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Absenteeism, Substitutes, and Complements and the Banzhaf Index

Author

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  • 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.

Suggested Citation

  • Thomas Quint, 2003. "Absenteeism, Substitutes, and Complements and the Banzhaf Index," Cowles Foundation Discussion Papers 1448, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1448
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    Keywords

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

    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 - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior

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