The prediction value

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.

Mostly Sunny: A Forecast of Tomorrow's Power Index Research

“…Carrying methods and insights from non-binary strategic voting over into this domain looks promising. The domain of conventional power index research has also been left by Koster et al's (2014) investigation of the predictive value of knowing an individual voter's decision or voting inclination. Taking the latter as input into a model of an opinion formation process could merge traditional power analysis with the analysis of social dynamics and networks.…”