Abstract
It is now well known that under some eminently acceptable behavioral rule in comparing various power sets every nonimposed, binary, multivalued social choice mechanism is strategy-proof or oligarchic. Various attempts have been made to resolve the paradox either by relaxing binariness or by weakening the notion of strategy-proofness. By relaxing both binariness and the notion of strategy-proofness this paper shows that the trade-off between weak strategy-proofness and various unacceptable power structures, such as oligarchy or dictatorship, would remain intact.
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