The prediction value

M. Koster, S. Kurz, I.D. Lindner, S. Napel

    Research output: Contribution to JournalArticleAcademicpeer-review


    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.

    Original languageEnglish
    Pages (from-to)433-460
    Number of pages28
    JournalSocial Choice and Welfare
    Issue number2
    Publication statusPublished - 2017


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