Voting for Pareto optimality: a multidimensional analysis

We compare unanimity rule and majority rule in their abilities to produce Pareto superior and Pareto optimal alternatives in fixed number of rounds of voting using a two-dimensional spatial voting model with random proposals, sincere proposals, and strategic proposals. Our findings show that for random or sincere proposals, majority rule is at least as likely to select a Pareto optimal outcome as unanimity rule. For strategic proposals, the subgame perfect equilibrium under unanimity rule is Pareto optimal. For other k-majority rules, the outcome is Pareto optimal or very close to it. For outcomes that are both Pareto optimal and Pareto superior, unanimity rule outperforms majority rule.     

Veto games: Spatial committees under unanimity rule

There exists a large literature on two-person bargaining games and distribution games (or divide-the-dollar games) under simple majority rule, where in equilibrium a minimal winning coalition takes full advantage over everyone else. Here we extend the study to an n-person veto game where players take turns proposing policies in an n-dimensional policy space and everybody has a veto over changes in the status quo. Briefly, we find a Nash equilibrium where the initial proposer offers a policy in the intersection of the Pareto optimal set and the Pareto superior set that gives everyone their continuation values, and punishments are never implemented. Comparing the equilibrium outcomes under two different agendas – sequential recognition and random recognition – we find that there are advantages generated by the order of proposal under the sequential recognition rule. We also provide some conditions under which the players will prefer to rotate proposals rather than allow any specific policy to prevail indefinitely.     

Institutional Arrangements and Logrolling: Evidence from the European Union

This article illustrates how voting rules used to pass a piece of legislation and the structure of the legislation, in terms of whether or not it has single or multiple issue dimensions, influence the frequency and the purpose of position changes in legislative negotiations. Through analysis of data on a set of legislative proposals negotiated in the European Union, I show that position changes are less common under unanimity rule than under majority rule. More importantly, I argue and show that when the negotiated legislation is multidimensional (i.e., contains multiple issues) and the voting rule is unanimity, position changing is a lucrative strategy for legislators. Multidimensional legislation creates opportunities for logrolling, and legislators’ veto power under the unanimity rule enables them to exploit these opportunities. Accordingly, under this scenario, legislators often engage in what I call a within‐legislation logroll and secure favorable legislative outcomes.     

Decision costs in legislative bargaining: an experimental analysis

We conduct an experiment to assess the effects of different decision rules on the costs of decision making in a multilateral bargaining situation. Specifically, we compare the amount of costly delay observed in an experimental bargaining game under majority and unanimity rule. Our main finding is that individual subjects are more likely to reject offers under unanimity rule. This higher rejection rate, as well as the requirement that all subjects agree, leads to more costly delay. This result provides empirical support for a classic argument in favor of less-than-unanimity decision rules put forth by Buchanan and Tullock (The calculus of consent: logical foundations of constitutional democracy, University of Michigan Press, Ann Arbor, 1962).     

The robustness of the optimal weighted majority rule to probability distortion

This study identifies the optimal collective decision rule in a dichotomous symmetric setting, allowing for probabilities distortion as originally assumed by Tversky and Kahneman (Journal of Risk and Uncertainty 5(4):297–323, 1992). We show that previous results that identified the weighted majority rule as the optimal one, and did not consider subjective probabilities, are robust to such distortion in the sense that neither the rule nor the weights are changed.     

Legislative bargaining with costly communication

We investigate the effects of voting rules on delay in a multilateral bargaining experiment with costly communication. Our design is based on a variant of the Baron–Ferejohn framework. Communication takes place after a proposer is selected and before a proposal is made. In contrast to prior experiments, communication is directly associated with costs in our setup. Specifically, every second of communication increases the probability that the game is terminated before a proposal can be made. In case of ‘breakdown’, each player receives an exogenously fixed disagreement value. Those values sum up to less than the amount of the available surplus, implying that delay owing to communication is costly. We vary the decision rule (majority versus unanimity) as well as the distribution of disagreement values (symmetric or asymmetric). We find that unanimity rule leads to longer communication delays and more frequent breakdowns in asymmetric, but not in symmetric situations.

     

Committee choice and the core under supramajority rule: Results from simulation of majority choice in 2-dimensional space

While simple-majority choice by committees is generally unstable, supramajority rule has been demonstrated to yield nonempty sets of stable outcomes: outcomes in the core. This paper reports results of a computer simulation of majority choice by committees under supramajority rule. The object is to explore the transition from unstable to stable committee choice with increasing supramajority rules. The findings are that supramajority rule limits the instability of committee choice; that stable committee choice is no more predictable than unstable committee choice; and that an optimal supramajority rule can be specified which minimizes instability and maximizes the predictability of committee choice. In all of the results, simple-majority rule plays virtually no role.     

