The influence relation for ternary voting games

Cameron Parker

Games and Economic Behavior, 2012, vol. 75, issue 2, 867-881

Abstract: Although simple games are very useful in modeling decision-making bodies, they allow each voter only two choices: to support or oppose a measure. This restriction ignores that voters often can abstain from voting, which is effectively different from the other two options. Following the approach of Felsenthal and Machover (1997), for modeling voting with abstentions, we will look at the extension of the influence relation for simple games to the Ternary Voting Game given in Tchantcho et al. (2008). That paper showed that the influence relation is ordinally equivalent to the classical Banzhaf and Shapley–Shubik indices in a class of games called weakly equitable. In this paper, we will show that this result does hold true for all Ternary Voting Games. Also we will show that adding a third voting option allows for asymmetric distribution of power that cannot be achieved by any simple game.

Keywords: Cooperative games; Ternary voting games; Ordinal equivalence; Hierarchies (search for similar items in EconPapers)
JEL-codes: C71 D72 (search for similar items in EconPapers)
Date: 2012
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (16)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:gamebe:v:75:y:2012:i:2:p:867-881

DOI: 10.1016/j.geb.2012.02.007

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