38 research outputs found
Egalitarian Judgment Aggregation
Egalitarian considerations play a central role in many areas of social choice
theory. Applications of egalitarian principles range from ensuring everyone
gets an equal share of a cake when deciding how to divide it, to guaranteeing
balance with respect to gender or ethnicity in committee elections. Yet, the
egalitarian approach has received little attention in judgment aggregation -- a
powerful framework for aggregating logically interconnected issues. We make the
first steps towards filling that gap. We introduce axioms capturing two
classical interpretations of egalitarianism in judgment aggregation and situate
these within the context of existing axioms in the pertinent framework of
belief merging. We then explore the relationship between these axioms and
several notions of strategyproofness from social choice theory at large.
Finally, a novel egalitarian judgment aggregation rule stems from our analysis;
we present complexity results concerning both outcome determination and
strategic manipulation for that rule.Comment: Extended version of paper in proceedings of the 20th International
Conference on Autonomous Agents and Multiagent Systems (AAMAS), 202
Egalitarian judgment aggregation
Egalitarian considerations play a central role in many areas of social choice theory. Applications of egalitarian principles range from ensuring everyone gets an equal share of a cake when deciding how to divide it, to guaranteeing balance with respect to gender or ethnicity in committee elections. Yet, the egalitarian approach has received little attention in judgment aggregation—a powerful framework for aggregating logically interconnected issues. We make the first steps towards filling that gap. We introduce axioms capturing two classical interpretations of egalitarianism in judgment aggregation and situate these within the context of existing axioms in the pertinent framework of belief merging. We then explore the relationship between these axioms and several notions of strategyproofness from social choice theory at large. Finally, a novel egalitarian judgment aggregation rule stems from our analysis; we present complexity results concerning both outcome determination and strategic manipulation for that rule.publishedVersio
Multi-Winner Voting with Approval Preferences
Approval-based committee (ABC) rules are voting rules that output a
fixed-size subset of candidates, a so-called committee. ABC rules select
committees based on dichotomous preferences, i.e., a voter either approves or
disapproves a candidate. This simple type of preferences makes ABC rules widely
suitable for practical use. In this book, we summarize the current
understanding of ABC rules from the viewpoint of computational social choice.
The main focus is on axiomatic analysis, algorithmic results, and relevant
applications.Comment: This is a draft of the upcoming book "Multi-Winner Voting with
Approval Preferences
Multi-Winner Voting with Approval Preferences
From fundamental concepts and results to recent advances in computational social choice, this open access book provides a thorough and in-depth look at multi-winner voting based on approval preferences. The main focus is on axiomatic analysis, algorithmic results and several applications that are relevant in artificial intelligence, computer science and elections of any kind. What is the best way to select a set of candidates for a shortlist, for an executive committee, or for product recommendations? Multi-winner voting is the process of selecting a fixed-size set of candidates based on the preferences expressed by the voters. A wide variety of decision processes in settings ranging from politics (parliamentary elections) to the design of modern computer applications (collaborative filtering, dynamic Q&A platforms, diversity in search results, etc.) share the problem of identifying a representative subset of alternatives. The study of multi-winner voting provides the principled analysis of this task. Approval-based committee voting rules (in short: ABC rules) are multi-winner voting rules particularly suitable for practical use. Their usability is founded on the straightforward form in which the voters can express preferences: voters simply have to differentiate between approved and disapproved candidates. Proposals for ABC rules are numerous, some dating back to the late 19th century while others have been introduced only very recently. This book explains and discusses these rules, highlighting their individual strengths and weaknesses. With the help of this book, the reader will be able to choose a suitable ABC voting rule in a principled fashion, participate in, and be up to date with the ongoing research on this topic
On the Strategyproofness of the Geometric Median
The geometric median of a tuple of vectors is the vector that minimizes the
sum of Euclidean distances to the vectors of the tuple. Classically called the
Fermat-Weber problem and applied to facility location, it has become a major
component of the robust learning toolbox. It is typically used to aggregate the
(processed) inputs of different data providers, whose motivations may diverge,
especially in applications like content moderation. Interestingly, as a voting
system, the geometric median has well-known desirable properties: it is a
provably good average approximation, it is robust to a minority of malicious
voters, and it satisfies the "one voter, one unit force" fairness principle.
However, what was not known is the extent to which the geometric median is
strategyproof. Namely, can a strategic voter significantly gain by misreporting
their preferred vector?
We prove in this paper that, perhaps surprisingly, the geometric median is
not even -strategyproof, where bounds what a voter can gain by
deviating from truthfulness. But we also prove that, in the limit of a large
number of voters with i.i.d. preferred vectors, the geometric median is
asymptotically -strategyproof. We show how to compute this bound
. We then generalize our results to voters who care more about some
dimensions. Roughly, we show that, if some dimensions are more polarized and
regarded as more important, then the geometric median becomes less
strategyproof. Interestingly, we also show how the skewed geometric medians can
improve strategyproofness. Nevertheless, if voters care differently about
different dimensions, we prove that no skewed geometric median can achieve
strategyproofness for all. Overall, our results constitute a coherent set of
insights into the extent to which the geometric median is suitable to aggregate
high-dimensional disagreements.Comment: 55 pages, 7 figure