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An important question in elections is determining whether a candidate can be a winner when some votes are absent. We study this determining winner with absent votes (WAV) problem with elections that take top-truncated ballots. We show that the WAV problem is NP-complete for single transferable vote, Maximin, and Copeland, and propose a special case of positional scoring rule such that the problem can be computed in polynomial time. Our results for top-truncated rankings differ from the results in full rankings as their hardness results still hold when the number of candidates or the number of missing votes are bounded, while we show that the problem can be solved in polynomial time in either case.more » « less
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For the assignment problem where multiple indivis- ible items are allocated to a group of agents given their ordinal preferences, we design randomized mechanisms that satisfy first-choice maximality (FCM), i.e., maximizing the number of agents as- signed their first choices, together with Pareto- efficiency (PE). Our mechanisms also provide guarantees of ex-ante and ex-post fairness. The generalizedeager Boston mechanism is ex-ante envy-free, and ex-post envy-free up to one item (EF1). The generalized probabilistic Boston mech- anism is also ex-post EF1, and satisfies ex-ante ef- ficiency instead of fairness. We also show that no strategyproof mechanism satisfies ex-post PE, EF1, and FCM simultaneously. In doing so, we expand the frontiers of simultaneously providing efficiency and both ex-ante and ex-post fairness guarantees for the assignment problem.more » « less
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The Condorcet criterion (CC) is a classical and well-accepted criterion for voting. Unfortunately, it is incompatible with many other desiderata including participation (PAR), half-way monotonicity (HM), Maskin monotonicity (MM), and strategy-proofness (SP). Such incompatibilities are often known as impossibility theorems, and are proved by worst-case analysis. Previous work has investigated the likelihood for these impossibilities to occur under certain models, which are often criticized of being unrealistic.We strengthen previous work by proving the first set of semi-random impossibilities for voting rules to satisfy CC and the more general, group versions of the four desiderata: for any sufficiently large number of voters n, any size of the group 1more » « less
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