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
2 ) Suppose instead that he acts as a price taker. Then the payoff function for the sellout game is the following modified form of (3 ): i gets his asking price Pi if he is bought, and otherwise. 3 ) In this case the voters at the low end of the curve can strategically raise their prices, and command a surplus. If a majority of k is required to win, n/2 < k < n, and M is sufficiently large (M ~ k P%+ 1 ) then each of the first k players can raise his price top= P%+ 1 , the opportunit y cost of the (k + l)st player; moreover these prices, (p, ...
D. We see that our stronger form of the paradox of quarreling occurs for all the indices of power and neither of the indices of satisfaction. Thus the behavior of the power indices is characteristic of power and cannot be attributed to its derivation from satisfaction. 3 The Paradox of Size The second paradox of power is closely related to the paradoxes of quarreling which we have just considered. Brams [ 1975, p. " This paradox presupposes that voters gain an advantage by forming a coalition which acts as a unit in whatever voting takes place.
The question that arises, however, is how bad a proxy are they? In other words, if we were to increase (or decrease) a voter's voting weight within a voting body, would his resulting power within the organization always increase (or dt:crease), but possible not in proportion to the increase in his weight, or could his int1uence actually decrease (or increase)? This note presents the results of two previous studies of this question done by FischerjSchotter 11978] and DreyerjSchotter 11978). This results are clear.