo is one equilibrium. The others are those points contained in the petals on the figurewhich are those x ∈ W(xo) – or the proposals that can defeat the initial status quo.

Ch. 93: Structure Induced Equilibrium in Spatial Committee Games 885

Figure 3. Outcomes from a 5-person spatial committee game under a forward moving and a backward movingagenda condition.

Under a backward voting agenda mechanism, the penultimate winner is paired with thestatus quo. In this experiment, under both a forward and backward agenda, the initialstatus quo was placed at (129, 218).

Simply eye-balling the figure it is clear that this form of an agenda mechanism hasan important effect on outcomes. Fully 8 of 12 final outcomes were at the initial statusquo, while the remaining 4 were in the win set of that status quo. By comparison, out-comes under the forward voting mechanism are scattered across the alternative space.Although 7 of 12 outcomes fall in the win set of the initial status quo, it does not consti-tute a prediction for the forward moving agenda manipulation. Also striking is that nooutcomes appear at the initial status quo. The pattern of outcomes across the two ma-nipulations differs considerably and so too does the process by which outcomes wereselected.

To get a sense of how these different manipulations affected the voting process, twosample agenda are illustrated in Figure 4. In each case the arrows indicate the direc-tion of changes to the agenda. Each agenda “step” represents a majority agreeing to anamendment and is given by an arrow pointing from the previous winner. The processesare different in that the backward agenda mechanism ends with a vote over the statusquo, while the forward agenda mechanism begins with a vote over the status quo.

886 R.K. Wilson

Figure 4. Representative agenda paths for a forward moving and a backward moving agenda experiment.

Under the backward voting agenda process (given by the blue diamonds) the firstthree amendments had the property that any of them could have defeated the final out-come. This is easily seen because each was an element of the win set of the initial statusquo. On the fourth vote, an alternative outside of W(xo) won a majority. In this sequencethe myopic vote by member 5 came back to haunt him. On the fifth vote xo easily de-feated the fourth amendment and member 5 was left worse off than if he had votedstrategically. In doing so, member 5 would have voted against the fourth amendment(the move outside of the win set) anticipating that at the last vote the third amendmentwould have become the final outcome and he would have been left better off. Myopicvoting by subjects was common in these experimental trials and points to why outcomesso often ended up at the initial status quo, xo. Of course, strategic voting is only possi-ble when the agenda is completely known. While the full agenda was known under thisbackward voting process, subjects did not anticipate the consequences of their votes,picking when to strategically vote against their short-run interests in order to gain long-term benefits. Instead, this agenda process, combined with myopic voting, exercised apowerful constraint on outcomes.

By contrast the agenda under a forward moving process (given by the green circles)is common to these experimental trials. The first move is to a point in the win set of theinitial status quo. Subsequent amendments illustrate a property that occurred over 30

Ch. 93: Structure Induced Equilibrium in Spatial Committee Games 887

percent of the time in these experimental trials: subjects built an agenda incorporatinga voting cycle. While theorists commonly warn against the possibility of voting cyclesthey are seldom observed. This is largely a function of the types of agenda mechanismsused in natural settings (which often limit the number of amendments that can be posed).Here voting cycles, rather than being rare events, are common. This is especially thecase under an unconstrained forward agenda process in which earlier alternatives canbe revisited.

5. Conclusion

Preferences matter, but so too do institutions. Markets, auction mechanisms and politi-cal institutions all affect outcomes. For students of collective choice, minimal decisionmaking institutions provide a baseline by which we expect outcomes that best canbe characterized as chaotic. Such outcomes are rarely predictable and the processesby which they are selected are marked by voting cycles and drifting through the al-ternative space. More interesting for collective choice theorists are those mechanismsintroduced into a minimal institutional setting that in turn brings predictability to out-comes.

Almost all institutions charged with making collective choices are richly layered withrules. The United States House of Representatives is one of the more rule-bound insti-tutions that has been studied extensively and empirical scholars take for granted thatits outcomes will be predictable and patterned. However, disentangling which struc-tural features matter and when they matter remains a task for theorists. Experimentalistscontinue to offer examples as to when institutions matter. Recent work includes bar-gaining between multiple institutions by Bottom et al. (2000); levels of communicationby Endersby (1993); and the endogenous choice of allocation rules by Walker et al.(2000).

The experiments discussed here illustrate two distinct structural changes to an agendaand note the impact of a rules change for the pattern of outcomes. Changing the collec-tive choice mechanism so that a single individual controls the agenda does two things.First it results in predictions about which outcomes will be chosen. Second it has a pre-dictable effect on the distribution of resources – the agenda setter gains benefits to thedetriment of others. This happens even though everyone has an equal vote over out-comes. Changing the collective choice mechanism so that amendments are ordered andthe initial status quo is voted last also enables precise predictions about which outcomeswill be chosen.

Paying attention to institutional structure is important. Knowing which institutionalstructures matter and assessing their impact is an important part of building our socialscience knowledge. Experiments, working hand-in-hand with theory, provide a usefulmeans for testing and assessing institutional change.

888 R.K. Wilson

Acknowledgements

Support by the National Science Foundation (SES 87-21250) is gratefully acknowl-edged as is support by the Workshop in Political Theory and Policy Analysis at IndianaUniversity. Neither organization bears any responsibility for the content of this article.

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