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Its restriction to the pair {$A$,$C$} is identical to that of the profile of the paradox of voting.
Starting from any alternative, moving to a socially preferred one, and from there to the next, you soon find yourself back where you started.[1] This is the "paradox of voting".
May explained this by analogy with the paradox of voting as the result of preferring one alternative to another when it is better by more criteria than not.
There is never to be a cycle of social preferences, like the one derived by pairwise majority decision in the paradox of voting, in Section 1. Arrow did not state SO as a separate condition.
Consider again the paradox of voting of Section 1. $A$ is strictly favoured above $B$, and $B$ above $C$; but, contrary to transitivity, $C$ is strictly favoured above $A$.
In this case there is always a preference profile like the one implicated in the paradox of voting in Section 1, from which pairwise majority decision derives a cycle.
Similar(52)
The paradoxes in voting patterns can be seen in Miami-Dade County, at the center of the ballot dispute.
This so-called "paradox of voting" has intrigued political scientists – especially those who like to see themselves as belonging to the "rational choice" school – for ages.
This illustrates the paradox of contemporary voting rights.
According to the "Downs' Paradox", the costs of voting can be higher than the benefits and this simple cost-benefit calculus leads to a poor electoral turnout.
And as we are likely to see on TV debates before the UK general election, the ongoing paradox of the idea of voting for a party that you don't agree with, or think are liars, in order to stop another party of liars that you don't agree with.
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