Cambridge Handbook of Experimental Political Science

Chapter 25 Legislative Voting and Cycling

Discoveries regarding the scope and meaning of majority rule instability have informed debate about the most fundamental questions concerning the viability of democracy. Are popular majorities the means of serving the public interest or a manifestation of the absence of equilibrium (Riker 1982)? Should majority rule legislatures be suspect or even avoided in favor of court decisions and bureaucratic delegation? Are the machinations of agenda setters the true source of what we take to be the legislative expression of majority rule? Are rules themselves subject to the vagaries of shifting majority coalitions (McKelvey and Ordeshook 1984)?

These and other questions were raised as a result of explorations in Arrovian social choice theory, which visualized group decisions as being the product of individual preferences and group decision rules such as majority rule. The biggest challenge to the research agenda was majority rule instability. In general, majority rule may not be able to produce a majority rule winner (an outcome that beats every other in a two-way vote). Rather, every possible outcome could lose to something preferred by some majority coalition. McKelvey (1976) showed that the potential for instability was profound, not epiphenomenal. A population of voters with known preferences might easily choose any outcome, or different outcomes at different times. If this were true, then how could scholars predict the outcome of a seemingly arbitrary and unconstrained majority rule institution, even with perfect knowledge of preferences? Was literally anything possible?

Limitations of Field Work on Legislative Instability

Political scientists tried to use legislative data to answer fundamental questions about the scope and meaning of majority rule instability. Riker (1986) uses historical examples to illustrate the potential for majority rule instability. A favorite case was the 1956 House debate on federal aid to education. Despite the fact that the majority party was prepared to pass the original bill over the status quo, Republicans and northern Democrats preferred the bill with the Powell Amendment, which would send no aid to segregated schools. Once amended, a third majority (southern Democrats and Republicans) preferred no bill at all. This seemed to be a graphic example of cyclic instability because some majority was ready to vote down any of the three alternatives (original bill, Powell Amendment, status quo) in favor of a different outcome. The outcomes “cycled,” and none of the three outcomes seemed to have a privileged position in terms of legitimacy, manipulability, or likelihood. The determinant of the final outcome seemed to have more to do with manipulation of the agenda than anything else.

Nevertheless, this case and others like it were open to debate. Riker (1986) made assumptions about the preferences of the legislators that were open to different interpretations. Wilkerson (1999) believed that the possibility of instability as manifested by “killer amendments” was minimal. In general, political scientists could only guess about the connection between voting behavior and the underlying preferences of legislators. Without a way to measure the independent variables (preferences and rules) or the dependent variables (legislative outcomes), rational actor models seemed singularly handicapped.

Of course, the effect of a shift in preferences or rules change might offer a “natural experiment” on the effect of such a change on policy outcomes, but usually such historic changes were hopelessly confounded with other historical trends that might affect the outcome. Were the 1961 rule changes governing the House Rules Committee responsible for the liberal legislation of the next decade or the manifestation of a change in preferences that would have brought that legislation into being in any case? Was the Republican ascendancy of 1994 the cause of welfare reform or the vehicle for public pressure that would have brought welfare reform about in any case? Research on readily observable features of legislatures – partisanship, committee composition, constituency, etc. – led to “ambiguous and debated correlations” (Druckman et al. 2006, 629). Experimental research offered the prospect of nailing down the causation that was inevitably obscured by field data.

Early Spatial Experiments: Fiorina and Plott

It did not take long after the emergence of early rational choice models of legislative decision making for the advantages of experiments to become apparent. Fiorina and Plott (1978) set out to assess McKelvey's (1976) demonstration that voting in two dimensions could cycle to virtually any point in the space. “McKelvey's result induces an interesting either–or hypothesis: ‘if equilibrium exists, then equilibrium occurs; if not, then chaos’” (Fiorina and Plott 1978, 590). In setting out to examine this hypothesis, Fiorina and Plott were the precursors of an experimental research agenda assessing the predictability of majority rule.

