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Contributions to Game Theory and Management, 2009, Volume 2, Pages 63–71
(Mi cgtm39)
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Weightedness for Simple Games with Less than 9 Voters
Josep Freixasab, Xavier Molinerocb a Dept. de Matemàtica Aplicada 3
b Escola Politècnica Superior d’Enginyeria de Manresa, E-08242 Manresa, Spain. Universitat Politècnica de Catalunya
c Dept. de Llenguatges i Sistemes Informàtics
Abstract:
In voting systems, game theory, switching functions, threshold
logic, circuits and electrical engineering,
coherent structures and systems' reliability and cryptography,
among other fields,
there is an important
problem that consists in determining the weightedness of a binary voting
system by means of trades among voters in sets of coalitions.
(Taylor and Zwicker, 1995) construct a sequence of games $G_k$ based on magic squares
which are $(k-1)$-trade robust but not $k$-trade robust, each one of
these games $G_k$ has $k^2$ players.
(Freixas and Molinero, 2008) propose a refinement on trade robustness
called invariant-trade robustness and prove that
as few as $2k+1$ voters are needed to find games being
$k$-invariant trade robust but not
$(k+1)$-invariant trade robust.
In this work we classify all simple games with
less than nine players according to the two criteria:
invariant-trade robustness and trade robustness.
The classification obtained in this work with eight players is new.
Moreover, some new experiments establish new conjectures about the trade
robustness of complete simple games.
Keywords:
Simple games, Asummability, Trade robustness, Invariant-trade robustness.
Citation:
Josep Freixas, Xavier Molinero, “Weightedness for Simple Games with Less than 9 Voters”, Contributions to Game Theory and Management, 2 (2009), 63–71
Linking options:
https://www.mathnet.ru/eng/cgtm39 https://www.mathnet.ru/eng/cgtm/v2/p63
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Abstract page: | 138 | Full-text PDF : | 74 | References: | 28 |
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