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"The True and Unabridged Story of a Most Protean Paradox The centuries-old Paradox of Voting is that majorities sometimes prefer x to y, y to z, and z to x ? a cycle. The discovery of the sources and consequences of such cycles, under majority rule and countless other regimes, constitutes much of the mathematical theory of voting and social choice. This book explores the big questions posed by the Paradox of Voting: positive questions about how to predict outcomes and explain observed stability, and normative questions about how to hold elections, how to take account of preference intensities, the relevance of social welfare to social choice, and challenges to formal "rationality," individual and social"--

The point has been made that vote trading may result in Pareto inefficient legislative outcome; yet vote trading can also result in beneficial consequences for legislators. In every legislative meeting, the outcome that would prevail in the absence of vote trading must be Pareto inefficient; there must be at least one potential vote trade that would make every legislator better off than he would be without vote trading. An example of legislative decision-making processes illustrates this case. Special reference is made to "The Paradox of Vote Trading," by W. H. Riker & S. J. Brams (American Political Science Review, 1973, 66) & "Problems of Majority Voting" by G. Tullock (Journal of Political Economy, 1959, 67) with respect to clarification of certain assumptions concerning the effects of vote trading. C. Grindle.