28 research outputs found
Set-Monotonicity Implies Kelly-Strategyproofness
This paper studies the strategic manipulation of set-valued social choice
functions according to Kelly's preference extension, which prescribes that one
set of alternatives is preferred to another if and only if all elements of the
former are preferred to all elements of the latter. It is shown that
set-monotonicity---a new variant of Maskin-monotonicity---implies
Kelly-strategyproofness in comprehensive subdomains of the linear domain.
Interestingly, there are a handful of appealing Condorcet extensions---such as
the top cycle, the minimal covering set, and the bipartisan set---that satisfy
set-monotonicity even in the unrestricted linear domain, thereby answering
questions raised independently by Barber\`a (1977) and Kelly (1977).Comment: 14 page
Characterizing the Top Cycle via Strategyproofness
Gibbard and Satterthwaite have shown that the only single-valued social
choice functions (SCFs) that satisfy non-imposition (i.e., the function's range
coincides with its codomain) and strategyproofness (i.e., voters are never
better off by misrepresenting their preferences) are dictatorships. In this
paper, we consider set-valued social choice correspondences (SCCs) that are
strategyproof according to Fishburn's preference extension and, in particular,
the top cycle, an attractive SCC that returns the maximal elements of the
transitive closure of the weak majority relation. Our main theorem implies
that, under mild conditions, the top cycle is the only non-imposing
strategyproof SCC whose outcome only depends on the quantified pairwise
comparisons between alternatives. This result effectively turns the
Gibbard-Satterthwaite impossibility into a complete characterization of the top
cycle by moving from SCFs to SCCs. It is obtained as a corollary of a more
general characterization of strategyproof SCCs.Comment: This paper is published at Theoretical Economics:
https://econtheory.org/ojs/index.php/te/article/view/512
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
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
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