The distortion of distributed voting

Abstract

Voting can abstractly model any decision-making scenario and as such it has been extensively studied over the decades. Recently, the related literature has focused on quantifying the impact of utilizing only limited information in the voting process on the societal welfare for the outcome, by bounding the distortion of voting rules. Even though there has been signi cant progress towards this goal, almost all previous works have so far neglected the fact that in many scenarios (like presidential elections) voting is actually a distributed procedure. In this paper, we consider a se ing in which the voters are partitioned into disjoint districts and vote locally therein to elect local winning alternatives using a voting rule; the nal outcome is then chosen from the set of these alternatives. We prove tight bounds on the distortion of well-known voting rules for such distributed elections both from a worst-case perspective as well as from a best-case one. Our results indicate that the partition of voters into districts leads to considerably higher distortion, a phenomenon which we also experimentally showcase using real-world data.

Peeking behind the ordinal curtain: Improving distortion via cardinal queries

“…The distortion framework was introduced by Procaccia and Rosenschein [2006], and has been studied subsequently in a series of papers, most prominently by Boutilier et al [2015], who consider a general social choice setting, under the unit-sum normalization; this general model was also previously studied by Caragiannis and Procaccia [2011] who considered different methods to translate the values of the agents for the alternatives into rankings (embeddings), and more recently by Filos-Ratsikas et al [2019] who bounded the distortion of deterministic mechanisms in district-based elections. A related model is that of distortion of social choice functions in a metric space, which was initiated by , and has since then been studied extensively [Anshelevich and Postl, 2017;Goel et al, 2017;Fain et al, 2019;Goel et al, 2018;Anshelevich and Zhu, 2018;Pierczynski and Skowron, 2019;Gross et al, 2017;Cheng et al, 2017Cheng et al, , 2018Feldman et al, 2016;Ghodsi et al, 2019;Borodin et al, 2019;Munagala and Wang, 2019].…”

A Novel Linguistic Decision Making Method Based on the Voting Model for Large-Scale Linguistic Decision making

“…Definition 5 [37] A district-based election is defined as a tuple ε = (M, N , D, W, V, f ), where M is a set of m alternatives, N is a set of n voters, D is a set of k districts that define a partition of the set of voters, W = (w d ) d∈D is a weight-vector consisting of a weight…”

“…For concreteness, district d ∈ D in Definition 5 contains n d voters such that d∈D n d = n, for each voter i ∈ N , d(i) ∈ D denotes i belongs to district d. The winner of each local election is awarded a weight that depends on the district, and the overall winner is chosen to be the alternative with the highest weight, that is, for every district d ∈ D, a local election between its members takes place, and the winner of this election is the alternative j d = f (v d ) that gets elected according to the voting rule f , where v d = (v i ) i:d(i)=d denotes the valuation sub-profile of the voters that belong to district d so that V = d∈D v d . The outcome of the district-based election ε is an alternative [37]…”

“…Unlike the flexible linguistic expression, numerical scale model, personalized individual semantics model of linguistic terms and double hierarchy linguistic term set, which aim to generalize, extend or improve classical fuzzy linguistic representation models and represent more complex linguistic assessments, in the paper, the voting model (concretely district-based election [37]) is employed to normalize the providing evaluation information process based on a huge amounts of decision makers, then multi linguistic decision matrix based on evaluation-based voting is developed to represent multi linguistic assessments of alternatives, accordingly, a new LS-MLDM framework is provide to deal with LS-MLDM problems, in which an uniform fusion method is developed to simultaneously fuse multi linguistic assessments of alternatives. Major contributions of the paper are summarized as follows:…”

Peeking Behind the Ordinal Curtain: Improving Distortion via Cardinal Queries

“…The distortion has been studied extensively in numerous settings, such as normalized valuations (Caragiannis and Pro-caccia 2011;Boutilier et al 2015;Filos-Ratsikas and Miltersen 2014;Filos-Ratsikas, Micha, and Voudouris 2019), metric preferences Anshelevich and Postl 2017;Goel, Krishnaswamy, and Munagala 2017;Fain et al 2019;Pierczynski and Skowron 2019;Munagala and Wang 2019), committee elections (Caragiannis et al 2017;Bhaskar, Dani, and Ghosh 2018), participatory budgeting (Goel et al 2019;Benade et al 2017), and matching and facility location (Filos-Ratsikas, Frederiksen, and Zhang 2014;Anshelevich and Sekar 2016;Feldman, Fiat, and Golomb 2016;Anshelevich and Zhu 2018).…”