Denis Mollison: Theory, statistics and politics of preferential voting

The single transferable vote (STV), or "choice voting", is a preferential system that allows the voter to put individual candidates in order of preference, yet achieves a result that is proportional as between political parties [1]. It has been used for local government elections in Scotland since 2007, and the detailed data available [2] (when 10,000 people vote, typically 2,000 different orders of preference may occur) allow investigation of many questions: of political interest, such as the distances between parties in the eyes of voters; of theoretical interest, such as whether Condorcet cycles occur; and of practical interest, such as whether the order of candidates on the voting paper influences the result.

Because it allows wards with different numbers of members, STV can be fitted well to natural communities, with ward boundaries that do not need to change as the population fluctuates. Such a scheme (devised by the speaker) for the UK parliament was considered in 2010 [3], but voted down in what remains probably the most unproportional parliament among western democracies.

Finally, the forthcoming referendum on independence for Scotland provides the impetus to consider the apparently simple but insoluble question of how to make a fair choice among three options: in this case, no change, full financial powers, and independence (or "breaking up the UK" as it is described by opponents). There are logical reasons for thinking that a sequence of two questions is a fair way to present the options, but the preferential data required to test this assessment are not available from the very simple questions that opinion pollsters like to ask.