Absenteeism, Substitutes, Complements and the Banzhaf Index

17 Pages Posted: 8 Apr 2004

See all articles by Thomas Quint

Thomas Quint

University of Nevada-Reno, Department of Mathematics

Date Written: November 2003

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

JEL Classification: C7, C71, D72

Suggested Citation

Quint, Thomas, Absenteeism, Substitutes, Complements and the Banzhaf Index (November 2003). Available at SSRN: https://ssrn.com/abstract=519624

Thomas Quint (Contact Author)

University of Nevada-Reno, Department of Mathematics ( email )

1664 North Virginia
Reno, NV 89557
United States
775-784-1366 (Phone)
775-784-6378 (Fax)

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