As campaigning for the AV referendum enters its final week, the New Scientist magazine has looked at the impacts of AV from a mathematical perspective.

One interesting point to emerge was that according to economist Dennis Leech of the University of Warwick, under AV it could prove costly to be too popular in first preference votes.

As the New Scientist reported: “he also highlights some problems with AV, including the finding that, in some situations, a candidate's chances of winning can actually be reduced if voters rank them higher on the list.”

Intrigued by this possibility, Full Fact went looking for answers.

Professor Leech makes this point in a blog that looks at the mathematical implications of both AV and First Past the Post.

He says: “A candidate who would win under AV… with a particular set of voter preferences, could actually become a loser if voters changed their preferences so as to make him or her more popular. This paradoxical possibility seems perverse and profoundly at odds with the democratic principle. AV can fail to reflect voters’ preferences in a direct and positive way. This is a well-known theoretical property of AV but we do not know how likely it is to be a problem in practice.”

This scenario is laid out in a practical example by the campaign website AV2011, which shows an election where Candidate A only wins if some of his/ her first preference votes are instead given to Candidate C to ensure they are not eliminated with the fewest votes. Instead under this scenario, Candidate B is first eliminated, with the majority of his/her second preference votes going to Candidate A.  If Candidate C had been eliminated in the first round, most of their second preferences would have gone to Candidate B, allowing Candidate B to win.

Clearly this is a hugely complicated possibility, which would be dependent upon a very particular voting set-up in a constituency. However it is theoretically possible that with AV a candidate could lose with a large number of first preference votes where they might have won if they had got fewer first preference votes.

If ever such a scenario did develop it could therefore add to the tactical considerations that AV could bring about (an issue that we’ve already looked at). As with many possibilities discussed during this campaign, whether it is a practical or purely hypothetical scenario would only become clear if the new electoral system was adopted. 

UPDATE

AV2011 got in touch with us about the example scenario from their website that we used in this article.

They pointed us to the example below from their website, as a better case study of a situation where is does not pay for a Candidate under AV to seek first preference votes from a wider audience than their own core voters.