Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userRange results for some social choice correspondences
86
0
0.0
(
0
)
Authors
Jerry S. Kelly
Ask ChatGPT about the research
No Arabic abstract
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
rate research
Read More
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 denoted by $mathcal{R}_{m}^k$, $widetilde{boldsymbol{Theta}}_k(m)$ and $INF(m)$ respectively. The main results about spectral extremal digraph by Guo and Liu in cite{MR2954483} and Li and Wang in cite{MR3777498} are generalized to $alpha$-spectral graph theory. As a by-product of our main results, an open problem in cite{MR3777498} is answered. Furthermore, we determine the digraphs with the first three minimal $alpha$-spectral radius among all strongly connected digraphs. Meanwhile, we determine the unique digraph with the fourth minimal $alpha$-spectral radius among all strongly connected digraphs for $0le alpha le frac{1}{2}$.
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 superpatterns 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 $mathcal{H}$ is 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.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
