6,701 research outputs found

    Characterization of Pareto Dominance

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    The Pareto dominance relation is shown to be the unique nontrivial partial order on the set of finite-dimensional real vectors satisfying a number of intuitive properties.Pareto dominance; characterization

    Extension of Preferences to an Ordered Set

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    If a decision maker prefers x to y to z, would he choose orderd set [x;z] or [y;x]? This article studies extension of preferences over individual alternatives to an ordered set which is prevalent in closed ballot elections with proportional representation and other real life problems where the decision maker is to choose from groups with an associated hierarchy inside. I introduce ve ordinal decision rules: highest-position, top-q, lexicographic order, max-best, highest-of-best rules and provide axiomatic characterization of them. I also investigate the relationship between ordinal decision rules and the expected utility rule. In particular, whether some ordinal rules induce the same (weak) ranking of ordered sets as the expected utility rule

    The computational complexity of rationalizing Pareto optimal choice behavior

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    We consider a setting where a coalition of individuals chooses one or several alternatives from each set in a collection of choice sets. We examine the computational complexity of Pareto rationalizability. Pareto rationalizability requires that we can endow each individual in the coalition with a preference relation such that the observed choices are Pareto efficient. We differentiate between the situation where the choice function is considered to select all Pareto optimal alternatives from a choice set and the situation where it only contains one or several Pareto optimal alternatives. In the former case we find that Pareto rationalizability is an NP-complete problem. For the latter case we demonstrate that, if we have no additional information on the individual preference relations, then all choice behavior is Pareto rationalizable. However, if we have such additional information, then Pareto rationalizability is again NP-complete. Our results are valid for any coalition of size greater or equal than two.

    The computational complexity of rationalizing Pareto optimal choice behavior.

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    We consider a setting where a coalition of individuals chooses one or several alternatives from each set in a collection of choice sets. We examine the computational complexity of Pareto rationalizability. Pareto rationalizability requires that we can endow each individual in the coalition with a preference relation such that the observed choices are Pareto efficient. We differentiate between the situation where the choice function is considered to select all Pareto optimal alternatives from a choice set and the situation where it only contains one or several Pareto optimal alternatives. In the former case we find that Pareto rationalizability is an NP-complete problem. For the latter case we demonstrate that, if we have no additional information on the individual preference relations, then all choice behavior is Pareto rationalizable. However, if we have such additional information, then Pareto rationalizability is again NP-complete. Our results are valid for any coalition of size greater or equal than two.
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