Truthful and Near-Optimal Mechanisms for Welfare Maximization in Multi-Winner Elections

Abstract

Mechanisms for aggregating the preferences of agents in elections need to balance many different considerations, including efficiency, information elicited from agents, and manipulability. We consider the utilitarian social welfare of mechanisms for preference aggregation, measured by the distortion. We show that for a particular input format called threshold approval voting, where each agent is presented with an independently chosen threshold, there is a mechanism with nearly optimal distortion when the number of voters is large. Threshold mechanisms are potentially manipulable, but place a low informational burden on voters. We then consider truthful mechanisms. For the widely-studied class of ordinal mechanisms which elicit the rankings of candidates from each agent, we show that truthfulness essentially imposes no additional loss of welfare. We give truthful mechanisms with distortion O(√m log m) for k-winner elections, and distortion O(√m log m) when candidates have arbitrary costs, in elections with m candidates. These nearly match known lower bounds for ordinal mechanisms that ignore the strategic behavior. We further tighten these lower bounds and show that for truthful mechanisms our first upper bound is tight. Lastly, when agents decide between two candidates, we give tight bounds on the distortion for truthful mechanisms.

A Few Queries Go a Long Way: Information-Distortion Tradeoffs in Matching

“…The approach of enhancing the input of algorithms by equipping them with cardinal queries that we adopt in this paper was first suggested by Amanatidis et al (2020b). Some other works (Abramowitz, Anshelevich, and Zhu 2019;Benade et al 2017;Bhaskar, Dani, and Ghosh 2018) have considered related but different models in which the designer has access to some cardinal information on top of the ordinal preferences. In a recent orthogonal approach, Mandal et al ( 2019) and Mandal, Shah, and Woodruff (2020) considered the communication complexity of voting algorithms and studied the tradeoffs between the distortion and the number of bits of information elicited from the agents.…”

Truthful ownership transfer with expert advice

“…Social welfare maximization without payments has been studied in many related papers in the computer science literature, in general social choice settings [7,19], as well as in restricted domains, such as matching and allocation problems [13,17,26]. Similarly to what we do here, Filos-Ratsikas and Miltersen [19] use one-voter cardinal truthful mechanisms to achieve improved welfare guarantees.…”

A Few Queries Go a Long Way: Information-Distortion Tradeoffs in Matching

“…For general social choice settings (i.e., voting), the distortion of ordinal algorithms has been studied in a long list of papers, e.g., see (Procaccia & Rosenschein, 2006;Anshelevich & Postl, 2017;Anshelevich et al, 2018;Boutilier et al, 2015;Caragiannis et al, 2017;Benade et al, 2017;Caragiannis et al, 2018;Fain et al, 2019;Filos-Ratsikas & Miltersen, 2014;Goel et al, 2017;Munagala & Wang, 2019;Feldman et al, 2016;Gkatzelis et al, 2020;Caragiannis et al, 2022). Most of the related work considers the standard case where only ordinal information is given, with a few notable exceptions (Abramowitz et al, 2019;Benade et al, 2017;Bhaskar et al, 2018;Filos-Ratsikas et al, 2020;Anshelevich et al, 2022). In this context, there is also a line of work that considers the effects of limited ordinal information on the distortion, e.g., see (Fain et al, 2019;Kempe, 2020;Gross, Anshelevich, & Xia, 2017).…”