The plurality majority converse (PMC), the strongest possible instance
of a plurality majority disagreement, is studied in the context of si
ngle peakedness. After sharpening some of the notions of unfolding the
ory we construct PMCs for the case where all voters' preference orders
are single peaked on a common ordering of the political parties conte
sting in an election. A PMC then appears to result from a particular d
istribution of the voters' preference orders in which the political ce
nter has been dissolved towards the extremes. The possibility of a PMC
in some of the elections in Weimar Germany is examined. Elections tha
t avoid plurality majority disagreements by having voters choose one o
f a constrained set of preference orders over the contesting parties a
re discussed.