Hotelling's model is typically explained using a linear beach where ice cream vendors choose to place their cart in a way to maximize clientele. Beach goers face some cost in coming back from the cart (the ice melts) and prefer to go to the closest one. Imagine there are two sellers, then both will choose to be located exactly next to each other in the middle of the beach. It would be more efficient for them to be placed at the first and second third, thus minimizing total travel for the beach goers, but competitive pressure pushed them to the middle.
In politics, imagine that voters are ranked according their right/left leanings on a line. A pair of political candidates, according to Hotelling, would then choose to hold essentially the same position in the middle of the spectrum. Of particular interest in this respect is the US primary system, where candidates are essentially similar within the party during the primary, and once nominated shift their positions to the middle for the presidential election.
How does this work out when there are three candidates? If you do not allow them to be on the same spot, then the equilibrium is unstable: they converge to the middle, and the one in the middle wants to outflank any one of the other two to gathers his half of the electorate. If you allow them to be on the same spot, they will all be in the middle, gathering exactly on third of the electorate. Now consider the results from Cyprus:
- Ioannis Kasoulides 33.51%
- Demetris Christofias 33.29%
- Tassos Papadopoulos 31.79%
That looks pretty much like a random draw to me...
PS: And for the lighter note: A Swedish song "dubbed" in English.