5,822 research outputs found

    Green in Simpler than Grue

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    Questions in Decision Theory

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    Free Will: A Rational Illusion

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    On the Union of Arithmetic Progressions

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    We show that for every Δ>0\varepsilon>0 there is an absolute constant c(Δ)>0c(\varepsilon)>0 such that the following is true. The union of any nn arithmetic progressions, each of length nn, with pairwise distinct differences must consist of at least c(Δ)n2−Δc(\varepsilon)n^{2-\varepsilon} elements. We observe, by construction, that one can find nn arithmetic progressions, each of length nn, with pairwise distinct differences such that the cardinality of their union is o(n2)o(n^2). We refer also to the non-symmetric case of nn arithmetic progressions, each of length ℓ\ell, for various regimes of nn and ℓ\ell

    Majority vote following a debate

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    Voters determine their preferences over alternatives based on cases (or arguments) that are raised in the public debate. Each voter is characterized by a matrix, measuring how much support each case lends to each alternative, and her ranking is additive in cases. We show that the majority vote in such a society can be any function from sets of cases to binary relations over alternatives. A similar result holds for voting with quota in the case of two alternatives.Case-based decision theory; voting theory; debates
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