“137 losers would be MPs under AV… Even one wannabe MP who finished EIGHTH might have made it into the Commons.” The Sun, 2 May 2011

“Candidates who came third in 137 seats at last year’s election could have ended up becoming MPs.” Daily Mail, 2 May 2011

The possibility that third-placed candidates may be able to leapfrog their way to Westminster has been one of the cornerstones of the No camp’s campaigning.

When the Prime Minister raised the issue last month Full Fact took a look at the international precedents for the election of candidates ranking third after the first round of counting going on to win under AV, and found that examples were extremely rare, if indeed they existed at all.

However reports surfaced earlier this week that suggested that as many as one fifth of all seats in the Commons could have been won by candidates coming from third in the first round of counting, and one candidate could even have triumphed from an unlikely eighth place. So just how likely is such a scenario?

The stories appearing in the Sun and the Daily Mail take their provenance from Conservative Party research into the matter, which in turn uses constituency data from the last election.

In 2010, some 218 MPs were elected with the support of at least half of the electorate, which if voting patterns were unchanged, would have produced exactly the same result under AV. (One attempt to account for changed voting patterns suggested that the number of MPs elected with majority support after the first round may rise to 234, excluding Northern Ireland).

Of the remaining seats, 295 were effectively two-horse races, where the combined number of ballots cast for other candidates were insufficient to get any other candidate ahead of either of the two front-runners.

However in the remaining 137 constituencies there were enough votes cast for third parties and minor candidates to theoretically see someone come from third place or lower after the first round of counting to eventually win.

However whilst theoretically the claim checks out, in practice the grounds for supposing 137 MPs might have been elected from third place are far shakier.

For example, the most extreme case highlighted by the research is that of Richard Turner-Thomas, who stood as an independent candidate in the Welsh constituency of Torfaen. Despite finishing eighth with just 607 of the 37,640 votes cast, it is claimed that Mr Turner-Thomas could have gone on to win under AV.

Whilst hypothetically this is true, it would require Mr Turner-Thomas to pick up virtually all the second and subsequent preferences cast – a feat that would belie his lowly finish in the original ballot. To get through the first two rounds of counting alone, Mr Turner-Thomas would have had to attract overwhelming second preference support from both Green Party and UKIP voters, something of an unlikely coalition.

A report published by the British Election Study’s Professor David Sanders suggested that 88 per cent of Green voters would give their second preference vote to one of the three main parties, whilst 71 per cent of UKIP voters would do likewise.

So whilst it might be theoretically conceivable for 137 MPs to have been elected from third place or lower under AV, the actual number is likely to be much smaller, and indeed it may not happen at all. So whilst the papers may be within their rights to raise this possibility, however unlikely, it certainly stretches credulity to claim, as the Sun does in its headline, that 137 third placed candidates "would be MPs" under AV. We will be contacting the paper to ensure that this is amended.