Tag Archives: social choice

Research news

A few papers are working their way through the journal system:

Once all these are finally done, I can get back to some work on generating functions, after several years, which I am very much looking forward to.

 

New algorithms for matching problems

A preprint with Jacky Lo, just submitted to arXiv and on my publications page. The paper was ultimately inspired by a Christmas party game, which shows that the line between work and play is hard to draw.

Abstract: The standard two-sided and one-sided matching problems, and the closely related school choice problem, have been widely studied from an axiomatic viewpoint. A small number of algorithms dominate the literature. For two-sided matching, the Gale-Shapley algorithm; for one-sided matching, (random) Serial Dictatorship and Probabilistic Serial rule; for school choice, Gale-Shapley and the Boston mechanisms. The main reason for the dominance of these algorithms is their good (worst-case) axiomatic behaviour with respect to notions of efficiency and strategyproofness. However if we shift the focus to fairness, social welfare, tradeoffs between incompatible axioms, and average-case analysis, it is far from clear that these algorithms are optimal. We investigate new algorithms several of which have not appeared (to our knowledge) in the literature before. We give a unified presentation in which algorithms for 2-sided matching yield 1-sided matching algorithms in a systematic way. In addition to axiomatic properties, we investigate agent welfare using both theoretical and computational approaches. We find that some of the new algorithms are worthy of consideration for certain applications. In particular, when considering welfare under truthful preferences, some of the new algorithms outperform the classic ones.

Average-case analysis of random assignment algorithms

With summer scholarship student Jacky Lo, I have just submitted this paper to COMSOC 2016. This is the first time I have seriously looked at resource allocation in social choice. It was
interesting and I may do more on this topic in future.

Abstract: The problem of one-sided matching without money (also known as house allocation), namely computing a bijection from a finite set of items to a finite set of agents each of whom has a strict preference order over the items, has been much studied. Symmetry considerations require the use of randomization, yielding the more general notion of random assignment. The two most commonly studied algorithms (Random Serial Dictatorship (RP) and Probabilistic Serial Rule (PS)) dominate the literature on random assignments.
One feature of our work is the inclusion of several new algorithms for the problem. We adopt an average-case viewpoint: although these algorithms do not have the axiomatic properties of PS and RP, they are computationally efficient and perform well on random data, at least in the case of sincere preferences. We perform a thorough comparison of the algorithms, using several standard probability distributions on ordinal preferences and measures of fairness, efficiency and social welfare.
We find that there are important differences in performance between the known algorithms. In particular, our lesser-known algorithms yield better overall welfare than PS and RP and better efficiency than RP, with small negative consequences for envy, and are computationally efficient. Thus provided that worst-case and strategic concerns are relatively unimportant, the new algorithms should be seriously considered for use in applications.

Distance-based voting rules

After a long gestation period in which I seemed to be publishing nothing, a few projects have reached maturity. With Benjamin Hadjibeyli, I have a preprint studying so-called distance rationalizable voting rules, which we recently submitted. These are voting rules in which we specify some notion of consensus winner, set up a distance measure on elections, and then choose the winner(s) based on minimizing the distance to a consensus election. This framework has been used by other authors over the years, particularly by Edith Elkind, Piotr Faliszewksi and Arkadii Slinko in a series of papers.

We deal with a lot of foundational issues and give some insight into the way Minkowski geometry relates to decisiveness of such rules. This includes both positive and negative results.

This work was inspired by discussions with Elchanan Mossel and Miklos Racz in Berkeley in 2013, about whether the Dodgson rule is a so-called hyperplane rule. That question is still not answered, but now the underbrush has been cleared, it makes sense to go back to it.

The Complexity of Safe Manipulation under Scoring Rules

This paper will appear in Proceedings of IJCAI ’11 and be presented at the conference in Barcelona in July.

Abstract: Slinko and White have recently introduced a new model of coalitional
manipulation of voting rules under limited communication, which they
call {em safe strategic voting}. The computational aspects of this
model were first studied by Hazon and Elkind, who provide
polynomial-time algorithms for finding a safe strategic vote under
$k$-approval and the Bucklin rule. In this paper, we answer an open
question of Hazon and Elkind by presenting a polynomial-time algorithm
for finding a safe strategic vote under the Borda rule. Our results for
Borda generalize to several interesting classes of scoring rules.

The probability of safe manipulation

This paper (joint with Reyhaneh Reyhani) will be presented at COMSOC 2010. It deals with the concept of “safe manipulation”, whereby an agent can attempt to manipulate the result of an election without risk, provided that voters of other preferences vote sincerely but irrespective of the number of like-minded voters that also try to vote strategically. It was introduced by Slinko and White in COMSOC 2008.

Abstract: The concept of safe manipulation has recently been introduced by Slinko and White. We show how to compute the asymptotic probability that a safe manipulation exists for a given scoring rule under the uniform distribution on voting situations (the so- called Impartial Anonymous Culture). The technique used is computation of volumes of convex polytopes. We present explicit numerical results in the 3-candidate case.

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Probability calculations under the IAC hypothesis

Mark C. Wilson and Geoffrey  Pritchard, Mathematical Social Sciences 54 (2007), 244-256.

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Abstract: We show how powerful algorithms recently developed for counting lattice points and computing volumes of convex polyhedra can be used to compute probabilities of a wide variety of events of interest in social choice theory. Several illustrative examples are given.

Exact results on manipulability of positional voting rules

Geoffrey Pritchard and Mark C. Wilson, Social Choice and Welfare 29 (2007), 487-513.

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Abstract:

We consider 3-candidate elections under a general scoring rule and derive precise conditions for a given voting situation to be strategically manipulable by a given coalition of voters. We present an algorithm that makes use of these conditions to compute the minimum size M of a manipulating coalition for a given voting situation.

The algorithm works for any voter preference model — here we present numerical results for IC and for IAC, for a selection of scoring rules, and for numbers of voters up to 150. A full description of the distribution of M is obtained, generalizing all previous work on the topic.

The results obtained show interesting phenomena and suggest several conjectures. In particular we see that rules “between plurality and Borda” behave very differently from those “between Borda and antiplurality”.