Abstract
Intransitive, incomplete and discontinuous preferences are not always irrational, but may be based on quite reasonable considerations. Hence, we pursue the possibility to build a theory of social choice on an alternative foundation, viz. on individual reference tournaments. Tournaments have been studied for a long time independently of rankings and a number of results are therefore just waiting to be applied in social choice. Our focus is on Slater's rule. A new interpretation of the rule is provided.
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