Quaternary dichotomous voting rules (original) (raw)
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ORIGINAL PAPER Quaternary dichotomous voting rules
2010
In this article, we provide a general model of “quaternary ” dichotomous voting rules (QVRs), namely, voting rules for making collective dichotomous deci-sions (to accept or reject a proposal), based on vote profiles in which four options are available to each voter: voting (“yes”, “no”, or “abstaining”) or staying home and not turning out. The model covers most of actual real-world dichotomus rules, where quorums are often required, and some of the extensions considered in the literature. In particular, we address and solve the question of the representability of QVRs by means of weighted rules and extend the notion of “dimension ” of a rule. 1
Preferences, actions and voting rules
SERIEs, 2011
In this paper we address several issues related to collective dichotomous decision-making by means of quaternary voting rules, i.e., when voters may choose between four actions: voting yes, voting no, abstaining and not turning up-which are aggregated by a voting rule into a dichotomous decision: acceptance or rejection of a proposal. In particular we study the links between the actions and preferences of the actors. We show that quaternary rules (unlike binary rules, where only two actions -yes or no-are possible) leave room for "manipulability" (i.e., strategic behaviour). Thus a preference pro…le does not in general determine an action pro…le. We also deal with the notions of success and decisiveness and their ex ante assessment for quaternary voting rules, and discuss the role of information and coordination in this context.
Collectively rational voting rules for simple preferences
Journal of Mathematical Economics, 2011
Collective rationality of voting rules, requiring transitivity of social preferences (or quasi-transitivity, acyclicity for weaker notions), has been known to be incompatible with other standard conditions for voting rules when there is no prior information, thus no restriction, on individual preferences Sen, 1970). proposes two restricted domains of individual preferences where majority voting generates transitive social preferences; they are the domain consisting of preferences that have at most two indifference classes, and the domain where any set of three alternatives is partitioned into two non-empty subsets and alternatives in one set are strictly preferred to alternatives in the other set. On these two domains, we investigate whether majority voting is the unique way of generating transitive, quasi-transitive, or acyclic social preferences. First of all, we rule out non-standard voting rules by imposing monotonicity, anonymity, and neutrality. Our main results show that majority rule is the unique voting rule satisfying transitivity, yet all other voting rules satisfy acyclicity (also quasi-transitivity on the second domain). Thus we find a very thin border dividing majority and other voting rules, namely, the gap between transitivity and acyclicity.
Consensus versus Dichotomous Voting
Studies in Fuzziness and Soft Computing, 2011
Consensus means general agreement among possibly di erent views, while dichotomus voting rules are a means of making decisions by using votes to settle di erences of view. How then can it often be the case that a committee whose only formal mechanism for decision-making is a dichotomus voting rule reaches a consensus? In this paper, based on a game-theoretic model developed in three previous papers, we provide an answer to this question.
On the Properties of Voting Systems
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.
Dynamically consistent voting rules
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).
Variable population voting rules
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 .
Homogeneity and monotonicity of distance-rationalizable voting rules
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.
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.