How many candidates are needed to make elections hard to manipulate?

In multiagent settings where the agents have different preferences, preference aggregation is a central issue. Voting is a general method for preference aggregation, but seminal results have shown that all general voting protocols are manipulable. One could try to avoid manipulation by using voting protocols where determining a beneficial manipulation is hard computationally. The complexity of manipulating realistic elections where the number of candidates is a small constant was recently studied (Conitzer 2002), but the emphasis was on the question of whether or not a protocol becomes hard to manipulate for some constant number of candidates. That work, in many cases, left open the question: How many candidates are needed to make elections hard to manipulate? This is a crucial question when comparing the relative manipulability of different voting protocols. In this paper we answer that question for the voting protocols of the earlier study: plurality, Borda, STV, Copeland, maximin, regular cup, and randomized cup. We also answer that question for two voting protocols for which no results on the complexity of manipulation have been derived before: veto and plurality with runoff. It turns out that the voting protocols under study become hard to manipulate at 3 candidates, 4 candidates, 7 candidates, or never

Reaction to Uncertainty and Market Mechanism:Experimental Evidence

Abstract Much of the evidence supporting the Ellsberg's paradox comes from experiments on individual choice and judgement. In this study, we address the issue whether, in market experiments, there is a tendency for anomalous behaviour to disappear or to be reduced as a consequence of market experience and feedback. We empirically test the validity of this assumption by running an auction market for the sale of both risky and uncertain prospects. We compare bidding behaviour and prices in market-like settings with valuations obtained from individual pricing tasks. We conclude that, with the repetition of the market experience, there is a tendency for subjective expected utility to perform better. However, economists' general assumption that, in laboratory experiments, poor performance of SEU is due to the lack of financial incentives or to the lack of market-like settings is by no means supported by our data.

Inequality and Uncertainty: Theory and Legal Applications

Welfarism is the principle that social policy should be based solely on individual well-being, with no reference to \u27fairness or rights. The propriety of this approach has recently been the subject of extensive debate within legal scholarship. Rather than contributing (directly) to this debate, we identify and analyze a problem within welfarism that has received far too little attentioncall this the ex ante/ex post problem. The problem arises from the combination of uncertainty-an inevitable feature of real policy choice-and a social preference for equality. If the policymaker is not a utilitarian, but rather has a social welfare function that is equity regarding to some degree, then she faces a critical choice. Should she care about the equalization of expected well-being (the ex ante approach), or should she care about the expected equalization of actual well-being (the ex post approach)? Should she focus on the equality of prospects or the prospects for equality? In this Article, we bring the ex ante/ex post problem to the attention of legal academics, provide novel insight into when and why the problem arises, and highlight legal applications where the problem figures prominently. We ultimately conclude that welfarism requires an ex post approach. This is a counterintuitive conclusion, because the ex post approach can conflict with ex ante Pareto superiority. Indeed, this Article demonstrates that the ex post application of every equity-regarding social welfare function-whatever its particular form-must conflict with ex ante Pareto superiority in specific situations. Among other things, then, this Article shows that legal academics who care about equity must abandon either their commitment to welfarism or their commitment to ex ante Pareto superiorit

Indivisibility, Fairness, Farsightedness and their Implications for Security

fair division, commitment, peace treaties, terrorist motivation