13 research outputs found
Fair Allocation based on Diminishing Differences
Ranking alternatives is a natural way for humans to explain their
preferences. It is being used in many settings, such as school choice, course
allocations and residency matches. In some cases, several `items' are given to
each participant. Without having any information on the underlying cardinal
utilities, arguing about fairness of allocation requires extending the ordinal
item ranking to ordinal bundle ranking. The most commonly used such extension
is stochastic dominance (SD), where a bundle X is preferred over a bundle Y if
its score is better according to all additive score functions. SD is a very
conservative extension, by which few allocations are necessarily fair while
many allocations are possibly fair. We propose to make a natural assumption on
the underlying cardinal utilities of the players, namely that the difference
between two items at the top is larger than the difference between two items at
the bottom. This assumption implies a preference extension which we call
diminishing differences (DD), where X is preferred over Y if its score is
better according to all additive score functions satisfying the DD assumption.
We give a full characterization of allocations that are
necessarily-proportional or possibly-proportional according to this assumption.
Based on this characterization, we present a polynomial-time algorithm for
finding a necessarily-DD-proportional allocation if it exists. Using
simulations, we show that with high probability, a necessarily-proportional
allocation does not exist but a necessarily-DD-proportional allocation exists,
and moreover, that allocation is proportional according to the underlying
cardinal utilities. We also consider chore allocation under the analogous
condition --- increasing-differences.Comment: Revised version, based on very helpful suggestions of JAIR referees.
Gaps in some proofs were filled, more experiments were done, and mor
07431 Abstracts Collection -- Computational Issues in Social Choice
From the 21st to the 26th of October 2007, the Dagstuhl Seminar 07431
on ``Computational Issues in Social Choice\u27\u27 was held
at the International Conference and Research Center (IBFI), Schloss Dagstuhl.
During the seminar, several participants presented their recent
research, and ongoing work and open problems were discussed.
The abstracts of the talks given during the seminar are collected in this paper.
The first section summarises the seminar topics and goals in general.
Links to full papers are provided where available
Implementation Theory
This surveys the branch of implementation theory initiated by Maskin (1977). Results for both complete and incomplete information environments are covered
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