In addressing this question, Fiorina and Plott (1978) created what became the canonical design for majority rule experiments. They used students as subjects, presenting them with two-dimensional sets of possible decision “outcomes” – the crucial dependent variable. The dimensions were presented in an abstract way intended to render them neutral of policy or personal preferences.

The two dimensions were salient only for their financial compensation; the students saw payoff charts showing concentric circles around their highest-paying “ideal point.” One student might receive a higher payoff in the upper right-hand corner, whereas others would prefer other areas in the space. The students were quite motivated by the payoffs, a fact that gave the experimenters control over the key independent variable – preferences.

The experimenter deliberately presented a passive, neutral face while reading instructions that incorporated a carefully specified regime of rules, determining exactly how a majority of voters could proceed to enact a policy change or to adjourn. They were recognized one at a time to make proposals, and each proposal was voted on against the most recent winning proposal. They could discuss alternatives and seek supporters for particular proposals. Subjects had few constraints beyond a prohibition against side payments and (famously) “no physical threats.” This procedure provided rigorous control over both preferences and rules.

However, did the students behave in a way that could generalize to real legislature – and was it important if they did not? As Fiorina and Plott (1978) put it, “What makes us believe […] that we can use college students to simulate the behavior of Congress members? Nothing” (576). They made no claims about the generalizability of the results, but they did make claims about the implications of the outcomes for theory. “[I]f a given model does not predict well relative to others under a specified set of conditions [designed to satisfy the specifications of the theory], why should it receive preferential treatment as an explanation of non-laboratory behavior…” (576)?

Fiorina and Plott (1978) designed two experimental settings: one with an equilibrium and one without. The equilibrium concept of interest was the majority rule equilibrium or core – an alternative that could defeat, in a two-way vote, any other alternative in the space. The core existed as a result of specially balanced preferences by the voters – the core was the ideal point of one voter, and the other pairs of voters had delicately opposing preferences on either side of the core. The Fiorina-Plott results provided significant support for the predictive power of the core, when it existed. Outcomes chosen by majority rule clustered close to the core. This conclusion was supported by subsequent experiments (McKelvey and Ordeshook 1984). Wilson (2008a, 875) analyzed experimental decision trajectories demonstrating the attractive power of the core. Majorities consistently proposed new alternatives that moved the group choice toward the core.

The other treatment did not satisfy the fragile requirements for a core (Figure 25.1). For example, player 1's ideal point, although a centrist outcome, could be defeated by a coalition of players 3, 4, and 5 preferring a move to the Northeast. The other treatment thus provided the crucial test of what would happen when anything could happen.¹

Figure 25.1. Outcomes of Majority Rule Experiments without a Core

Source: Fiorina and Plott (1978)

However, Fiorina and Plott's (1978) noncore experiments showed a great deal more “clustering” than could have been expected, given McKelvey's (1976) result (Figure 25.1). The variance in the outcomes was greater without a core than it was with a core – but the differences were not as striking as they had expected. They concluded, “The pattern of experimental findings does not explode, a fact which makes us wonder whether some unidentified theory is waiting to be discovered and tested” (Fiorina and Plott 1978, 590).

Fiorina-Plott's (1978) invitation to theorize on the apparent constraint of noncore majority rule was taken up promptly by at least two schools of thought. One school held that subjects acting on their preferences in reasonable ways produced constrained, centrist results – corelike, even without a core. The other school emphasized that institutional structure and modifications of majority rule generated the predictable constraint on majority rule. The first school examined hypotheses about the effects of preferences changes (holding rules constant), and the second, the effects of rule changes (holding preferences constant). Experimenters could randomly assign subjects to legislative settings that varied by a tweak of the rules or a tweak of the preferences, allowing conclusions about causation that were impossible with natural legislative data.

1. Institutional Constraints on Majority Rule Instability

The behavioral revolution of the 1950s and 1960s consciously minimized the importance of formal rules in social interaction. In light of that, probably the most innovative and far-reaching idea that came out of Arrovian social choice was neoinstitutionalism – the claim that rules can have an independent and sometimes counterintuitive effect on legislative outcomes.

