Consistency and the Competitive Outcome Function
In this paper we are interested in the social choice theory of allocating resources, which are available and can be consumed in integer units only. Since goods are available in integer units only, the social choice theory for such problems cannot exploit any smoothness property, which may otherwise have been embedded in the preferences of the agents. This makes the outcome function approach for the study of such problems quite compelling. Our purpose here is to study outcome functions, which are efficient and consistent. We provide an example to show that the competitive social choice function may not be converse consistent. The competitive outcome function is easily observed to be efficient, consistent and converse consistent. What we are able to show here is that any efficient and consistent outcome function which is “reasonably well-behaved” for two-agent problems, must be a sub-correspondence of the competitive outcome function. Our proof of this result requires the converse consistency of the competitive outcome function.
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