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Full-Text Articles in Social and Behavioral Sciences
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 …