Title:	Power, Voting, and Voting Power: 30 Years After
Authors:	Manfred J. Holler Hannu Nurmi
Keywords:	Voting
Issue Date:	2013
Publisher:	Springer
Description:	Political, economic, social life is essentially governed according to the power of agents, be they individuals, institutions, states, countries, etc. As a consequence, it is not surprising that power is a major ingredient of social science. Although this appears today as self-evident, it was not the case some decades ago. In 1938, no less than Bertrand Russell devoted a volume to this topic. I am afraid that this book has been rather neglected.1 Russell wrote on page 4: In the course of this book I shall be concerned to prove that the fundamental concept in social science is Power, in the same sense in which Energy is the fundamental concept in physics. Standard microeconomic theory which culminates with the beautiful construction of (Walrasian) general equilibrium theory by Kenneth Arrow, Gérard Debreu, and Lionel McKenzie not only neglects power, but, in some sense, negates it. The general equilibrium framework appears as an ideal situation to which society should tend: perfect competition. The best mathematical tool to model perfect competition was introduced by Robert Aumann. It consists in assuming a continuum of agents, so that each agent’s influence (on prices) is negligible. Whatever the formalization, either a finite number of agents, an infinite countable set of agents or a continuum, with perfect competition, agents are so-called price takers. However, in the real world, there exist markets where there are only a few agents (at least on one side of the market) and these agents will possess market power. In the microeconomic theory Bible (Mas-Colell et al. 1995), Market Power is the title of Chap. 12 (there are 23 chapters). Within Aumann’s measure-theoretic framework it has been possible to formalize at the same time negligible and powerful agents. There is a fundamental difficulty to mix the finite and the infinite, the continuous and the discrete and, in spite of remarkable works by Benyamin Shitovitz and others in the 1970s, the mainstream microeconomic research has followed another route, more or less forgetting the general equilibrium approach, a regression to my view. The ideal of equality has its social choice theoretic version as anonymity. Equality here means basically equality of power. Having equal power for agents does not mean that they have no power (unless we consider that they are elements of a continuum). Rather it means that they have the same power, possibly weak depending on their number. Having the same power leads to the possibility that some agents may have more power than others. Then rather than viewing power as an absolute concept we can consider that it is a relative concept where the different power of various agents can be compared. In the three famous impossibility results of social choice theory (Arrow, Sen and Gibbard–Pattanaik–Satterthwaite Theorems), the notion of power is implicit, hidden in admissible or repulsive concepts. In Arrow’s Theorem, given independence of irrelevant alternatives, a sufficient heterogeneity of agents’ preferences and some level of collective rationality, there is a consistency problem between unanimity—the fact that all the agents taken together as a group are powerful over all social states—and the absence of dictatorship—the fact that a given single individual is powerful over all these social states. In Sen’s theorem (the impossibility of a Paretian liberal) there is an inconsistency between unanimity again and the fact that at least two agents are powerful over at least two social states, this fact being justified by an interpretation in terms of individual rights or freedom of choice within a personal sphere, an idea going back to John Stuart Mill. In Gibbard–Pattanaik–Satterthwaite’s theorem, the conflict is basically between non-dictatorship again and the possibility for an agent to obtain a benefit from acting strategically by misrepresenting her ‘sincere’ preference.
URI:	http://10.6.20.12:80/handle/123456789/52532
ISBN:	978-3-642-35929-3
Appears in Collections:	Population Studies

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.