Paulos' Hypothetical 1992 Primary Election

Problem During the 1992 Presidential race, mathematician John Allen Paulos offered the following hypothetical primary with five Democratic candidates competing for the votes of 55 delegates from the mythic state of Nebrarkamassacalowa

Bill Clinton (C)   Paul Tsongas (T)   Tom Harkin (H)   Bob Kerrey (K)   Jerry Brown (B)

Number of Delegates with Preference Ranking

Ranking	18	12	10	9	4	2
First Choice	T	C	B	K	H	H
Second Choice	K	H	C	B	C	B
Third Choice	H	K	H	H	K	K
Fourth Choice	B	B	K	C	B	C
Fifth Choice	C	T	T	T	T	T

Solutions to Paulos Problem

Tsongas' argument: only first-place votes count, with a plurality controlling (18 to 12)

Clinton's argument: majority needed, so run-off between top two first-place vote-getters (37 to 18)

Brown's argument: majority needed, so successively eliminate lowest finisher and redistribute votes (final tally 37 to 18)

Kerrey's argument: consider overall rankings by awarding 5 points for first, 4 for second, etc. (191 to Harkin's 189, Brown's 162, Clinton's 156 and Tsongas' 127)

Harkin's argument: consider only head-to-head contests (28-27 over closest rival).