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Abstract

In Chapter 1, I provide new impossibility results for the problem of selecting a committee of a fixed number of members out of a set of candidates in the presence of veto power. I show that even limited veto power makes many committee selection mechanisms of interest manipulable. This applies in particular (i) to mechanisms the range of which contains a degenerate lottery in which a committee is chosen for sure and (ii) to mechanisms that are constructed from extensive game forms with a finite number of strategies. These impossibilities hold on a large set of domains including the domain of additive preferences and even when probabilistic mechanisms are allowed. In Chapter 2, I introduce the dominance threshold, a new measure of strategic complexity based on “level-k” thinking. I use this measure to compare mechanisms used in practice to select juries in jury trials. In applying this measure, I overturn some commonly held beliefs about which jury selection mechanisms are strategically simple. In particular, I show that sequential mechanisms tend to be strategically simpler than mechanisms that involve simultaneous moves: By generating imperfect information games, simultaneous mechanisms increase the amount of guesswork needed to determine optimal strategies. In Chapter 3, I show that, in the context of one-to-one two-sided matching, the deferred acceptance mechanism cannot be improved upon in terms of manipulability in the sense of Pathak and S¨onmez (2013) or Arribillaga and Mass´o (2015) without compromising stability. I also identify conflicts between manipulability and fairness. Stable mechanisms that minimize the set of individuals who match with their least preferred achievable mate are shown to be maximally manipulable among the stable mechanisms. These mechanisms are also more manipulable than the deferred acceptance mechanism. I identify a similar conflict between fairness and manipulability in the case of the median stable mechanisms.