5 research outputs found
Anonymous, neutral, and resolute social choice revisited
We revisit the incompatibility of anonymity and neutrality in singleton-valued social choice. We first analyze the irresoluteness structure these two axioms together with Pareto efficiency impose on social choice rules and deliver a method to refine irresolute rules without violating anonymity, neutrality, and efficiency. Next, we propose a weakening of neutrality called consequential neutrality that requires resolute social choice rules to assign each alternative to the same number of profiles. We explore social choice problems in which consequential neutrality resolves impossibilities that stem from the fundamental tension between anonymity, neutrality, and resoluteness.Series: Department of Strategy and Innovation Working Paper Serie
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.Comment: arXiv admin note: text overlap with arXiv:1503.0402
Most Equitable Voting Rules
In social choice theory, anonymity (all agents being treated equally) and
neutrality (all alternatives being treated equally) are widely regarded as
``minimal demands'' and ``uncontroversial'' axioms of equity and fairness.
However, the ANR impossibility -- there is no voting rule that satisfies
anonymity, neutrality, and resolvability (always choosing one winner) -- holds
even in the simple setting of two alternatives and two agents. How to design
voting rules that optimally satisfy anonymity, neutrality, and resolvability
remains an open question.
We address the optimal design question for a wide range of preferences and
decisions that include ranked lists and committees. Our conceptual contribution
is a novel and strong notion of most equitable refinements that optimally
preserves anonymity and neutrality for any irresolute rule that satisfies the
two axioms. Our technical contributions are twofold. First, we characterize the
conditions for the ANR impossibility to hold under general settings, especially
when the number of agents is large. Second, we propose the
most-favorable-permutation (MFP) tie-breaking to compute a most equitable
refinement and design a polynomial-time algorithm to compute MFP when agents'
preferences are full rankings