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Absenteeism, Substitutes, and Complements and the Banzhaf Index

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Author Info
Thomas Quint (University of Nevada, Reno)
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.

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File URL: http://cowles.econ.yale.edu/P/cd/d14a/d1448.pdf
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Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 1448.

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Length: 16 pages
Date of creation: Dec 2003
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Handle: RePEc:cwl:cwldpp:1448

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Related research
Keywords: Simple game; Shapley-Shubik power index; Banzhaf index; Absenteeism; Multilinear extension; Balanced contributions; Substitute; Complement;

Find related papers by JEL classification:
C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Models of Political Processes: Rent-seeking, Elections, Legislatures, and Voting Behavior

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