This page illustrates the results of STV using a two-dimensional issue space.
By reducing the winner count to one, IRV can also be demonstrated. There are always 10 candidates,
but the number of preferences expressed by the voters can be adjusted, to view the effects of
missing out on some of the preference information. By reducing the preferences to just one, with
two STV winners (noting that no preferences would be able to transfer), you can simulate an ordinary
two-round runoff.
The original intent of this page was to explore the possibility of using three-winner STV as
the first phase of a two-round single-winner method. Suppose that three candidates are found who
represent the voters evenly. If voters were
obliged to rank all three candidates, we would have a good chance of finding the median voter's
preferred candidate, either because there is a majority favorite (perhaps if the three
candidates were not chosen well) or because, assuming voter sincerity and the validity of the notion
of an underlying issue space, the median voter's first preference might receive no or nearly no last
preferences. (Though for strategy reasons we probably wouldn't actually use "minimum last preference
count" as an election method.)
The likely truth of this is more obvious if the "plot height" of the issue space is small, since
it's harder then to divide the electorate into thirds without a clear center.
Each dot represents one vote plus a small random amount. Candidates are also voters.
In the second plot, voters are colored according to some candidate that they helped to elect with
at least 1/4th of their vote. When there are multiple such candidates for the voter, one
is chosen at random to provide the color. Voters who are unable to contribute to the election of any
candidate remain colored black.