Consistent collective decisions under majorities based on difference of votes

The main criticism to the aggregation of individual preferences under majority rules refers to the possibility of reaching inconsistent collective decisions from the election process. In these cases, the collective preference includes cycles and even could prevent the election of any alternative as the collective choice. The likelihood of consistent outcomes under a class of majority rules constitutes the aim of this paper. Specifically, we focus on majority rules that require certain consensus in individual preferences to declare an alternative as the winner. Under majorities based on difference of votes, the requirement asks to the winner alternative to obtain a difference in votes with respect to the loser alternative taking into account that individuals are endowed with weak preference orderings. Same requirement is asked to the restriction of these rules to individual linear preferences

A geometric examination of majorities based on difference in support

Reciprocal preferences have been introduced in the literature of social choice theory in order to deal with preference intensities. They allow individuals to show preference intensities in the unit interval among each pair of options. In this framework, majority based on difference in support can be used as a method of aggregation of individual preferences into a collective preference: option a is preferred to option b if the sum of the intensities for a exceeds the aggregated intensity of b in a threshold given by a real number located between 0 and the total number of voters. Based on a three dimensional geometric approach, we provide a geometric analysis of the non transitivity of the collective preference relations obtained by majority rule based on difference in support. This aspect is studied by assuming that each individual reciprocal preference satisfies a g-stochastic transitivity property, which is stronger than the usual notion of transitivit

On the stability of a scoring rules set under the IAC

A society facing a choice problem has also to choose the voting rule itself from a set of different possible voting rules. In such situations, the consequentialism property allows us to induce voters\u27 preferences on voting rules from preferences over alternatives. A voting rule employed to resolve the society\u27s choice problem is self-selective if it chooses itself when it is also used in choosing the voting rule. A voting rules set is said to be stable if it contains at least one self-selective voting rule at each profile of preferences on voting rules. We consider in this paper a society which will make a choice from a set constituted by three alternatives {a, b, c} and a set of the three well-known scoring voting rules {Borda, Plurality, Antiplurality}. Under the Impartial Anonymous Culture assumption (IAC), we will derive a probability for the stability of this triplet of voting rules. We use Ehrhart polynomials in order to solve our problems. This method counts the number of lattice points inside a convex bounded polyhedron (polytope). We discuss briefly recent algorithmic solutions to this method and use it to determine the probability of stabillity of {Borda, Plurality, Antiplurality} set

Strategy proofness and unanimity in many-to-one matching markets

In this paper, we consider a standard model of many-to-one matching markets. First, we study the relation between strategy-proofness and unanimity under a certain requirement and we prove these two properties become equivalent. Second, we illustrate that this result has an immediate impact on the relation between strategy-proofness and Maskin monotonicity. Finally, we determine a close connexion between strategy-proofness and implementation literature. We provide under certain minimal requirements the foundation for reasoning the equivalence among dominant strategy implementation, standard Nash implementation, and partially honest Nash implementation

Strategy proofness and unanimity in many-to-one matching markets

In this paper, we consider a standard model of many-to-one matching markets. First, we study the relation between strategy-proofness and unanimity under a certain requirement and we prove these two properties become equivalent. Second, we illustrate that this result has an immediate impact on the relation between strategy-proofness and Maskin monotonicity. Finally, we determine a close connexion between strategy-proofness and implementation literature. We provide under certain minimal requirements the foundation for reasoning the equivalence among dominant strategy implementation, standard Nash implementation, and partially honest Nash implementation

Strategy proofness and unanimity in many-to-one matching markets

In this paper, we consider a standard model of many-to-one matching markets. First, we study the relation between strategy-proofness and unanimity under a certain requirement and we prove these two properties become equivalent. Second, we illustrate that this result has an immediate impact on the relation between strategy-proofness and Maskin monotonicity. Finally, we determine a close connexion between strategy-proofness and implementation literature. We provide under certain minimal requirements the foundation for reasoning the equivalence among dominant strategy implementation, standard Nash implementation, and partially honest Nash implementation

Strategy proofness and unanimity in many-to-one matching markets

In this paper, we consider a standard model of many-to-one matching markets. First, we study the relation between strategy-proofness and unanimity under a certain requirement and we prove these two properties become equivalent. Second, we illustrate that this result has an immediate impact on the relation between strategy-proofness and Maskin monotonicity. Finally, we determine a close connexion between strategy-proofness and implementation literature. We provide under certain minimal requirements the foundation for reasoning the equivalence among dominant strategy implementation, standard Nash implementation, and partially honest Nash implementation