Transitive preferences in a circular order
Some help with the following problem (from Political Economy, but mainly logic) would be much appreciated!
"Citizens of a country are uniformly distributed over a circle of radius 2 (interior excluded). The country has to choose a location for its capital city, which can be any point on the circle. There is a single road in this country which coincides with the circle. Thus, citizens can travel only along the circle. Each citizen's most preferred location is the point on the circle where she is located. The farther the location is from a citizen's most preferred location, the less she likes it.
Q) Does majority voting generate a complete and transitive social preference relation over the set of locations? If not, why not? If yes, what is the social preference relation?"