Once again, natural legislative settings did not supply much definitive evidence one way or the other. Even if scholars could point to a significant rule change – for example, the change in the Senate cloture rule in 1975 – and even if that change coincided with a change in the pattern of legislation, it was impossible to sort out whether the rule change was causal, spurious, or incidental to the policy change. One research agenda that followed from Arrovian social choice was to examine the effect of rules themselves, while holding preferences constant.

Procedural Rules: Structure-Induced Equilibrium

The institutional approach was kicked off by Shepsle (1979), who initiated a florescence of theory about institutions as constraints on majority rule instability. For example, Shepsle argues that germaneness rules, which limited voting to one dimension at a time, would induce a structure-induced equilibrium located at the issue-by-issue median.

McKelvey and Ordeshook (1984) ran experiments showing that issue-by-issue voting does not seem to constrain outcomes to the proposed structure-induced equilibrium, as long as subjects can communicate openly. In Figure 25.2, player 5 is the median voter in the X dimension, as is player 4 in the Y dimension. The results indicate a good deal of logrolling, for instance, by the 1, 2, and 5 coalition, that pulls outcomes away from the structure-induced equilibrium. They conclude that theorists who “seek to uncover the effects of procedural rules and institutional constraints must take cognizance of incentives and opportunities for people to disregard those rules and constraints” (201). The germaneness rule does not seem a sturdy source of majority rule stability.

Figure 25.2. Majority Rule with Issue-by-Issue Voting

Source: McKelvey and Ordeshook (1984)

Forward and Backward Agendas

Wilson (1986, 2008b) ran experiments on a different procedural variation – forward-moving agendas versus backward-moving agendas. A forward-moving agenda considers the first proposal against the status quo, the second alternative against the winner of the first vote, and so on. Each new proposal is voted on against the most recent winner. Presumably, the first successful proposal will be in the winset of the status quo, where the winset of X is the set of alternatives that defeat X by majority rule. A core has an empty winset, but when there is no core, every alternative has a nonempty winset. The winset of the status quo is the propeller-shaped figure shown in Figure 25.3.

Figure 25.3. Effect of Backward and Forward Agendas

Source: Wilson (2008b)

An alternative is a backward-moving agenda, in which alternatives are voted on in backward order from the order in which they were proposed. If alternatives 1, 2, and 3 are proposed in that order, then the first vote is between 2 and 3, with the winner against 1, and the winner of that against the status quo. With this agenda, the final outcome should be either the status quo or an alternative in the winset of the status quo. Theoretically, a backward-moving agenda is more constrained – more predictable – than a forward-moving agenda.

Figure 25.3 shows one typical voting trajectory for each treatment. The soft gray line shows a typical forward-moving agenda. The first proposal was in the winset of the status quo, backed by voters 2, 3, and 4. Subsequent moves were supported by coalitions 3, 4, and 5; then 1, 2, and 5; and then 2, 3, and 4 to restore the first successful proposal and complete a cycle. A forward-moving agenda did nothing to constrain majority rule instability.

The dark line shows that the first alternative introduced was not in the winset of the status quo, so the final vote resulted in the imposition of the status quo. This could have been avoided with strategic voting by player 5 on the penultimate step, leaving the committee with an outcome closer to 5's ideal point than the status quo.

Overall, Wilson (2008b, 886) reports that eight of twelve experiments run with the backward-moving agenda treatment were at the initial status quo, and the other four trials were in the winset of the status quo. This contrasted sharply with the forward-moving agenda, which never ended at the original status quo and frequently cycled through the policy space.

The conclusion is that forward-moving agendas do not constrain majority rule instability or provide the leverage necessary for accurate prediction. However, the backward-moving agenda is an institution that does effectively constrain majority rule.

Monopoly Agenda Control

In simple majority rule, every majority coalition has the power and motivation to move an outcome from outside its Pareto-preferred set to some point inside. No point outside the Pareto set of every majority coalition can be in equilibrium. When the Plott symmetry conditions hold, a single internal voter's ideal point is included in every majority coalition's Pareto set. Because there is no point that is internal to the Pareto sets of all decisive coalitions, there is no core. Instability is the result of too many decisive majority coalitions.

