arXiv subjects

Michele Gori

Publications and source records attributed to Michele Gori.

9 recordsLinked to original sources

arXiv2025

Manipulation of social choice correspondences under incomplete information

We study the manipulability of social choice correspondences in situations where individuals have incomplete information about others' preferences. We propose a general concept of manipulability that depends on the extension rule used to derive preferences over sets of alternatives from preferences over alternatives, as well as on individuals' level of information. We then focus on the manipulability of social choice correspondences when the Kelly extension rule is used, and individuals are assumed to have the capability to anticipate the outcome of the collective decision. Under these assumptions, we introduce some monotonicity and sensitivity properties for social choice correspondences that combined imply manipulability. Then we prove a result of manipulability for unanimous positional social choice correspondences, and present a detailed analysis of the manipulability properties for the Borda, the plurality, the negative plurality and the Copeland social choice correspondences.

econ.TH↗

arXiv2024

Resolute and symmetric mechanisms for two-sided matching problems

We focus on the one-to-one two-sided matching model with two disjoint sets of agents of equal size, where each agent in a set has preferences on the agents in the other set modeled by a linear order. A matching mechanism associates a set of matchings to each preference profile; resoluteness, that is the capability to select a unique matching, and stability are important properties for a matching mechanism. The two versions of the deferred acceptance algorithm are resolute and stable matching mechanisms but they are unfair since they strongly favor one side of the market. We introduce a property for matching mechanisms that relates to fairness; such property, called symmetry, captures different levels of fairness and generalizes existing notions. We provide several possibility and impossibility results mainly involving the most general notion of symmetry, known as gender fairness, resoluteness, stability, weak Pareto optimality and minimal optimality. In particular, we prove that: resolute, gender fair matching mechanisms exist if and only if each side of the market consists of an odd number of agents; there exists no resolute, gender fair, minimally optimal matching mechanism. Those results are obtained by employing algebraic methods based on group theory, an approach not yet explored in matching theory.

econ.TH↗

arXiv2024

A generalization to networks of Young's characterization of the Borda rule

We prove that, for any given set of networks satisfying suitable conditions, the net-oudegree network solution, the net-indegree network solution, and the total network solution are the unique network solutions on that set satisfying neutrality, consistency and cancellation. The generality of the result obtained allows to get an analogous result for social choice correspondences: for any given set of preference profiles satisfying suitable conditions, the net-oudegree social choice correspondence, the net-indegree social choice correspondence and the total social choice correspondence are the unique social choice correspondences on that set satisfying neutrality, consistency and cancellation. Using the notable fact that several well-known voting rules coincide with the restriction of net-oudegree social choice correspondence to appropriate sets of preference profiles, we are able to deduce a variety of new and known characterization theorems for the Borda rule, the Partial Borda rule, the Averaged Borda rule, the Approval Voting, the Plurality rule and the anti-Plurality rule, among which Young's characterization of the Borda rule and Fishburn's characterization of the Approval Voting.

cs.GT↗

arXiv2021

Paths and flows for centrality measures in networks

We consider the number of paths that must pass through a subset $X$ of vertices of a network $N$ in a maximum sequence of arc-disjoint paths connecting two vertices $y$ and $z$. We show that when $X$ is a singleton, that number equals the difference between the maximum flow value from $y$ to $z$ in $N$ and the maximum flow value from $y$ to $z$ in the network obtained by $N$ setting to zero the capacities of arcs incident to $X$. That fact theoretically justifies the common identification of those two concepts in network literature. We also show that the same equality does not hold when $|X|\geq 2.$ Consequently, two conceptually different group centrality measures involving paths and flows can naturally be defined, both extending the classic flow betweenness centrality.

math.CO↗

arXiv2019

Breaking ties in collective decision making

Many classical social preference (multiwinner social choice) correspondences are resolute only when two alternatives and an odd number of individuals are considered. Thus, they generally admit several resolute refinements, each of them naturally interpreted as a tie-breaking rule. In this paper we find out conditions which make a social preference (multiwinner social choice) correspondence admit a resolute refinement fulfilling suitable weak versions of the anonymity and neutrality principles, as well as reversal symmetry (immunity to the reversal bias).

math.CO↗

arXiv2018

The flow network method

In this paper we propose an in-depth analysis of a method, called the flow network method, which associates with any network a complete and quasi-transitive binary relation on its vertices. Such a method, originally proposed by Gvozdik (1987), is based on the concept of maximum flow. Given a competition involving two or more teams, the flow network method can be used to build a relation on the set of teams which establishes, for every ordered pair of teams, if the first one did at least as good as the second one in the competition. Such a relation naturally induces procedures for ranking teams and selecting the best $k$ teams of a competition. Those procedures are proved to satisfy many desirable properties.

cs.GT↗

arXiv2016

Resolute refinements of social choice correspondences

Many classical social choice correspondences are resolute only in the case of two alternatives and an odd number of individuals. Thus, in most cases, they admit several resolute refinements, each of them naturally interpreted as a tie-breaking rule, satisfying different properties. In this paper we look for classes of social choice correspondences which admit resolute refinements fulfilling suitable versions of anonymity and neutrality. In particular, supposing that individuals and alternatives have been exogenously partitioned into subcommittees and subclasses, we find out arithmetical conditions on the sizes of subcommittees and subclasses that are necessary and sufficient for making any social choice correspondence which is efficient, anonymous with respect to subcommittees, neutral with respect to subclasses and possibly immune to the reversal bias admit a resolute refinement sharing the same properties.

econ.GN↗

arXiv2015

On the reversal bias of the Minimax social choice correspondence

We introduce three different qualifications of the reversal bias in the framework of social choice correspondences. For each of them, we prove that the Minimax social choice correspondence is immune to it if and only if the number of voters and the number of alternatives satisfy suitable arithmetical conditions. We prove those facts thanks to a new characterization of the Minimax social choice correspondence and using a graph theory approach. We discuss the same issue for the Borda and Copeland social choice correspondences.

math.CO↗

arXiv2015

Symmetric majority rules

In the standard arrovian framework and under the assumption that individual preferences and social outcomes are linear orders on the set of alternatives, we study the rules which satisfy suitable symmetries and obey the majority principle. In particular, supposing that individuals and alternatives are exogenously partitioned into subcommittees and subclasses, we provide necessary and sufficient conditions for the existence of reversal symmetric majority rules that are anonymous and neutral with respect to the considered partitions. We also determine a general method for constructing and counting those rules and we explicitly apply it to some simple cases.

math.GR↗