619 research outputs found

    Maximin Safety: When Failing to Lose is Preferable to Trying to Win

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    We present a new decision rule, \emph{maximin safety}, that seeks to maintain a large margin from the worst outcome, in much the same way minimax regret seeks to minimize distance from the best. We argue that maximin safety is valuable both descriptively and normatively. Descriptively, maximin safety explains the well-known \emph{decoy effect}, in which the introduction of a dominated option changes preferences among the other options. Normatively, we provide an axiomatization that characterizes preferences induced by maximin safety, and show that maximin safety shares much of the same behavioral basis with minimax regret.Comment: 14 page

    Semigroups with if-then-else and halting programs

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    The "if–then–else" construction is one of the most elementary programming commands, and its abstract laws have been widely studied, starting with McCarthy. Possibly, the most obvious extension of this is to include the operation of composition of programs, which gives a semigroup of functions (total, partial, or possibly general binary relations) that can be recombined using if–then–else. We show that this particular extension admits no finite complete axiomatization and instead focus on the case where composition of functions with predicates is also allowed (and we argue there is good reason to take this approach). In the case of total functions — modeling halting programs — we give a complete axiomatization for the theory in terms of a finite system of equations. We obtain a similar result when an operation of equality test and/or fixed point test is included

    External Norms and Rationality of Choice

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    Ever since Sen (1993) criticized the notion of internal consistency of choice, there exists a widespread perception that the standard rationalizability approach to the theory of choice has difficulties in coping with the existence of external norms. We introduce a concept of norm-conditional rationalizability and show that external norms can be made compatible with the methods underlying the rationalizability approach. This claim is substantiated by characterizing norm-conditional rationalizability by means of suitably modified revealed preference axioms in the theory of rational choice on general domains due to Richter (1966; 1971) and Hansson (1968).

    Uncertainty About Evidence

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    We develop a logical framework for reasoning about knowledge and evidence in which the agent may be uncertain about how to interpret their evidence. Rather than representing an evidential state as a fixed subset of the state space, our models allow the set of possible worlds that a piece of evidence corresponds to to vary from one possible world to another, and therefore itself be the subject of uncertainty. Such structures can be viewed as (epistemically motivated) generalizations of topological spaces. In this context, there arises a natural distinction between what is actually entailed by the evidence and what the agent knows is entailed by the evidence -- with the latter, in general, being much weaker. We provide a sound and complete axiomatization of the corresponding bi-modal logic of knowledge and evidence entailment, and investigate some natural extensions of this core system, including the addition of a belief modality and its interaction with evidence interpretation and entailment, and the addition of a "knowability" modality interpreted via a (generalized) interior operator.Comment: In Proceedings TARK 2019, arXiv:1907.0833

    Minimal Stable Sets in Tournaments

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    We propose a systematic methodology for defining tournament solutions as extensions of maximality. The central concepts of this methodology are maximal qualified subsets and minimal stable sets. We thus obtain an infinite hierarchy of tournament solutions, which encompasses the top cycle, the uncovered set, the Banks set, the minimal covering set, the tournament equilibrium set, the Copeland set, and the bipartisan set. Moreover, the hierarchy includes a new tournament solution, the minimal extending set, which is conjectured to refine both the minimal covering set and the Banks set.Comment: 29 pages, 4 figures, changed conten
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