Majority rule in multi-dimensional spatial models

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.

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.

Foundations of spatial preferences

Strategic Voting in Two-Party Legislative Elections

Simple normative rules imply simple positive rules

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

Measuring well-being by a multidimensional spatial model in OECD Better Life Index framework

Condorcet's paradox for weak preference orderings

Connecting pairwise and positional election outcomes

Opposing candidates for a political office often differ in their professional backgrounds and previous political experience, leading to both real and perceived differences in political capabilities. We analyze a formal model in which candidates with different productivities in two policy areas compete for voters by choosing how much money or effort they would allocate to each area if elected. The model has a unique equilibrium that differs substantially from the standard median voter model. Although candidates compete for the support of a moderate voter type, this cutoff voter differs from the expected median voter. Moreover, no voter type except the cutoff voter is indifferent between the candidates in equilibrium. The model also predicts that candidates respond to changes in the preferences of voters in a very rigid way. From a welfare perspective, candidates are “excessively moderate”: almost certainly, a majority of voters would prefer that the winning candidate focus more on his or her strength.

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.

Data warehouses and OLAP systems help to interactively analyze huge volume of data. This data, extracted from transactional databases, frequently contains spatial information which is useful for decision-making process. Integration of spatial data in multidimensional models leads to the concept of SOLAP (Spatial OLAP). Using a spatial measure as a geographical object, i.e. with geometric and descriptive attributes, raises problems regarding the aggregation operation in its semantic and implementation aspects. This paper shows the requirements for a multidimensional spatial data model and presents a multidimensional data model which is able to support complex objects as measures, inter-dependent attributes for measures and aggregation functions, use of ad-hoc aggregation functions and n to n relations between fact and dimension, in order to handle geographical data, according to its particular nature in an OLAP context.

Legislative scholars recognize that legislative output is affected by the legislature’s institutional design. Let us assume that the goals are to avoid chaos and to enhance welfare. Toward these goals there are many variations. Strong committees (Shepsle and Weingast 1987), strong ruling parties (Cox and McCubbins 2004), institutions fostering legislative exchange (Weingast and Marshall 1988) and a strong agenda setter (Dahm and Glazer 2015) all can contribute to the interests a legislature’s members (see also Krehbiel 2004). In this chapter, we explore the potential gains from electing a strong agenda setter who holds the power to steer policy toward the setter’s own policy preferences. In the US context, one can loosely label this setter as a strong “speaker.” Would the election of a strong speaker lead to policies that represent the views of the chamber? And would it be possible to elect a strong speaker whose views are representative of the party in an open vote, given that theoretical models of multi-dimensional voting on policy suggest the absence of a predictable equilibrium outcome and the specter of endless cycling?

Riker's view of the dynamical forces of political systems singles out disequilibrium, strategic voting and agenda‐manipulation as the pervasive features determining the nature of political change. We shall investigate these characteristics in some detail and thereafter evaluate the methodological aspects of Riker's theory. Some observations on the general relevance of the equilibrium analysis of multi‐dimensional spatial voting models for the study of political institutions are also made.