By P. Levine, J.-P. Ponssard (auth.), S. J. Brams, A. Schotter, G. Schwödiauer (eds.)
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Additional info for Applied Game Theory: Proceedings of a Conference at the Institute for Advanced Studies, Vienna, June 13–16, 1978
They all count the coalitions for which a voter is critical and differ only in their normalizations. B and C/ will attribute unit power to a voter only if he is a dictator. CP, on the other hand, gives a voter unit power if he holds a veto. All these indices give a dummy voter, a voter who is never critical, zero power. 42 Chr. H. 2 Satisfaction We shall define a measure of satisfaction for simple games based on work by Nevison/Schoepke/Zicht [1978). The measure which we shall define applies to any simple game and is based on the following model.
Straffin [ 1978] also develops this approach to power. Further generalization suggests that a suitable definition for power derived from any source in a voting situation would be the gain in satisfaction over that which could be expected by a dummy. Since in voting situations we are able to measure satisfaction and structural power, we have a basis for further inquiry into power derived from other sources. 3. The Paradoxes of Power In this section we discuss two "paradoxes" of power which have been presented in the literature.
This says that p = 11 ,p 2 s I N I no set is profitable and the set N yields zero profit. Thus condition ( 4) is satisfied, since the empty set is also a maximum profit set in this case. If the core is empty, however, then there are no strong equilibrium prices that permit the players to divide the whole value of the game. In this situation an outside entrepreneur will always be able to realize a surplus. This fact is illustrated in the following application. A Fair Wage Problem Let 1, 2, ... , n designate laborers who are available for hire by entrepreneurs.
Applied Game Theory: Proceedings of a Conference at the Institute for Advanced Studies, Vienna, June 13–16, 1978 by P. Levine, J.-P. Ponssard (auth.), S. J. Brams, A. Schotter, G. Schwödiauer (eds.)