The Evolution of Collective Choice Under Majority Rule

We have observed that some recent results cast serious doubts uponthe applicability of majority rule as a device for forming a group-willout of individual wills. On the other hand, majority rule has manyproperties to recommend it. Especially, the decisiveness propertyshould please anyone interested in efficiency considerations. How-ever, when it comes to the second major criterion, consistency, major-ity rule with pairwise comparison of alternatives often leads to diffi-culties. Indeed, we have seen that there is typically no core or Con-dorcet winner when the policy space is multidimensional real space.And when there is no core, the situation looks grim indeed for major-ity rule: literally any outcome may become the majority winner. Somerelief of this very strong result is provided by the fact that no majoritycycles can go through the outcomes that belong to the M2 bargainingset. This finding, of course, solves the problem facing majority rule onlyinsofar as a method can be devised by which the M2 bargaining set out-comes can be determined in a reliable way. Here, thus, we are con-fronted with the sincerity problem. The absence of the core can lead to chaotic trajectories of votingoutcomes in multidimensional space. However, there are ways of over-coming the difficulties if a sufficient amount of flexibility is allowedin institutional design. If we consider the various nonequilibrium solu-tion concepts, and the minimax set in particular, we can always designa decision rule which (under mild restrictions) makes the vote-maximiz-ing outcome trajectory enter the solution set. The flexibility needed isgreat, indeed: the decision rule, λ-majority, must be alterable for eachvoting situation. The determination of the winner in a pair-wise comparison of alter-natives is not the main source of the difficulties surrounding majorityrule. As a matter of fact, the method of building the agenda is the mostcrucial part of the problem of cyclical majorities. In multicandidatecontests the occurrence of cyclical majorities has motivated the studyof other.decision procedures in addition to the majority comparisonof alternatives. The most recent proposal, approval voting, is morestrategyproof than its competitors in the class of single-ballot, non-ranked voting systems. At the moment the relationships betweenapproval voting and majority rule are not clear. It seems that furtherstudy of the interrelationships of these procedures is called for. Thefeatures in which approval voting is superior to majority comparisonof pairs of alternatives, however, are not, strictly speaking, procedural,but are external to the method of making collective decisions.

We consider the elections of a seat-posted committee, and investigate the propensity of seat-wise majority voting to choose a committee that fulfills the majority will with respect to preferences over committees. Voters have seat-wise preferences and preferences over committees are derived from seat-wise preferences by means of a neutral preference extension. Neutrality means that the names of candidates do not play any role. The majority committee paradox refers to a situation where a Condorcet winner exists for each seat, and a Condorcet winner committee also exists but does not coincide with the combination of seat-wise Condorcet winners. The majority committee weak paradox refers to a situation where the combination of seat-wise Condorcet winners is not a Condorcet winner among committees. We characterize the domains of preference extensions immune to each of the paradoxes.

In Ruling Majorities and Reasoning Pluralities, Professor Saul Levmore explores the “division of labor” between the various thresholds of agreement required for collective action—supermajority, simple majority, or plurality rule. His particular emphasis is on the choice between the last two options. To improve our understanding of this choice in various settings, Professor Levmore considers the relationship between two well-known contributions to the study of group decisionmaking, namely, the Condorcet Jury Theorem and the Condorcet Criterion, which have not generally been treated together. This essay explores the relationship between these two insights in the context of judicial decisionmaking. Counterintuitively, the essay demonstrates that while the Condorcet Criterion continues to hold great promise as a tool of decision in en banc appellate courts, the Condorcet Jury Theorem is most appealing in judicial contexts that appear less collegial and thus less like a jury. In contexts in which jurists engage in deliberation and in which they anticipate that their outputs will have precedential effect, the Jury Theorem has little if any role to play. In contrast, the Theorem might prove more useful in evaluating low-level judicial outputs or decisions that otherwise are not expected to be treated as precedent. Thus, common law trial court decisions and civil law court decisions are more likely to be useful benchmarks in a Condorcet Jury Theorem analysis. It is because such courts do not anticipate that their decisions will have the force of precedent that they are more likely to be derived from governing legal texts, and thus more prone to characterizations of accuracy, than are judicial outputs that are driven by policy concerns and are generated with the understanding that they will be treated as precedent.

A sufficient condition is derived for a policy y to be a Condorcet winner, when the set of feasible policies is some subsety ofR N with non-empty interior. Voters are assumed to differ in some scalar characteristic w. The sufficient condition refers only to voters' preferences over the set of preferred policies (of the various other voters). This set is a one-dimensional curve inR N> . The condition is that the indifference curves of each typew through the preferred policyy* (v) of any typev all be collinear. If the condition holds, then the preferred policyy* (m) of the median type of voter will be a Condorcet winner. If there are only three types of voter, then the above condition is also necessary for the existence of a Condorcet winner.