Majority rule outcomes and the choice of germaneness rules

Much work in the field spatial models has concerned the conditions under which majority rule is stable in a multi-dimensional policy space. Some have suggested that legislative practices such as germaneness rules (Shepsle, 1979; Denzau and Mackay, 1981, 1983; Krehbiel, 1987) and different types of agendas (Shepsle and Weingast, 1984; Banks, 1985; McKelvey, 1986) either induce stability or limit the set of possible outcomes. However, they do not consider how stable the choice of these rules may be. This paper shows how the choice of germaneness rules inherits the instability of the policy space. While the use of any particular germaneness rule limits the set of possible outcomes (Feld and Grofman, 1988), it is shown that the process of choosing these rules is unstable.     

The majority vote rule and runoff primaries in the United States

The major parties in the United States use primary elections to select party candidates for general elections. While most employ a simple plurality vote rule for this purpose, some states, primarily southern, employ a majority rule that requires a runoff between the top two vote recipients if no candidate receives a majority in the initial primary. Data on primaries for state Governor and U.S. Senator from 1980 to 2002 are used to examine contemporary concerns about runoffs. Included in the findings are (1) the problem that majority runoffs address – candidates being selected based on low levels of voter support is not a frequent outcome under the plurality rule; (2) the vast majority of selections is based on a majority of votes in a primary, regardless of whether a simple plurality or majority is required; and (3) runoff primaries are necessary in roughly one-third of the contested primaries held in the majority vote context, and in about one-third of them the primary leader loses the runoff.     

Unanimity and exposure in the EU Council of Ministers – or how the Dutch won and lost the ICTY debate

How are unanimity negotiations commonly settled in the EU Council of Ministers? Important contributions have been made to our understanding of the ‘consensual’ decision‐making dynamics in the Council, but most studies focus on explaining the sheer absence of votes in legislative decision making under the qualified majority rule. This study seeks to explain how vetoes are averted, or curtailed, in unanimity decision making. These unanimity negotiations are explained as attempts to induce or prevent high‐level exposure. The degree of exposure in turn depends on the degree of lower level contestation. A process tracing analysis of one prolonged debate is performed from the perspective of one Member State – the Netherlands – which played a very prominent obstructing role. By analysing when, why and where (at what level) the Dutch won or lost, one can come closer to understanding the dynamic interplay between the different Council levels.     

If you like the alternative vote (a.k.a. the instant runoff), then you ought to know about the Coombs rule

We consider four factors relevant to picking a voting rule to be used to select a single candidate from among a set of choices: (1) avoidance of Condorcet losers, (2) choice of Condorcet winners, (3) resistance to manipulability via strategic voting, (4) simplicity. However, we do not try to evaluate all voting rules that might be used to select a single alternative. Rather, our focus is restricted to a comparison between a rule which, under the name ‘instant runoff,’ has recently been pushed by electoral reformers in the US to replace plurality-based elections, and which has been advocated for use in plural societies as a means of mitigating ethnic conflict; and another similar rule, the ‘Coombs rule.’ In both rules, voters are required to rank order candidates. Using the instant runoff, the candidate with the fewest first place votes is eliminated; while under the Coombs rule, the candidate with the most last place votes is eliminated. The instant runoff is familiar to electoral system specialists under the name ‘alternative vote’ (i.e., the single transferable vote restricted to choice of a single candidate). The Coombs rule has gone virtually unmentioned in the electoral systems literature (see, however, Chamberlin et al., 1984). Rather than considering the properties of these two rules in the abstract, we evaluate them in the politically realistic situations where voters are posited to have (at least on balance) single-peaked preferences over alternatives. Evaluating the two rules under this assumption, we argue that the Coombs rule is directly comparable in that Coombs is always as good as AV with respect to two of our four criteria and it is clearly superior to AV with respect to one of the four criteria, namely criterion (2), and is potentially inferior only with respect to criterion (3). Key to this argument are two new propositions. The first new result shows that, under the posited assumption, for four alternatives or fewer, AV is always as likely or more likely to select the Condorcet winner than plurality. The second new result shows that, under the same assumptions, the Coombs rule will always select the Condorcet winner regardless of the number of alternatives.     

The fairness of discounting: A majority rule approach

A model of majority rule is developed in which each of a finite number of generations votes on a redistribution of income between itself and the other generations. In voting, each generation expresses tastes for its own income and for the distribution of income across generations. The model is then used to derive the conditions under which discounting is justified — namely those conditions for which the majority rule exhibits a positive marginal rate of time preference. It is demonstrated that when each generation is wealthier than those preceding it, the parameters representing the taste for income equality must be relatively high for the majority rule to exhibit a positive marginal rate of time preference.     

