Warut Suksompong

The impossibility of extending random dictatorship to weak preferences

Random dictatorship has been characterized as the only social decision scheme that satisfies efficiency and strategyproofness when individual preferences are strict. We show that no extension of random dictatorship to weak preferences satisfies these properties, even when significantly weakening the required degree of strategyproofness.

Computing an Approximately Optimal Agreeable Set of Items

We study the problem of finding a small subset of items that is agreeable to all agents, meaning that all agents value the subset at least as much as its complement. Previous work has shown worst-case bounds, over all instances with a given number of agents and items, on the number of items that may need to be included in such a subset. Our goal in this paper is to efficiently compute an agreeable subset whose size approximates the size of the smallest agreeable subset for a given instance. We consider three well-known models for representing the preferences of the agents: ordinal preferences on single items, the value oracle model, and additive utilities. In each of these models, we establish virtually tight bounds on the approximation ratio that can be obtained by algorithms running in polynomial time.

Who can win a single-elimination tournament?

A single-elimination (SE) tournament is a popular way to select a winner both in sports competitions and in elections. A natural and well-studied question is the tournament fixing problem (TFP): given the set of all pairwise match outcomes, can a tournament organizer rig an SE tournament by adjusting the initial seeding so that the organizers favorite player wins? We prove new sufficient conditions on the pairwise match outcome information and the favorite player, under which there is guaranteed to be a seeding where the player wins the tournament. Our results greatly generalize previous results. We also investigate the relationship between the set of players that can win an SE tournament under some seeding (so-called SE winners) and other traditional tournament solutions. In addition, we generalize and strengthen prior work on probabilistic models for generating tournaments. For instance, we show that every player in an

On the structure of stable tournament solutions

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Approximate maximin shares for groups of agents

player tournament generated by the Condorcet random model will be an SE winner e...

Asymptotic Existence of Fair Divisions for Groups

A fundamental property of choice functions is stability, which, loosely speaking, prescribes that choice sets are invariant under adding and removing unchosen alternatives. We provide several structural insights that improve our understanding of stable choice functions. In particular, (1) we show that every stable choice function is generated by a unique simple choice function, which never excludes more than one alternative, (2) we completely characterize which simple choice functions give rise to stable choice functions, and (3) we prove a strong relationship between stability and a new property of tournament solutions called local reversal symmetry. Based on these findings, we provide the first concrete tournament—consisting of 24 alternatives—in which the tournament equilibrium set fails to be stable. Furthermore, we prove that there is no more discriminating stable tournament solution than the bipartisan set and that the bipartisan set is the unique most discriminating tournament solution which satisfies standard properties proposed in the literature.

Asymptotic existence of proportionally fair allocations

We investigate the problem of fairly allocating indivisible goods among interested agents using the concept of maximin share. Procaccia and Wang showed that while an allocation that gives every agent at least her maximin share does not necessarily exist, one that gives every agent at least

On the efficiency of localized work stealing

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Democratic Fair Allocation of Indivisible Goods

of her share always does. In this paper, we consider the more general setting where we allocate the goods to groups of agents. The agents in each group share the same set of goods even though they may have conflicting preferences. For two groups, we characterize the cardinality of the groups for which a constant factor approximation of the maximin share is possible regardless of the number of goods. We also show settings where an approximation is possible or impossible when there are several groups.

Simple pricing schemes for the cloud

The problem of dividing resources fairly occurs in many practical situations and is therefore an important topic of study in economics. In this paper, we investigate envy-free divisions in the setting where there are multiple players in each interested party. While all players in a party share the same set of resources, each player has her own preferences. Under additive valuations drawn randomly from probability distributions, we show that when all groups contain an equal number of players, a welfare-maximizing allocation is likely to be envy-free if the number of items exceeds the total number of players by a logarithmic factor. On the other hand, an envy-free allocation is unlikely to exist if the number of items is less than the total number of players. In addition, we show that a simple truthful mechanism, namely the random assignment mechanism, yields an allocation that satisfies the weaker notion of approximate envy-freeness with high probability.