The rules can create stability by mandating that some majority coalitions are not decisive. For example, the rules may specify that every proposal to be considered must be approved by a single actor – the agenda monopolist. In other words, every majority coalition that does not include the agenda monopolist is not decisive.

This greatly reduces the number of decisive majority coalitions. In particular, the intersection of the Pareto sets for all decisive coalitions is guaranteed to include only one point – the agenda setter's ideal point. As a result, the core of a game with an agenda monopolist necessarily includes the agenda setter's ideal point.

To test the effect of this institutional feature on majority rule instability, Wilson (2008b) ran experiments with constant preferences and no simple majority rule core. In one treatment, there was an open agenda, and in the other, a monopoly agenda setter. In this latter case, the agenda setter's ideal point was the unique core. Wilson showed that the outcomes in the open agenda had high variance; the outcomes with an agenda setter had lower variance and were significantly biased toward the agenda setter's ideal point.

Figure 25.4 shows the trajectory for a typical agenda setter experiment. The agenda setter, player 5, consistently plays off the coalition with 1 and 2 against the coalition with 3 and 4. The power to do so means, of course, that majority rule instability can be replaced by coherence – at the cost of making one player a dictator.

Figure 25.4. Effect of Monopoly Agenda Setting

Source: Wilson (2008b)

2. Preference-Based Constraints on Majority Rule Instability

Shepsle's (1979) original hypothesis – that institutional variations of majority rule can sharply constrain majority rule instability and allow prediction of experimental outcomes – has proven both true and of the utmost significance for studying democracy. Rules defining control over the agenda, the size of the majority, or bicameralism have all been shown to lead to an improvement in prediction accuracy.

However, the patterning of outcomes in simple majority rule experiments, as illustrated in Figure 25.1, reveals that institutional rules are a sufficient, but not necessary, condition for constraint. Experimental outcomes cluster with simple majority rule – even without monopoly agenda control, germaneness rules, or a backward-moving agenda.

Despite the fact that McKelvey (1976) was the author of what came to be known as the “chaos” theorem, he himself was an early advocate of finding a preference-based solution concept. That is, he believed that the actions of rational voters, negotiating alternative majority coalitions to advance their own preferences, would somehow constrain majority rule to a reasonable subset of the entire policy space – without requiring the constraint of rules other than simple majority rule. McKelvey, Ordeshook, and Winer (1978) advanced the solution concept known as the “competitive solution” for simple majority rule games. By understanding coalition formation as a kind of market that established the appropriate “price” for coalitional pivots, McKelvey et al. generated predictions that worked rather well for five-person spatial games. However, the authors gave up on the competitive solution when other experimental results, using discrete alternatives, proved to be sensitive to cardinal payoffs (McKelvey and Ordeshook 1983).

The Uncovered Set

An alternative preference-based solution concept was the uncovered set, developed in the context of discrete alternatives by Miller (1980). It is a solution concept that identifies a set of moderate outcomes in the “center” of the space of ideal points as the likely outcome of strategic voting and the coalition formation process.

Outcomes that are far from the “center” of the ideal points are certain to be covered, where a covered alternative B is one such that there is some alternative A that beats B, and every alternative X that beats A also beats B. If A covers B, then it implies that B is a relatively unattractive alternative with a large enough winset to encompass the winset of A.²

An alternative is in the uncovered set if it is not covered by any other alternative. If D is uncovered, then, for every C that beats D, then there is some alternative X such that D beats X and X beats C. This means that an uncovered alternative can either defeat every other alternative directly or via an intermediate alternative. The uncovered set is the set of centrist outcomes that constitute the (unstable) center of the policy space.

Early theoretical results showed that the uncovered set had several striking characteristics. For one thing, the uncovered set was shown to be a subset of the Pareto set. For another, it shrank in size as preference profiles approximated those producing a core, and it collapsed to the core when the core existed (Cox 1987).

