Generalized Decision Scoring Rules: Statistical, Computational, and Axiomatic Properties

Abstract

We pursue a design by social choice, evaluation by statistics and computer science paradigm to build a principled framework for discovering new social choice mechanisms with desirable statistical, computational, and social choice axiomatic properties. Our new framework is called generalized decision scoring rules (GDSRs), which naturally extend generalized scoring rules [Xia and Conitzer 2008] to arbitrary preference space and decision space, including sets of alternatives with fixed or unfixed size, rankings, and sets of rankings. We show that GDSRs cover a wide range of existing mechanisms including MLEs, Chamberlin and Courant rule, and resolute, irresolute, and preference function versions of many commonly studied voting rules. We provide a characterization of statistical consistency for any GDSR w.r.t. any statistical model and asymptotically tight bounds on the convergence rate. We investigate the complexity of winner determination and a wide range of strategic behavior called vote operations for all GDSRs, and prove a general phase transition theorem on the minimum number of vote operations for the strategic entity to succeed. We also characterize GDSRs by two social choice normative properties: anonymity and finite local consistency.