The possible existence of various voting paradoxes has been the focus of numerous investigations. This research has largely been dominated by studies that are associated with Condorcet’s Paradox. There is widespread, but not universal, acceptance of the notion that the PMRW is the best candidate for selection in an election process, when such a candidate exists. When Condorcet’s Paradox occurs, there is no PMRW in three-candidate elections, and there is a need to find some other voting mechanism to determine a winner in such cases.
There is a resulting interest in determining estimates of the likelihood that a PMRW exists in various situations. This observation is intensified by the fact that we have seen that the conditions that are necessary for Condorcet’s Paradox to exist are the same as the conditions that are required for the existence a number of other paradoxes, like the Paradox of Multiple Elections and the Vote Trading Paradox. In some cases there are links between the conditions that are necessary for other paradoxes to exist and the conditions for Condorcet’s Paradox, as with the No Show Paradox. Researchers even feel obligated to show that the conditions that are necessary for other paradoxes, like Ostrogorski’s Paradox, to exist are not the same as the conditions that are required for Condorcet’s Paradox to exist.