The uncovered set has proven to be of interest to both noncooperative game theory and cooperative game theory. The reason is that, as McKelvey (1986) argues, the uncovered set contains the noncooperative equilibria arising under a variety of institutional rules.

Shepsle and Weingast (1984) propose that “the main conclusion is that institutional arrangements, specifically mechanisms of agenda construction, impose constraints on majority outcomes” (49). McKelvey (1986) took away a quite different interpretation. In an article provocatively titled “Covering, Dominance and Institution-Free Properties of Social Choice,” McKelvey (1986) argues that if a single solution concept encompasses the equilibrium results of a variety of institutions, then the choice process is “institution free.” That is, “the actual social choice may be rather insensitive to the choice of institutional rules” (McKelvey 1986, 283).

In the article, McKelvey (1986) demonstrates that various distinct institutions theoretically lead to equilibrium outcomes inside the uncovered set. He confirmed the result that legislative voting under a known, fixed agenda should lead inside the uncovered set. Cooperative coalition formation should lead to outcomes in the uncovered set, as should two-candidate elections. Hence, McKelvey could argue, constraint on simple majority rule instability seemed to be “institution-free” – the ideal points of voters provide enough information to predict where outcomes should end up, even without knowing exactly which of the three institutions would be used to select the outcome.

The problem was that neither McKelvey nor anyone else knew exactly how much the uncovered set constrained majority rule decision making because no one had a way to characterize the uncovered set for a given set of preferences.

Looking Backward with the Uncovered Set

The recent invention of an algorithm for precise estimation of the uncovered set (Bianco, Jeliazkov, and Sened 2004) has allowed the testing of that solution concept against previously reported experimental results (Bianco et al. 2006) and with new data (Bianco et al. 2008). Figure 25.1 is a case in point because it shows the Fiorina-Plott (1978) noncore experiments. The uncovered set for their experimental configuration of preferences is shown as the small shaded region. In Figure 25.1, the uncovered set is a relatively precise and promising predictor of the noncore experiments. The same is true for the uncovered set shown (as a gray shaded region) for the McKelvey-Ordeshook experiments on germaneness and communication – nearly all outcomes were in the uncovered set (Figure 25.2). For the McKelvey-Ordeshook experiments, with different proposal rules and different degrees of constraint on communication, the uncovered set performs equally well.

We can do the same with other majority rule experiments run in two-dimensional policy space with simple majority rule. The results for a series of simple majority rule experiments are shown in Table 25.1. Out of 272 total majority rule experiments administered by eight different teams of experimentalists, ninety-three percent were in the uncovered set.

Table 25.1. Testing the Uncovered Set with Previous Majority Rule Experiments

Source: Bianco et al. (2006).

Testing the Uncovered Set

Although the results in Table 25.1 are noteworthy, the experiments reported there were not designed to test the uncovered set. In particular, several of these experiments typically imposed maximal dispersion of ideal points, resulting in quite large uncovered sets – perhaps an “easy test” of the uncovered set. Consequently, Bianco et al. (2008) designed computer-mediated, five-person, majority rule experiments with two treatments creating relatively small and nonoverlapping uncovered sets – designed to be a difficult case for the uncovered case.

The two treatments were based on two configurations of preferences shown in Figures 25.5a and 25.5b. In each case, the preferences were “clustered” rather than maximally dispersed; this had the effect of producing smaller uncovered sets. Configurations 1 and 2 are identical except for the location of player 1's ideal point. In configuration 1, player 1 was clustered with players 4 and 5; in configuration 2, player 1 was in an even tighter majority cluster with players 2 and 3. The change in player 1's ideal point shifted the uncovered set dramatically.

The alternative hypothesis is what may be called the partisan hypothesis, based on the obvious clustering of ideal points. Poole and Rosenthal (1997), Bianco and Sened (2005), and others have estimated the preferences of real-world legislatures – finding that they are organized in two partisan clusters. So, the differences between the two configurations could be thought of as a shift of majority party control with a change in representation of district 1. The members of the majority cluster in either configuration could easily and quickly pick an alternative within the convex hull of their three ideal points and, resisting the attempts by the members of the minority cluster, vote to adjourn.

