Here is an excellent example of social choice paradoxes in practice: the voting system for the Olympic Venue. The article illustrates cycles, failure of unanimity and violations of independence of irrelevant alternatives. A great teaching aid, I will certainly be using it next time I teach my intermediate micro course. I thank Taresh Batra for the pointer.
By the way, there is another perfect social choice example from the olympics. In the 2002 women’s figure skating competition, Michelle Kwan was leading Sarah Hughes when the final skater, Irina Slutskaya took the ice. Slutskaya put in a sub-par performance which was nevertheless good enough to surpass Kwan. But the real suprise was that this performance by Slutskaya reversed the ranking of Kwan and Hughes so that Hughes leaped ahead of both Kwan and Slutskaya and won the gold. In the end, Hughes took the gold, Slutskaya took silver, and Kwan went home with the bronze medal. Here is a an old story.