single-peakedness

The property that the available options can be ranked along a continuum in such a way that every voter's preferences can be represented in one of three ways:

(1) she likes the ‘left’most option best and each successively more ‘right’ist option less the more ‘right’-wing it is;
(2) she likes the ‘right’most option best and each successively more ‘left’ist option less the more ‘left’-wing it is;
(3) she likes some intermediate option best and each other successively less as it becomes more ‘left’- or ‘right’-wing.

‘Left’ and ‘right’ are so printed because the continuum need not be literally from left to right. If single-peakedness holds, the median voter's favourite option is the Condorcet winner, and will win a simple majority vote against any other. If it does not hold (for instance, because some voters consider the ‘centre’ option the worst, however the options are arranged along the continuum), then there may be a cycle in majority rule. See also Condorcet; Black.