Figure 25.5. Sample Majority Rule Trajectory for Configuration 1

Source: Bianco et al. (2008), used with permission of The Society for Political Methodology.

It is worth noting that the uncovered set in this setting is primarily located between the Pareto sets for the majority and minority parties, and thus will only occur if there is a significant amount of cross-partisan coalition formation and no party solidarity. In other words, in configuration 1, if players 4 and 5 can offer player 3 an outcome that is more attractive than that offered by players 1 and 2, then the uncovered set has a chance of being realized. But if player 3, for example, refuses offers especially made to move him or her away from his or her “natural” allies, then the outcome should be well within the Pareto set of the partisan coalition, rather than in the uncovered set.

Figure 25.5a shows a sample committee trajectory for configuration 1. As can be seen, there was a great deal of majority rule instability. A variety of coalitions formed, including coalitions across clusters. However, the instability was constrained by the borders of the uncovered set. Despite frequent successful moves to outcomes close to the contract curve between players 1 and 3, players 4 and 5 were repeatedly able to pull the outcome modestly in their direction by offering player 3 more than player 1 had offered.

Configuration 2 is more difficult; any outcome in the Pareto set of the tight cluster of 1, 4, and 5 is very attractive to these three voters – making it hard for 2 and 3 to offer proposals that will break up the 1-4-5 coalition. Yet, even here, players 2 and 3 occasionally make proposals that attract support from members of the majority cluster. This tends to pull outcomes out of the 1-2-3 Pareto triangle toward the minority cluster. The result is cycling within the smaller uncovered set.

Twenty-eight experiments were done with each treatment. Figure 25.6a shows the final outcome in the twenty-eight configuration 1 experiments. The percentage of final outcomes in the uncovered set was 100 percent. Figure 25.6b shows the final outcomes in the twenty-eight configuration 2 experiments. In four committees, the outcome seemed to be influenced by fairness considerations.

Figure 25.6. (a) Uncovered Set and Outcomes for Configuration 1

(b) Uncovered Set and Outcomes for Configuration 2

Source: Bianco et al. (2008), used with permission of The Society for Political Methodology.

In seven of the committees, the opposite occurred – the partisan 1-4-5 coalition formed and imposed an outcome in their Pareto triangle but outside the uncovered set. In either case, the presence of an extremely tight cluster of three ideal points seemed to decrease the likelihood of the kind of multilateral coalition formation that could pull outcomes into the uncovered set. Overall, the proportion of configuration 2 outcomes in the uncovered set was still 60.7 percent.

Although fairness considerations or partisan solidarity can result in outcomes outside the uncovered set, it seems fair to say that, as long as the coalition formation process is cross-partisan and vigorous, the outcome will likely be within the uncovered set. Overall, the uncovered set experiments suggest that the majority rule coalition formation process does constrain outcomes, as argued by McKelvey (1986). Even more important, outcomes tend to converge to centrist, compromise outcomes.

3. Challenges and Opportunities for Further Research

Even though the past generation of majority rule experiments has largely tested either an institutional effect or preference-based effect on majority rule outcomes, the McKelvey (1986) hypothesis offers a research agenda that involves both institutions and preferences, both noncooperative and cooperative game theory.

The McKelvey Challenge: Endogenous Agendas in Legislatures

Since McKelvey (1986) wrote his article “Covering, Dominance and Institution-Free Properties of Social Choice,” scholarly research on legislative institutions has flowered, especially with the aid of noncooperative game theory (e.g., Baron and Ferejohn 1989). However, little of that research has served to respond to McKelvey's challenge to examine whether the equilibria of noncooperative games associated with particular institutional rules are in fact located in the uncovered set.

One institution McKelvey (1986) was interested in was that in which amendments are generated by an open amendment process from the floor, in the absence of complete information about how the amendments might be ordered or what additional motions might arise. The proposal stage would be followed by a voting stage in which all voters would know the agenda. Viewing this institution as an n-person, noncooperative game, the equilibrium should be contained in the uncovered set as long as voters vote sophisticatedly.

