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We call a coalition C ⊆ N of individuals a decisive coalition for alternative a versus alternative b if \(N_{a\succ b}^P\supseteq C\) implies \(a\succ b\)

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We call a coalition C ⊆ N of individuals a decisive coalition for alternative a versus alternative b if \(N_{a\succ b}^P\supseteq C\) implies \(a\succ b\)

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To say that f is weakly Paretian is the same as to say that the grand coalition N is decisive, and to say that f is dictatorial is the same as to say that there exists a singleton that is decisive.

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To say that f is weakly Paretian is the same as to say that the grand coalition N is decisive, and to say that f is dictatorial is the same as to say that there exists a singleton that is decisive.

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To say that f is weakly Paretian is the same as to say that the grand coalition N is decisive, and to say that f is dictatorial is the same as to say that there exists a singleton that is decisive.

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To say that f is weakly Paretian is the same as to say that the grand coalition N is decisive, and to say that f is dictatorial is the same as to say that there exists a singleton that is decisive.

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A social welfare function f is independent of irrelevant alternatives if, for any two alternatives a, b ∈ A, the relative ranking of a and b by the social preference order only depends on the relative rankings of a and b provided by the individuals

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A social welfare function f is independent of irrelevant alternatives if, for any two alternatives a, b ∈ A, the relative ranking of a and b by the social preference order only depends on the relative rankings of a and b provided by the individuals

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We call C weakly decisive for a vs. b if we have at least that \(N_{a\succ b}^P=C\) implies \(a\succ b\)

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The practical acceptability of a voting rule or a fair allocation mechanism depends not only on its normative properties, but also on its implementability in a reasonable time frame.

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The practical acceptability of a voting rule or a fair allocation mechanism depends not only on its normative properties, but also on its implementability in a reasonable time frame.

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a decision problem P is defined as a pair L P ,Y P where L P is a formal language, whose elements are called instances, and Y P ⊆ L P is the set of positive instances.

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the problem of deciding whether a directed graph is acyclic is defined by the set L P of all directed graphs, while Y P is the set of all directed acyclic graphs.

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arch) problem (L P, S P, R P ) in terms of graph theory is: find a nondominated vertex in a directed graph, if any and find all vertices with maximum outdegree are both search problems. Solving the function problem on instance I ∈ L P <span>consists in outputting some S ∈ S P such that (I,S) ∈ R P , if any, and “no solution” otherwise.<span><body><html>

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Formally, an algorithm is polynomial if there exists a k ∈\(\mathbb{N}\) such that its running time is in O(n k ), where n is the size of the input. Here, O(n k ) denotes the class of all functions that, for large values of n, grow no faster than c · n k for some constant number c (this is the “Big-O notation”). For instance, wh

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and columella. View Media Gallery Previous Next: Nerves Blood Supply and Lymphatics <span>The nose, like the rest of the face, has an abundant blood supply. The arterial supply to the nose may be principally divided into (1) branches from the internal carotid, namely the branches of the anterior and posterior ethmoid arteries from the ophth

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