• Publications
  • Influence
Fair Division of a Graph
TLDR
It is proved that for acyclic graphs a maximin share allocation always exists and can be found efficiently, and design efficient algorithms for special cases where the underlying graph has simple structure, and/or the number of agents---or, less restrictively, thenumber of agent types---is small.
Proportionality and the Limits of Welfarism
TLDR
An attractive committee rule is introduced which satisfies a property intermediate between the core and extended justified representation (EJR), and is computable in polynomial time, and it is shown that the new rule provides a logarithmic approximation to the core.
Proportionality and Strategyproofness in Multiwinner Elections
TLDR
It is proved that no multiwinner voting rule can simultaneously satisfy a weak form of proportionality (a weakening of justified representation) and aweak form of strategyproofness in the domain of committee elections.
Graphical Hedonic Games of Bounded Treewidth
TLDR
The problem of allocating indivisible goods can be modelled as a hedonic game, so that the results imply tractability of finding fair and efficient allocations on appropriately restricted instances.
Recognising Multidimensional Euclidean Preferences
TLDR
It is shown that for every other fixed dimension d > 1, the recognition problem is equivalent to the existential theory of the reals (ETR), and so in particular NP-hard, and it is proved that the domain of d-Euclidean preferences does not admit a finite forbidden minor characterisation for any d >1.
Preferences Single-Peaked on a Circle
TLDR
This work proves that Proportional Approval Voting can be computed in polynomial time for profiles that are single-peaked on a circle, and gives a fast recognition algorithm of this domain, provides a characterisation by finitely many forbidden subprofiles, and shows that many popular singleand multi-winner voting rules arePolynomial-time computable on this domain.
Complexity of Hedonic Games with Dichotomous Preferences
TLDR
This work shows that an individually stable outcome always exists and can be found in polynomial time, and provides efficient algorithms for cases in which agents approve only few coalitions, and in which they only approve sets of size 2 (the roommates case).
Truthful Aggregation of Budget Proposals
TLDR
This paper seeks budget aggregation mechanisms that are incentive compatible when each voter's disutility for a budget division is equal to the 1 distance between that division and the division she prefers most, and defines a notion of proportionality to capture this idea of fairness.
Proportional Participatory Budgeting with Cardinal Utilities
TLDR
A simple and attractive voting rule is constructed that satisfies one of two axioms of proportionality that guarantee proportional representation to groups of voters with common interests, and that can be evaluated in polynomial time.
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