Chapter 16: Voting mysteries: a picture is worth a thousand words
What makes voting paradoxes so intriguing is that voting appears to be conceptually simple. So, why the puzzles? Following the ‘picture is worth a thousand words’ adage, the approach adopted here (starting with Saari 1995, 2008a) uses nothing more complicated than the geometry of a triangle or an ordinary cube to explain several paradoxes. Suppose two proposals designed to help teachers are defeated: Proposition S, to increase salaries, received only 40 percent of the vote; Proposition B, to improve benefits, received 45 percent. The voters clearly have a negative attitude about the teachers because a solid majority, 55 percent, voted against both proposals; an added 5 percent voted to improve benefits but not for a salary increase; only 40 percent wanted to improve salaries and benefits. Is this interpretation correct? It may not be because the same tallies occur should a vast majority, 85 percent of the voters, strongly support the teachers. But with budgetary constraints, the community can afford only one option. As such, 40 percent voted for a salary increase but against benefits; 45 percent voted to improve benefits, but against the salary; and only 15 percent voted against both.
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