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We consider approval-based committee voting, i.e., the setting where each voter approves a subset of candidates, and these votes are then used to select a fixed-size set of winners (committee). We propose a natural axiom for this setting, which we call justified representation (JR). This axiom requires that if a large enough group of voters exhibits(More)
Runoff voting rules such as single transferable vote (STV) and Baldwin's rule are of particular interest in computational social choice due to their recursive nature and hardness of manipulation, as well as in (human) practice because they are relatively easy to understand. However, they are not known for their compliance with desirable axiomatic properties(More)
In (computational) social choice, how ties are broken can affect the axiomatic and computational properties of a voting rule. In this paper, we first consider settings where we may have multiple winners. We formalize the notion of parallel universes tiebreaking with respect to a particular tree that represents the computation of the winners, and show that(More)
Algorithms for solving Stackelberg games are used in an ever-growing variety of real-world domains. Previous work has extended this framework to allow the leader to commit not only to a distribution over actions, but also to a scheme for stochastically signaling information about these actions to the follower. This can result in higher utility for the(More)
We study a dynamic social choice problem in which an alternative is chosen at each round according to the reported valuations of a set of agents. In the interests of obtaining a solution that is both efficient and fair, we aim to maximize the Nash social welfare, which is the product of all agents' utilities. We present three novel rules and discuss some of(More)
In many multiagent environments, a designer has some, but limited control over the game being played. In this paper, we formalize this by considering incompletely specified games, in which some entries of the payoff matrices can be chosen from a specified set. We show that it is NP-hard for the designer to make this choices optimally, even in zero-sum(More)
We study the societal tradeoffs problem, where a set of voters each submit their ideal tradeoff value between each pair of activities (e.g., " using a gallon of gasoline is as bad as creating 2 bags of landfill trash "), and these are then aggregated into the societal tradeoff vector using a rule. We introduce the family of distance-based rules and show(More)
We study the problem of finding a recommendation for an un-informed user in a social network by weighting and aggregating the opinions offered by the informed users in the network. In social networks, an informed user may try to manipulate the recommendation by performing a false-name manipulation, wherein the user submits multiple opinions through fake(More)
1 Overview In the last lecture we looked at the online Set Cover problem which we solved by LP rounding. We then extended this to an algorithm for the online Facility Location problem (which we observed was equivalent to Set Cover), obtaining a competitive ratio of log 2 (max{m, n}). In this lecture we extend this to an approximation algorithm for the(More)