Critical strategies under approval voting: Who gets ruled in and ruled out

<p class="MsoBodyText2" style="text-align: justify; line-height: normal; margin: 0in 0.6in 0pt 0.5in; tab-stops: .5in;"><span style="font-size: 10pt;"><span style="font-family: Times New Roman;">While several surveys on technology diffusion have been undertaken, few attempts have been made to synthesize existing research to provide a framework for examining the role of governments.<span style="mso-spacerun: yes;">  </span>Is government intervention really required to remedy market failures caused by network externalities?<span style="mso-spacerun: yes;">  </span>This paper covers recent developments in this area, focusing on works in stochastic evolutionary game theory.<span style="mso-spacerun: yes;">  </span>We relate the results of equilibrium selections to the role of governments. JEL classification: L1, L53 Keywords: Path Inefficiency; Market Failure; Network Externalities</span></span></p>

Schelling models of segregation attempt to explain how a population of agents or particles of two types may organise itself into large homogeneous clusters. They can be seen as variants of the Ising model. While such models have been extensively studied, unperturbed (or noiseless) versions have largely resisted rigorous analysis, with most results in the literature pertaining models in which noise is introduced, so as to make them amenable to standard techniques from statistical mechanics or stochastic evolutionary game theory. We rigorously analyse the one-dimensional version of the model in which one of the two types is in the minority, and establish various forms of threshold behaviour. Our results are in sharp contrast with the case when the distribution of the two types is uniform (i.e. each agent has equal chance of being of each type in the initial configuration), which was studied in Brandt et al. (in: STOC ’12: proceedings of the 44th symposium on theory of computing, pp. 789–804, 2012) and Barmpalias et al. (in: 55th Annual IEEE symposium on foundations of computer science, Oct 18–21, Philadelphia, FOCS’14, 2014).

Simple normative rules imply simple positive rules

On the model dependence of majority preference relations reconstructed from ballot or survey data

We examine legislative policy making in institutions with two empirically relevant features: agenda setting occurs in real time and the default policy evolves. We demonstrate that these institutions select Condorcet winners when they exist, provided a sufficient number of individuals have opportunities to make proposals. In policy spaces with either pork barrel or pure redistributional politics (where a Condorcet winner does not exist), the last proposer is effectively a dictator or near-dictator under relatively weak conditions.

Condorcet's paradox for weak preference orderings

In one-dimensional environments with single-peaked preferences we consider social welfare functions satisfying Arrow''s requirements, i.e. weak Pareto and independence of irrelevant alternatives. When the policy space is a one-dimensional continuum such a welfare function is determined by a collection of 2N strictly quasi-concave preferences and a tie-breaking rule. As a corollary we obtain that when the number of voters is odd, simple majority voting is transitive if and only if each voters preference is strictly quasi-concave.

Short-Term Deviations from Simple Majority Voting

Majority rule is based on decisions taken by a (simple or weighted) majority vote. Binary voting, however, is inaccurate. Other more reliable decision-making voting methodologies exist. Indeed, just as there are numerous voting procedures which can be used in elections, so too there are (rather fewer but) several voting procedures which can be used in decision-making. Some of the latter are non-majoritarian. If, then, it were possible to identify the collective will of the elected chamber by a procedure which was non-majoritarian, the logic on which the principle of majority rule is based would become obsolescent. In which case, governance could be based on an all-party coalition. Accordingly, this chapter examines majoritarian decision-making and electoral systems. It questions the democratic legitimacy of forming a majoritarian government, be it a single-party administration or a multi-party coalition. It looks at two other democratic structures, the first consociational and the second consensual, and it analyses other decision-making methodologies. Finally, it outlines a taxonomy of decision-making.

Spontaneous law is less enamored with simple majorities than is much of formal law, at least in appellate courts, legislatures, the electoral college, and plebiscites, where simple majoritarianism is the common requirement for action. In contrast, young children who are asked to vote on a name for their athletic team are often observed entertaining numerous nominations and then raising their hands as each nomination is called out-with no apparent restriction on the number of times a given little hand may be raised. The winner is the option that attracts the most votes. Experienced adults are often startled when these young voters raise their hands repeatedly, each casting numerous ballots. But in fact, the practice can be understood as a spontaneous example of approval voting.