Vote Trading and the Voting Paradox: Rejoinder

David H. Koehler

doi:10.2307/1958413

Vote Trading and the Voting Paradox: Rejoinder

American Political Science Review ◽

10.2307/1958413 ◽

1975 ◽

Vol 69 (3) ◽

pp. 967-969 ◽

Cited By ~ 2

Author(s):

David H. Koehler

Keyword(s):

Voting Paradox ◽

Vote Trading

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Collective Choice, Separation of Issues and Vote Trading

American Political Science Review ◽

10.1017/s0003055400265209 ◽

1977 ◽

Vol 71 (3) ◽

pp. 999-1010 ◽

Cited By ~ 43

Author(s):

Thomas Schwartz

Keyword(s):

Choice Model ◽

Winning Coalition ◽

Spatial Models ◽

Solution Concept ◽

Collective Choice ◽

Voting Paradox ◽

Vote Trading ◽

Natural Solution ◽

Feasible Outcome

In legislatures and committees, a number of issues are voted on separately, leading to an outcome consisting of positions on each of these issues. I investigate the effects this separation of issues has on collective choices, assuming a very abstract collective choice model, whose assumptions are presupposed by many less abstract models, notably spatial models. Assuming the model, if there exists an undominated outcome (one to which no winning coalition prefers any other feasible outcome), it must be chosen in the absence of vote trading, although vote trading can (perversely) lead to a very different outcome. But vote trading does not necessarily lead to a “voting paradox” situation, contrary to several recent papers. The model enables us to define a natural solution concept for the case where every feasible outcome is dominated. Variations on this concept are explored. The effects of weakening the model are investigated.

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

American Political Science Review ◽

10.2307/1958410 ◽

1975 ◽

Vol 69 (3) ◽

pp. 954-960 ◽

Cited By ~ 23

Author(s):

David H. Koehler

Keyword(s):

Voting Paradox ◽

Logical Equivalence ◽

Cyclical Majority ◽

Vote Trading ◽

The Impact

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.

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