Abstract Median voter results have played a central role in public economic analyses where there is a linearly ordered set of policy alternatives that is to be voted on. In these analyses, the median voter results themselves have been based on voters' preferences being single-peaked with respect to the ordering for this set. In this paper, we derive conditions that are both necessary and sufficient for such single-peakedness to occur whenever we have economic decision-makers. This leads to certain new median voter results. In addition, it also reveals some important limitations on median voter analyses.