This is the “paradox of voting”. Discovered by the Marquis de Condorcet (1785), it shows that possibilities for choosing rationally can be lost when individual preferences are aggregated into social preferences. Voter 1 has \(A\) at the top of his individual ordering. This voter’s preferences can be maximized, by choosing \(A\). The preferences of 2 or 3 can also be maximized, by choosing instead their maxima, \(B\) or \(C\). Pairwise majority decision doesn’t result in a social maximum, though. \(A\) isn’t one because a majority prefers something else, \(C\).  Likewise, \(B\) and \(C\) are not social maxima. The individual preferences lend themselves to maximization; but, because they cycle, the social preferences do not.