CONDITIONS ON PREFERENCES THAT GUARANTEE A SIMPLE MAJORITY WINNER.

In recent years, a number or authors have identified conditions on individual preference orders that imply transitive majorities or which imply that at least one alternative is not beaten by any other alternative under simple majority comparison. Within the context of a three-alternative situation, this paper summarizes these contributions and proves several new results that complete an analysis of sets of individual preference orders that guarantee a simple-majority winner among the three alternatives. Along with guarantees and odd-guaratees for sets of strict partial orders authors of this article consider the guaratees notions when all orders are required to be weak orders. Four definitions will be used to identify restrictions on individual preference orders taht will be used in the analysis. The article further presents numerical presentation of the research topic.