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Absenteeism, Substitutes, Complements, And The Banzhaf Index, Thomas Quint
Absenteeism, Substitutes, Complements, And The Banzhaf Index, Thomas Quint
Cowles Foundation Discussion Papers
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 …
Absenteeism, Substitutes, And Complements In Simple Games, Thomas Quint, Martin Shubik
Absenteeism, Substitutes, And Complements In Simple Games, Thomas Quint, Martin Shubik
Cowles Foundation Discussion Papers
A voting with absenteeism game is defined as a pair (G;r) where G is an n-player (monotonic) simple game and r is an n-vector for which r i is the probability that player i attends a vote. We define a power index for such games, called the absentee index. We axiomatize the absentee index and provide a multilinear extension formula for it. Using this analysis we re-derive Myerson’s (1977, 1980) “balanced contributions” property for the Shapley-Shubik power index. In fact, we derive a formula which quantitatively gives the amount of the ‘balanced contributions” in terms of the coefficients of the …