Circle Pictograms for Vote Vectors
Eivind Stensholt · SIAM Review · 1996
Let $a,b$, and c be three alternatives in an election and let $abc$ be the fraction of the electorate with preference order $a \succ b \succ c$, etc. This paper introduces the pictogram for the vote vector $V = (abc\,acb\,cab\,cba\,bca\,bac)$, which consists of a circle and three pairwise intersecting chords. It is proven that for any V there exists a unique pictogram such that the six domains along the circumference, listed counterclockwise, are proportional to the components of V. The Condorcet paradox is discussed by means of pictograms and other simple geometric ideas. Real political opinion poll data are visualized with pictograms, and it is shown how political movements can be monitored this way.