Mathematical Model of the Single Transferable Vote Election

The Single Transferable Vote (STV) is a voting system used in some parts of Britain and Australia today. We model the voting system by randomly generating N candidates over [0,1], and assigning areas closest to them. As N increases, the probability that the STV election and the plurality election will produce the same result decreases. In single-winner elections candidates at .5 have the highest chance of winning when there are two or three candidates. Candidates around .4 and .6 have the highest chance of winning as the number of candidates increases beyond 4. When the initial area before the first elimination is computed for an STV election, it tends to be lower than the initial area of a plurality election. When multiple winners are introduced, the number of relative maxima corresponds to the number of winners in the election. This is the case with both the STV and plurality election, but the maxima and minima are much more distinct for the STV election. When candidates are placed in multiple dimensions, both elections see the maxima of winners near the center. In the STV election, the difference is more distinct; candidates near the middle have a higher chance of winning, and candidates near the edge have a lower chance of winning.