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The prediction value

Maurice Koster (), Sascha Kurz, Ines Lindner and Stefan Napel ()
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Maurice Koster: University of Amsterdam
Sascha Kurz: University of Bayreuth
Ines Lindner: VU University

Social Choice and Welfare, 2017, vol. 48, issue 2, 433-460

Abstract: Abstract We introduce the prediction value (PV) of player i as the difference between the conditional expectations of v(S) when i cooperates or not in a probabilistic TU game. The latter combines a standard TU game and a probability distribution over the set of coalitions. The PV reflects the importance of information about a given player’s behavior for predicting, e.g., committee decisions that are subject to opinion interdependencies. The PV is characterized by anonymity, linearity, a consistency requirement and two normalization conditions. Every multinomial probabilistic value, hence every binomial semivalue, coincides with the PV for a particular family of probability distributions. So the PV can be regarded as a power index in specific cases. Conversely, some semivalues—including the Banzhaf but not the Shapley value—can be interpreted in terms of informational importance.

Keywords: Influence; Voting games; Cooperative games; Banzhaf value; Shapley value (search for similar items in EconPapers)
Date: 2017
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