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تسجيل مستخدم جديدRange results for some social choice correspondences
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Jerry S. Kelly
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Determination of the range of a variety of social choice correspondences: Plurality voting, the Borda rule, the Pareto rule, the Copeland correspondence, approval voting, and the top cycle correspondence
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A social choice correspondence satisfies balancedness if, for every pair of alternatives, x and y, and every pair of individuals, i and j, whenever a profile has x adjacent to but just above y for individual i while individual j has y adjacent to but
just above x, then only switching x and y in the orderings for both of those two individuals leaves the choice set unchanged. We show how the balancedness condition interacts with other social choice properties, especially tops-only. We also use balancedness to characterize the Borda rule (for a fixed number of voters) within the class of scoring rules.
In this paper, we characterize the extremal digraphs with the maximal or minimal $alpha$-spectral radius among some digraph classes such as rose digraphs, generalized theta digraphs and tri-ring digraphs with given size $m$. These digraph classes are
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Necessary and sufficient conditions are derived for a social choice correspondence to be the one that selects the Pareto optimal alternatives.
A {it superpattern} is a string of characters of length $n$ that contains as a subsequence, and in a sense that depends on the context, all the smaller strings of length $k$ in a certain class. We prove structural and probabilistic results on superpa
tterns for {em preferential arrangements}, including (i) a theorem that demonstrates that a string is a superpattern for all preferential arrangements if and only if it is a superpattern for all permutations; and (ii) a result that is reminiscent of a still unresolved conjecture of Alon on the smallest permutation on $[n]$ that contains all $k$-permutations with high probability.
The classical Kruskal-Katona theorem gives a tight upper bound for the size of an $r$-uniform hypergraph $mathcal{H}$ as a function of the size of its shadow. Its stability version was obtained by Keevash who proved that if the size of $mathcal{H}$ i
s close to the maximum, then $mathcal{H}$ is structurally close to a complete $r$-uniform hypergraph. We prove similar stability results for two classes of hypergraphs whose extremal properties have been investigated by many researchers: the cancellative hypergraphs and hypergraphs without expansion of cliques.
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