Absenteeism, Substitutes, and Complements and the Banzhaf Index

Thomas Quint
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Thomas Quint: University of Nevada, Reno

No 1448, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: 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 (search for similar items in EconPapers)
JEL-codes: C7 C71 D72 (search for similar items in EconPapers)
Pages: 16 pages
Date: 2003-12
New Economics Papers: this item is included in nep-mic
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