Preference Intervals

A preference interval stores information about a voter's preferences for candidates. We visualize this, unsurprisingly, as an interval. We take the interval \([0,1]\) and divide it into pieces, where each piece is proportional to the voter's preference for a particular candidate. If we have two candidates \(A,B\), we fix an order of our interval and say that the first piece will denote our preference for \(A,\) and the second for \(B\). As an abuse of notaton, one could write \((A,B)\), where we let \(A\) represent the candidate and the length of the interval. For example, if a voter likes candidate \(A\) a lot more than \(B\), they might have the preference interval \((0.9, 0.1)\). This can be extended to any number of candidates, as long as each entry is non-negative and the total of the entries is 1.

We have not said how this preference interval actually gets translated into a ranked ballot for a particular voter. That we leave up to the ballot generator models, like the Plackett-Luce model.

It should be remarked that there is a difference, at least to VoteKit, between the intervals \((0.9,0.1,0.0)\) and \((0.9,0.1)\). While both say there is no preference for a third candidate, if the latter interval is fed into VoteKit, that third candidate will never appear on a generated ballot. If we feed it the former interval, the third candidate will always appear at the bottom of the ballot.

VoteKit provides an option, from_params, which allows you to randomly generate preference intervals. For more on how this is done, see the page on Simplices.