Labour’s leadership contest has been thrown wide open by Jeremy Corbyn’s entry into the race. I say this not because I expect Corbyn to win, but because his intervention could change who else does.
To see why, consider how the voting system works. Party members, and others taking part, place 1 against their first choice, 2 against their second choice and so on. When the votes are in, first preferences are counted. If one of the candidates reaches 50 per cent, s/he wins. But if none reaches 50 per cent, the candidate with the fewest first preferences is eliminated, and their supporters’ second preferences are counted; and so on until a winner emerges.
Now, to assess Corbyn’s impact, consider the two following examples. These are illustrations, not predictions. (Ballot papers are not sent out until mid-August; much could change between now and then.) My purpose is to show what could happen rather than what will happen.
Example 1.
Suppose Corbyn hadn’t stood, and the first preference votes were:Andy Burnham 48 per cent
Yvette Cooper 28 per cent
Liz Kendall 24 per cent
Burnham is close to victory on the first count, and wins on the second count with only a tiny number of the second preferences of Kendall’s supporters
Example 2.
Corbyn stands. He picks up the great majority of left-wing voters.For the purposes of this illustration, I assume that (a) around one-in-three voters support Corbyn and (b) Burnham’s first-preference support is hurt disproportionately.
Here is what could now happen:
Jeremy Corbyn 30 per cent
Andy Burnham 26 per cent
Yvette Cooper 24 per cent
Liz Kendall 20 per cent
On these figures, Kendall would be eliminated. Now suppose that her supporters’ second preference divide: 10 per cent Cooper, 6 per cent Burnham, 4 per cent Corbyn. Then the second count produces this outcome:
Jeremy Corbyn 34 per cent
Yvette Cooper 34 per cent
Andy Burnham 32 per cent
Now Burnham is eliminated. If we assume that the next available preferences of his supporters are: Cooper 20 per cent, Corbyn 12 per cent, then Yvette Cooper wins the run-off 54-46 per cent.
Plainly, slight variations in any of those assumptions will produce different outcomes. Indeed, that’s the point: order of elimination could matter as much as the intrinsic popularity of the candidates.
But whatever the detailed numbers, the basic arithmetic of elimination ballots cannot be changed. In a four-way contest, any candidate who wins at least one-third of the votes in the second count is certain of a place in the run-off. It is quite possible that Corbyn will pass this test. Most of his supporters’ second preferences may well be for Burnham—but if he is in the run-off, they won’t count. Hence the possibility of Burnham being eliminated when, had Corbyn not stood, he might have romped to an easy victory.
For those with a passion for democratic theory, the point can be made more strongly. It is possible that Burnham would be the “Condorcet winner” of Labour’s leadership race. The Marquis de Condorcet was an 18th century French mathematician and philosopher who said that elections involving three or more candidates should be won by whoever beats his or her rivals in a series of matched one-on-one contests. In this case—again, this is an illustration, not a prediction—Burnham might well beat Corbyn, Cooper and Kendall in separate, simultaneous, straight fights. However, that is not how Labour will choose its leader, and instead he might be eliminated, so Labour may not end up with a Condorcet-approved victor.
In this blog I have not considered the merits of the candidates, or the political consequences of different outcomes (including what voters and Labour’s enemies might make of a strong Corbyn showing, even if he doesn’t win). We can ponder these another time. Meanwhile, the nature of the elimination system means that Labour’s next few weeks could be surprisingly fraught, which will delight some denizens of the world of politics more than others.
