Vote Trading and the Voting Paradox: A Proof of Logical Equivalence

Riker and Brams have demonstrated the paradox of vote trading (“… that rational trades by all members [may] make everyone worse off”). In so doing the authors indicate the existence of an apparent disequilibrium when vote trading occurs. I extend this latter point and prove that the preference conditions required for vote trading are the same as those which produce the cyclical majority; the conditions for vote trading and the cyclical majority are logically equivalent. The conclusion briefly indicates the impact of this finding with respect to the work of a number of other authors and gives some idea of the restrictions which would be required to eliminate vote trading among rational legislators.