= Single-peaked preferences
{title2=$a\text{ is a peak on a common linear axis}$}
A strict preference order is single-peaked on an axis when moving away from its most preferred alternative along either one side of the axis makes alternatives less preferred. Comparisons between opposite sides need not follow symmetric physical distance. A profile is single-peaked when all voters' orders share such an axis. This restricted domain admits the <median voter rule>, unlike the unrestricted-domain conclusion of the <Gibbard-Satterthwaite theorem>.
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