ORIGINAL PAPER Quaternary dichotomous voting rules

Mathematical Social Sciences, 2012

By extending manipulability indices defined for single-valued social choice rules to the multi-valued case, we explore the degree of manipulability of seven multi-valued social choice rules. Our analysis is based on computational experiments.

Journal of Economic Theory, 2015

This paper studies families of social choice functions (SCF's), i.e. a collection of social choice functions {Φ A }, where the family is indexed by the option set of choices. These (sets of) functions arise in sequential choice problems where at each stage a set of options is given to a population of voters and a choice rule must aggregate stated preferences to generate an aggregate choice. In such settings, the aggregate decision-making process should reflect some form of consistency across choice problems. We characterize the class of (sequences of) SCF's that satisfy two properties: (i) strategy-proofness and (ii) a notion of dynamic consistency inspired by Sen's α from choice theory. When the aggregate choice is anonymous, this class turns out to be exactly the set of q-rules, i.e. rules in which the selected alternative is the most preferred alternative of the voter at the q-th N-tile of the population (where N is the set of voters). This nests median voter schemes when no phantom voters are admitted in the decision rule. Without anonymity we obtain a class that we call "vote-by-committee" rules, the name due to some similarities with a class of SCF's axiomatized in Barberá et al. (1991).

Theory and Decision, 1992

The formal framework of social choice theory is generalized through the introduction of separate representations of preferences and choices. This makes it possible to treat voting as a procedure in which decisions are actually made by interacting participants, rather than as a mere mechanism for aggregation. The extended framework also allows for non-consequentialist preferences that take procedural factors into account. Concepts such as decisiveness, anonymity, neutrality, and stability are redefined for use in the new context. The formal results obtained confirm the universality of strategic voting.

Let X be a set of social alternatives, and let V be a set of 'votes' or 'signals'. (We do not assume any structure on X or V). A variable population voting rule F takes any number of anonymous votes drawn from V as input, and produces a nonempty subset of X as output. The rule F satisfies reinforcement if, whenever two disjoint sets of voters independently select some subset Y ⊆ X , the union of these two sets will also select Y. We show that F satisfies reinforcement if and only if F is a balance rule. If F satisfies a form of neutrality, then F satisfies reinforcement if and only if F is a scoring rule (with scores taking values in an abstract linearly ordered abelian group R); this generalizes a result of .

Scandinavian Political Studies, 1981

The article focuses on the problem of choosing the ‘best’ voting procedure for making collective decisions. The procedures discussed are simple majority rule, Borda count, approval voting, and maximin method. The first three have been axiomatized while the maximin method has not yet been given an axiomatic characterization. The properties, in terms of which the goodness of the procedures is assessed, are dictatorship, consistency, path independence, weak axiom of revealed preference, Pareto optimality, and manipulability. It turns out that the picture emerging from the comparison of the procedures in terms of these properties is most favorable to the approval voting.

SSRN Electronic Journal, 2022

Different voting rules are commonly used to settle collective decisions. A promising way to assess voting rules, for which little is known, is to compare the expressive utility that voters derive from voting with each rule. In this paper, we first propose an ordinal theory of expressive voting that allows us to compare voting rules in terms of the expressive utility that voters derive from voting (their expressive power). Our theory provides a novel testable implication according to which expected turnout increases with expressive power. We then ran an online experiment to test this implication in a controlled environment. We find that if voters are made aware of different voting rules, turnout is higher in voting rules with higher expressive power. Our results also suggest that, all else equal, the higher the expressive power of a voting rule the higher the expressive utility derived from voting and the better the voting rule represents voters' actual preferences. These results suggest that the expressive power of voting rules is a relevant criterion when deciding which voting rule to use in economic and political decisions.

2011

Distance rationalizability is a framework for classifying voting rules by interpreting them in terms of distances and consensus classes. It also allows to design new voting rules with desired properties. A particularly natural and versatile class of distances that can be used for this purpose is that of votewise distances [12], which "lift" distances over individual votes to distances over entire elections using a suitable norm. In this paper, we continue the investigation of the properties of votewise distance-rationalizable rules initiated in . We describe a number of general conditions on distances and consensus classes that ensure that the resulting voting rule is homogeneous or monotone. This complements the results of , where the authors focus on anonymity, neutrality and consistency. We also introduce a new class of voting rules, that can be viewed as "majority variants" of classic scoring rules, and have a natural interpretation in the context of distance rationalizability.

Social Choice and Welfare, 2007

The aim of this paper is to find normative foundations of Approval Voting when individuals have dichotomous preferences. We show that a social choice function is anonymous, neutral, strategy-proof and strictly monotone if and only if it is Approval Voting and interpret this result as an extension of May’s theorem (Econometrica 20:680–684, 1952). Then, we show that Approval Voting is the only strictly symmetric, neutral and efficient social choice function. This result is related to a characterization of Baigent and Xu (Math Soc Sci 21:21–29, 1991).

2003

There are many ways to aggregate individual preferences to a collective preference or outcome. The outcome is strongly dependent on the aggregation procedure (election mechanism), rather than on the individual preferences. The Dutch election procedure is based on proportional representation, one nation-wide district, categoric voting and the Plurality ranking rule, while the British procedure is based on non-proportional representation, many districts, categoric voting and the Plurality choice rule to elect one candidate for every district. For both election mechanisms we indicate a number of paradoxes. The German hybrid system is a combination of the Dutch and British system and hence inherits the paradoxes of both systems. The STV system, used in Ireland and Malta, is based on proportional representation (per district) and on ordinal voting. Although designed with the best intentions – no vote should be wasted – , it is prone to all kinds of paradoxes. May be the worst one is that more votes for a candidate may cause him to lose his seat. The AV system, used in Australia, is based on non-proportional representation (per district) and on ordinal voting. It has all the unpleasant properties of the STV system. The same holds for the French majority-plurality rule. Arrow’s impossibility theorem is presented, roughly saying that no ‘perfect’ election procedure exists. More precisely, it gives a characterization of the dictatorial rule: it is the only preference rule that is IIA and satisfies the Pareto condition. Finally we mention characterizations of the Borda rule, the Plurality ranking rule, the British FPTP system and of k-vote rules.

2010

We explore the relationship between two approaches to rationalizing voting rules: the maximum likelihood estimation (MLE) framework originally suggested by Condorcet and recently studied in and the distance rationalizability (DR) framework (Meskanen and Nurmi 2008; Elkind, Faliszewski, and Slinko 2009). The former views voting as an attempt to reconstruct the correct ordering of the candidates given noisy estimates (i.e., votes), while the latter explains voting as search for the nearest consensus outcome. We provide conditions under which an MLE interpretation of a voting rule coincides with its DR interpretation, and classify a number of classic voting rules, such as Kemeny, Plurality, Borda and Single Transferable Vote (STV), according to how well they fit each of these frameworks. The classification we obtain is more precise than the ones that result from using MLE or DR alone: indeed, we show that the MLE approach can be used to guide our search for a more refined notion of distance rationalizability and vice versa.