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Reconstructing Weighted Voting Schemes from Partial Information About Their Power Indices by Bennett, Huck; De, Anindya; Servedio, Rocco A.; Vlatakis-Gkaragkounis, Emmanouil-Vasileios is a scholarly article available to read on EtoBox.

What is Reconstructing Weighted Voting Schemes from Partial Information About Their Power Indices about?

A number of recent works [Goldberg 2006; O'Donnell and Servedio 2011; De, Diakonikolas, and Servedio 2017; De, Diakonikolas, Feldman, and Servedio 2014] have considered the problem of approximately reconstructing an unknown weighted voting scheme given information about various sorts of ``power indices'' that characterize the level of control that individual voters have over the final outcome. In the language of theoretical computer science, this is the problem of approximating an unknown linear threshold function (LTF) over $\{-1, 1\}^n$ given some numerical measure (such as the function's $n$ ``Chow parameters,'' a.k.a. its degree-1 Fourier coefficients, or the vector of its $n$ Shapley indices) of how much each of the $n$ individual input variables affects the outcome of the function. In this paper we consider the problem of reconstructing an LTF given only partial information about its Chow parameters or Shapley indices; i.e. we are given only the Chow parameters or the Shapley indices corresponding to a subset $S \subseteq [n]$ of the $n$ input variables. A natural goal in this partial information setting is to find an LTF whose Chow parameters or Shapley indices corresponding

Author

Bennett, Huck; De, Anindya; Servedio, Rocco A.; Vlatakis-Gkaragkounis, Emmanouil-Vasileios

Published

2020

Language

EN