A characterization of strategy-proof voting rules for separable weak orderings

We consider the problem of choosing a subset of a finite set of indivisible objects (public projects, facilities, laws, etc.) studied by Barbera et al. (1991). Here we assume that agents' preferences are separable weak orderings. Given such a preference, objects are partitioned into three types, "goods", "bads", and "nulls". We focus on "voting rules", which rely only on this partition rather than the full information of preferences. We characterize voting rules satisfying strategy-proofness (no one can ever be better off by lying about his preference) and null-independence (the decision on each object should not be dependent on the preference of an agent for whom the object is a null). We also show that serially dictatorial rules are the only voting rules satisfying efficiency as well as the above two axioms. We show that the "separable domain" is the unique maximal domain over which each rule in the first characterization, satisfying a certain fairness property, is strategy-proof

Voting by Committees under Constraints

We consider social choice problems where a society must choose a subset from a set of objects. Specifically, we characterize the families of strategy-proof voting procedures when not all possible subsets of objects are feasible, and voters' preferences are separable or additively representable.Voting, strategy-proofness, additive and separable preferences

On Domains That Admit Well-behaved Strategy-proof Social Choice Functions

In this paper, we investigate domains which admit "well-behaved", strategy-proof social choice functions. We show that if the number of voters is even, then every domain that satisfies a richness condition and admits an anonymous, tops-only, unanimous and strategy-proof social choice function, must be semi-single-peaked. Conversely every semi-single-peaked domain admits an anonymous, tops-only, unanimous and strategy-proof social choice function. Semi-single-peaked domains are generalizations of single-peaked domains on a tree introduced by Demange (1982). We provide sharper versions of the results above when tops-onlyness is replaced by tops-selectivity and the richness condition is weakened.Voting-rules, Strategy-proofness, Restricted Domains, Tops-Only domains.

Tops-Only Domains

In this paper we consider the standard voting model with a finite set of alternatives A and n voters and address the following question : what are the characteristics of domains D that induce the property that every strategy-proof social choice function f : Dn -> A satisfying unanimity, has the tops-only property? We first impose a minimal richness condition which ensures that for every alternative a, there exists an admissible ordering where a is maximal. We identify conditions on D that are sufficient for strategy-proofness and unanimity to imply tops onlyness in the general case of n voters and in the special case, n = 2. We provide an algorithm for constructing tops-only domains from connected graphs with elements of A as nodes. We provide several applications of our results. Finally, we relax the minimal richness assumption and partially extend our results.Voting, social choice, tops-only domain

Dichotomous Preferences and Power Set Extensions

This paper is devoted to the study of how to extend a dichotomous partition of a universal set X into good and bad objects to an ordering on the power set of X. We introduce a family of rules that naturally take into account the number of good objects and the number of bad objects, and provide axiomatic characterizations of two rules for ranking sets in such a context

Markov Equilibrium in Models of Dynamic Endogenous Political Institutions

This paper examines existence of Markov equilibria in the class of dynamic political games (DPGs). DPGs are dynamic games in which political institutions are endogenously determined each period. The process of change is both recursive and instrumental: the rules for political aggregation at date t+1 are decided by the rules at date t, and the resulting institutional choices do not affect payoffs or technology directly. Equilibrium existence in dynamic political games requires a resolution to a political fixed point problemin which a current political rule (e.g., majority voting) admits a solution only if all feasible political rules in the future admit solutions in all states. If the class of political rules is dynamically consistent, then DPGs are shown to admit political fixed points. This result is used to prove two equilibrium existence theorems, one of which implies that equilibrium strategies, public and private, are smooth functions of the economic state. We discuss practical applications that require existence of smooth equilibria.Recursive, dynamic political games, political fixed points, dynamically consistent rules

Good and bad objects: the symmetric difference rule

We consider the problem of ranking sets of objects, the members of which are mutually compatible. Assuming that each object is either good or bad, we axiomatically characterize a cardinality-based rule which arises naturally in this dichotomous setting.