We know that voters sometimes make mistakes (i.e., fail to vote in a sophisticated manner) (Wilson 2008b). So, the outcome of such endogenous agenda institutions is an open question for experimental research. Given McKelvey's (1986) result, there are three logical possibilities: 1) outcomes will be at the noncooperative equilibrium (and therefore in the uncovered set); 2) outcomes will be in the uncovered set, but not at the noncooperative equilibrium; or 3) outcomes will be outside the uncovered set (and therefore not at the noncooperative equilibrium).

There is a large and established psychological literature on negotiation, touching on the effect of such factors as risk preferences, cognitive biases, trust, egalitarian norms, cultural considerations, and ethical considerations. Because implementation of majority rule ultimately boils down to negotiating majority coalitions, it is important to begin to incorporate insights from that literature into the design of majority rule experiments. For example, the core is a cooperative solution concept that assumes a contract enforcement mechanism, which is uniformly lacking in majority rule experiments. Why does the core work so well in experiments that uniformly lack any contract enforcement mechanism? One answer is suggested by Bottom, Eavey, and Miller (1996). In this experiment related to examining an institution of decentralized agenda control, getting to the core from some status quos required forming and then reneging on a coalition – actions that many subjects were unwilling to undertake. Groups were “constrained by a complicated set of social norms that prevents the frictionless coalition formation and dissolution assumed by cooperative game theory” (318). The net result is that informal social processes may substitute for formal contract enforcement, resulting in experimental support for cooperative solution concepts such as the core and the uncovered set.

Fairness and Other Nonordinal Considerations

The Fiorina-Plott (1978) experiments were designed in such a way that subject payoffs fell off very quickly from ideal points. As a result, there was no single outcome that would give three voters a significant payoff; at least one majority coalition voter had to vote for an outcome that yielded only pennies. And there was certainly no outcome that could provide a lucrative payoff for all five voters.

In one sense, this was a difficult test for the core. It proved a good predictor, even though it did not create a gleeful majority coalition. However, it also raised the question of whether the choice of the core was sensitive to changes in cardinal payoffs that left the ordinal payoffs unchanged. Eavey (1991) ran simple majority rule experiments with the same ordinal preferences as in Fiorina and Plott (1978), but Eavey constructed less steep payoff gradients for the voters to the west, creating a benign Rawlsian alternative to the east; that is, the point that maximized the payoff of the worst-paid voter lay east of the core and gave all five members of the committee a moderate payoff. Although the attraction of the core was still apparent (Grelak and Koford 1997), the new cardinal payoffs tended to pull outcomes in the direction of the fair point because participants in these face-to-face committees seemed to value outcomes supported by supermajorities, rather than a minimal winning coalition. Further research is needed to explore the sensitivity of computer-mediated experiments to cardinal payoffs. Understanding the degree of sensitivity to cardinal values is potentially important for evaluating our ability to control subjects' induced valuation of alternatives.

Figure 25.7. Senatorial Ideal Points and Proposed Amendments for Civil Rights Act of 1964

Source: Jeong et al. (2009)

One challenge facing students of majority rule has been persistently voiced since Fiorina and Plott (1978). Their defense of experiments was grounded in an acknowledged need for parallel experimental and field research: “we reject the suggestion that the laboratory can replace creative field researchers” (576). Since that time, parallelism in research has been advocated a good many more times than it has been attempted.

The recent development of techniques for estimating the spatial preferences of real-world legislators offers the prospect of parallel research using laboratory and real-world data. An ideal point estimation method called “agenda-constrained” estimation (Clinton and Meirowitz 2001; Jeong 2008) relies on the knowledge of the agenda and legislative records on roll call votes on amendments; with this information, they obtain estimates of both legislative preferences and the alternative outcomes legislators are voting on. This information is just what is needed to test the uncovered set with real legislative data.

