COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 1448

Absenteeism, Substitutes, Complements, and the Banzhaf Index

Thomas Quint

December 2003

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
AMS Classification: 91A12, 91B12