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The prediction value. (English) Zbl 1392.91008

Summary: 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.

MSC:

91A12 Cooperative games
91B12 Voting theory
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