Absenteeism, Substitutes, Complements and the Banzhaf Index
17 Pages Posted: 8 Apr 2004
Date Written: November 2003
We consider the voting-with-absenteeism game of Quint-Shubik (2003). In that paper we defined a power index for such games, called the absentee index. Our analysis was based on the theory of the Shapley-Shubik power index (SSPI) for simple games.
In this paper we do an analogous analysis, based on the Banzhaf index instead of the SSPI. The result is a new index, called the absentee Banzhaf index. We provide an axiomatization and multilinear extension formula for this index. Finally, we re-explore Myerson's (1977, 1980) "balanced contributions" property, and the concept of substitutes and complements for simple games (Quint-Shubik 2003), again basing our analysis on the Banzhaf index instead of the SSPI.
Keywords: Simple game, Shapley-Shubik power index, Banzhaf index, absenteeism, multilinear extension, balanced contributions, substitute, complement
JEL Classification: C7, C71, D72
Suggested Citation: Suggested Citation