Absenteeism, Substitutes, and Complements in Simple Games

19 Pages Posted: 22 Mar 2004

See all articles by Thomas Quint

Thomas Quint

University of Nevada-Reno, Department of Mathematics

Martin Shubik

Yale University - School of Management; Yale University - Cowles Foundation

Date Written: November 2003

Abstract

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 multilinear extension of the game.

Finally, we define the notion of substitutes and complements in simple games. We compare these concepts with the familiar concepts of dummy player, veto player, and master player.

Keywords: Simple game, Shapley-Shubik power index, absenteeism, multilinear extension, balanced contributions, substitute, complement

JEL Classification: C7, C71, D72

Suggested Citation

Quint, Thomas and Shubik, Martin, Absenteeism, Substitutes, and Complements in Simple Games (November 2003). Available at SSRN: https://ssrn.com/abstract=519463

Thomas Quint

University of Nevada-Reno, Department of Mathematics ( email )

1664 North Virginia
Reno, NV 89557
United States
775-784-1366 (Phone)
775-784-6378 (Fax)

Martin Shubik (Contact Author)

Yale University - School of Management ( email )

Box 208200
New Haven, CT 06520-8200
United States

Yale University - Cowles Foundation ( email )

Box 208281
New Haven, CT 06520-8281
United States
203-432-3694 (Phone)
203-432-6167 (Fax)

HOME PAGE: http://cowles.econ.yale.edu/P/au/d_shubik.htm

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