For example, Figure 25.7 shows estimates of senators’ ideal points and a trajectory of winning outcomes using Senate voting on 109 roll call amendments for the Civil Rights Act of 1964. It also depicts the estimated uncovered set given the locations of the senators over the two key dimensions of the bill – scope and enforcement. The uncovered set lies between the cluster of ideal points of the strongest civil rights supporters and the strongest opponents. As in the laboratory experiments, the senators created a variety of cross-cluster coalitions; the civil rights opponents repeatedly tried to weaken the enforcement or limit the scope by picking off the weakest supporters in one dimension or the other (Jeong, Miller, and Sened 2009).

The coalitional negotiations in the Senate were much like that in experiments: new coalitions were formed to propose and vote on new amendments, and as these succeeded or failed, coalitional negotiations continued to generate yet more amendments. The administration bill, as modified by the House, was located in the uncovered set. An amendment to guarantee a trial by jury for those state and local officials found in contempt for their opposition to civil rights was popular enough to generate a majority coalition that moved the bill to location B to the left of the civil rights bill. A leadership substitute form of the bill was much stricter in enforcement at point C, but a weakening amendment protecting southern officials from double jeopardy brought the location of the bill back inside the uncovered set, where it remained despite a slight weakening of scope. The second to last vote pitted the administration bill as amended against the leadership substitute as amended; the final vote ran the leadership substitute against the perceived status quo. The final bill, located at E, was well within the uncovered set.

What does the date in Figure 25.7 suggest for an integrated research agenda involving both Senate data and experiments? One possibility is that preferences estimated from real-world legislators on actual legislation may be replicated in the laboratory; thus, a unique legislative history can potentially be repeated many times over. The debate on the civil rights bill can be replayed by inducing preferences similar to those of the senators to determine whether a similar outcome occurs. We can find out whether, given the preferences of legislators, the outcome was in some sense inevitable or whether a dispersion of final outcomes could have been the basis for alternative histories.

Modifications in real-world preferences can be examined to examine counterfactuals such as 1) what would have happened to this bill if Midwestern Republicans had been less supportive of the civil rights act? or 2) could the bill have been passed if Tennessee's senators had been more opposed?

The same preferences can be examined under different institutional rules to examine what might have occurred if the legislature had operated under a different set of rules. What if the Senate had used a different agenda procedure or had enacted the 1975 cloture reform before 1964?

4. Conclusion

Experimental research has to some extent substantiated the concern with majority rule instability. As Wilson (2008b) noted, given appropriate institutions, “voting cycles, rather than being rare events, are common” (887). Given an open, forward agenda and minimally diverse preferences, cycles can be readily observed.

Nevertheless, experiments have also shown that cycles are contained within the uncovered set and can be tamed by institutional rules and procedures. There is a place for more theoretical endeavors and further experimental research on ideological (spatial) decision making – both in the lab and in parallel fieldwork on questions generated by experimental research. Indeed, the results of majority rule experiments have both informed the political science debate about the meaning and limits of majority rule (McKelvey and Ordeshook 1990, 99–144) and guided theorists as they seek explanations for both the observed instabilities of majority rule and the observed constraints on that instability. If, as McKelvey (1986) hypothesized, a variety of institutional rules can only manipulate outcomes within the uncovered set, then the degree to which behind-the-scenes agenda setters can manipulate the outcome of majority rule processes is itself limited.

References

Baron, David, and John Ferejohn. 1989. “Bargaining in Legislatures.” American Political Science Review 83: 1181–206.

Bianco, William T., Ivan Jeliazkov, and Itai Sened. 2004. “The Uncovered Set and the Limits of Legislative Action.” Political Analysis 12: 256–76.

Bianco, William T., Michael S. Lynch, Gary J. Miller, and Itai Sened. 2006. “‘Theory Waiting To Be Discovered and Used’: A Reanalysis of Canonical Experiments on Majority Rule Decision-Making.” Journal of Politics 68: 837–50.

Bianco, William T., Michael S. Lynch, Gary Miller, and Itai Sened. 2008. “The Constrained Instability of Majority Rule: Experiments on the Robustness of the Uncovered Set.” Political Analysis 16: 115–37.