Strategy-proof preference rules

By virtue of the Kemeny distance strategy-proofness of preference rules is defined. It is shown that a preference rule, which assigns a complete relation to every profile of complete relations is non-imposed and strategy-proof if and only if it is pairwise voting in committees. So, non-imposedness and strategy-proofness together imply the independence of irrelevant alternatives condition. Furthermore, it is shown that in this setting pairwise voting in committees coincides with coordinatewise veto voting. Taking acyclic preference rules into consideration, which assign an acyclic complete relation to every profile of acyclic complete relations, it follows that under strategy-proofness and non-imposition the independence of irrelevant alternatives is equivalent to indifference monotonicity. Now it follows that an acyclic preference rule is non-imposed, strategy-proof and indifference monotonic if and only if it is coordinatewise veto voting with respect to a cycle free assignment of disagreements.mathematical economics and econometrics ;

Intransitive aggregated preferences

An impossibility theorem for preference aggretating rules is discussed. In this theorem no transitivity condition or acyclicity condition is imposed on the preferences: neither on the individual level nor on the aggregated level. Under the conditions that aggregation is non-dictatorial, Pareto-optimal, neutral and independent of irrelevant alternatives, it follows that the aggregated preferences are much more complex and therefore less ordered than the individual preferences.mathematical economics and econometrics ;

Collective Choice Rules on Convex Restricted Domains

We study sets of preferences that are convex with respect to the betweeness relation induced by the Kemeny distance for preferences. It appears that these sets consist of all preferences containing a certain partial ordering and the other way around all preferences containing a given partial ordering form a convex set. Next we consider restricted domains where each agent has a convex set of preferences. Necessary and sufficient conditions are formulated under which a restricted domain admits unanimous, strategy-proof and non-dictatorial choice rules. Loosely speaking it boils down to admitting monotone and non-image-dictatorial decision rules on two alternatives where the other alternatives are completely disregarded.mathematical economics;

Maximal Domains for Strategy-Proof or Maskin Monotonic Choice Rules

Domains of individual preferences for which the well-known impossibility theorems of Gibbard-Satterthwaite and Muller-Satterthwaite do not hold are studied. To comprehend the limitations these results imply for social choice rules, we search for the largest domains that are possible. Here, we restrict the domain of individual prefer ences of precisely one individual. It turns out that, for such domains, the conditions of inseparable pair and of inseparable set yield the only maximal domains on which there exist non-dictatorial, Pareto-efficient and strategy-proof social choice rules. Next, we characterize the maximal domains which allow for Maskin monotone, non-dictatorial and Pareto-efficient social choice rules.mathematical economics;

Impossibilities with Kemeny updating

Impossibility theorems for preference correspondences based on a new monotonicity concept arediscussed. Here monotonicity means that if preferences update in such a way that they get closerto an outcome then at the new situation this outcome remains chosen. Strong monotonicity requiresfurther that in those cases the outcome at the new profile is a subset of the outcome at the oldprofile. It is shown that only dictatorial preference correspondences are unanimous and stronglymonotone.microeconomics ;

Update Monotone Preference Rules

Collective decisions are modeled by preference correspondences (rules). In particular, we focus ona new condition: "update monotonicity" for preference rules. Although many so-called impossibilitytheorems for the choice rules are based on -or related to- monotonicity conditions, this appealingcondition is satisfied by several non-trivial preference rules. In fact, in case of pairwise,Pareto optimal, neutral, and consistent rules; the Kemeny-Young rule is singled out by thiscondition. In case of convex valued, Pareto optimal, neutral and replication invariant rules;strong update monotonicity implies that the rule equals the union of preferences which extend allpreference pairs unanimously agreed upon by k agents, where k is related to the number ofalternatives and agents. In both cases, it therewith provides a charaterization of these rules.microeconomics ;

Arrow's Theorem for One-Dimensional Single-Peaked Preferences

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 voter�s preference is strictly quasi-concave.mathematical economics;

Restricted domains with Pareto free pairs

Among the domains restricted by Pareto free pairs we determine those allowing for preference rules being anonymous and independent of irrelevant alternatives. Essentially such preference rules appear to be based on a priority ordered at which adjacent alternatives can only be swapped in order is all agents agree with this swap

Maximal Domains for Strategy-proof or Maskin Monotonic Choice Rules

Domains of individual preferences for which the well-known impossibility Theorems of Gibbard-Satterthwaite and Muller-Satterthwaite do not hold are studied. First, we introduce necessary and sufficient conditions for a domain to admit non-dictatorial, Pareto efficient and either strategy-proof or Maskin monotonic social choice rules. Next, to comprehend the limitations the two Theorems imply for social choice rules, we search for the largest domains that are possible. Put differently, we look for the minimal restrictions that have to be imposed on the unrestricted domain to recover possibility results. It turns out that, for such domains, the conditions of inseparable pair and of inseparable set yield the only maximal domains on which there exist non-dictatorial, Pareto efficient and strategy-proof social choice rules. Next, we characterize the maximal domains which allow for Maskin monotonic, non-dictatorial and Pareto-optimal social choice rules.Strategy-proofness; Maskin monotonicity; Restricted domains; Maximal domains

Tournaments as collective decisions

Unless all tournaments are admissible as individual preferences, we show that, structure diversity of the range of a Pareto-optimal, neutral, non-dictatorial, and independent of irrelevant alternatives preference rules is greater than the structure diversity in the individual preferences upon which these preference rules are based