Majority rule and the public provision of a private good

This paper extends the literature on the socialization of commodities by developing a model of voting over the public provision of a private good: health care. The private use of health care is modeled as a supplement rather than as an exclusive alternative to public health care. A majority rule equilibrium is shown to exist. The equilibrium characterization is an example of Director's Law of Income Redistribution. A ban on private health care activities is shown to be opposed by a majority of voters. Implications for the size and distribution of private health care expenditures are drawn.     

Probability calculations for transitivity of simple majority rule with anonymous voters

Let P(n, 4) denote the probability that there is a pairwise simple majority rule winner on four candidates with n voters under the impartial anonymous culture condition. Similarly, let P^t(n, 4) denote the probability that the complete ranking obtained by pairwise simple majority voting on four candidates with n voters is transitive under the impartial anonymous culture condition. We obtain representations for P(n, 4) and P^t(n, 4), and computed values for each for odd n with 3 n 19.This research was supported through a fellowship from the Center for Advanced Study, University of Delaware.     

The effect of membership rules and voting schemes on the success of international climate agreements

We empirically test the role of membership rules and voting schemes for climate change coalitions with the STAbility of COalitions model (STACO). The model comprises twelve world regions and captures long-run effects of greenhouse gas accumulation. We apply three stability concepts that capture the notion of open membership and exclusive membership with majority and unanimity voting. We show that exclusive membership leads to superior outcomes than open membership and that unanimity voting is preferable to majority voting in welfare and environmental terms. Our results suggest restricting membership in future international environmental agreements and they provide a rationale for unanimity voting as applied in many international organizations.     

Rule omission,rule migration and the limits of financial industry power

This paper seeks to deepen our understanding of financial industry lobbying efforts that result in specific regulatory rules being dropped from the regulatory agenda, or what we call ‘rule omission’. Critically, existing research either ignores rule omission or characterizes it as the pinnacle of lobbying success. We argue that only in carefully mapping out industry preferences and tracking what happens to rules following their omission can we say something about the extent to which finance wins or loses in its effort to shape regulation. Our analysis is based on two in-depth case studies from the European Union: (1) solvency rules in the Institutions for Occupational Retirement Provision Directive (IORPP II), where rule omission does reflect a strong case of industry influence; and (2) short selling rules in the Alternative Investment Fund Managers Directive (AIFMD), a case of rule omission resulting in more stringent rules over industry activities.     

What happens when majority rule breaks down?

Computational results of Niemi and Weisberg are extended to investigate the number of alternatives in the top cycle set (possible winning alternatives in a sequence of pairwise votes) when there is no Condorcet winner. With n alternatives we assume a large number of voters each equally likely to select any of the n! preference orderings. If no Condorcet winner exists, the number of members of the top cycle set is always more likely to be n or n?1 than between 3 and n?2 inclusive. As n grows the probability that all alternatives are in the top cycle set approaches 1.     

Inferiority of restricted majority decision rules

The case in which a group of decision makers appoints a committee to choose between two symmetrical alternatives by a simple majority vote, namely restricted majority decision rule, is one member of the set of weighted majority decision rules. It is shown that for any group of decision makers one of the restricted majority decision rules is always the worst of all weighted majority decision rules. This inferiority exists both in terms of the efficiency and in terms of effectiveness of the decision rule. The importance of this finding should be kept in mind when deciding the size of the committee because a seemingly irrelevant change in the number of decision makers may result in the inferior rule, instead of the optimal rule, being used. Moreover, because of the widespread use of restricted majority decision rules and the relatively small number of such rules, the probability of the inferior rule being used is relatively high.     

A Conditional Defense of Plurality Rule: Generalizing May's Theorem in a Restricted Informational Environment

May's theorem famously shows that, in social decisions between two options, simple majority rule uniquely satisfies four appealing conditions. Although this result is often cited in support of majority rule, it has never been extended beyond decisions based on pairwise comparisons of options. We generalize May's theorem to many-option decisions where voters each cast one vote. Surprisingly, plurality rule uniquely satisfies May's conditions. This suggests a conditional defense of plurality rule: If a society's balloting procedure collects only a single vote from each voter, then plurality rule is the uniquely compelling electoral procedure. To illustrate the conditional nature of this claim, we also identify a richer informational environment in which approval voting, not plurality rule, is supported by a May-style argument.     

The political economy of voluntary public service

We characterize the voluntary public service policy that minimizes the expected cost of delivering a public service (e.g., jury or military service). We then examine whether a majority rule voting procedure will implement the voluntary public service policy (VPS) whenever it entails lower expected cost than mandatory public service (MPS). We find that majority rule often favors MPS in the sense that majority rule implements MPS when VPS would secure the requisite public service at lower expected cost.