For me, Ed Miliband’s victory in the Labour-leadership contest, announced on Saturday, is an illustration of the flaws of the AV system, used for the election.

For a start, it feels as though David Miliband was the rightful winner and was cheated of victory by the voting system as much as he was defeated by the union vote in the electoral-college system. More Labour MPs / MEPs and ordinary members chose Miliband Sr as the best person for the job at every stage of the contest, including when the second, third or fourth preferences of those who’d initially voted for candidates other than the Miliband duo were added to his total. However, it was Ed Miliband’s leadership in the other college – the ‘Affiliated Members’, or unions – that brought him overall victory in the fourth round.

Fair enough, Labour decided to choose their leader via this electoral-college system, so no one can complain if one of the three colleges swung the ballot in Ed Miliband’s favour. However, it did so only in the fourth round, i.e. again via the second, third or fourth preferences of people who’d voted for one or all of the three other candidates as their first, second and third choice. So effectively, the views of voters who regard Ed Miliband as not the best candidate for the job – including those who regard him as only the fourth-best person for the job – were allowed to trump the choice of the plurality of voters who definitely regarded David Miliband as the best person in the running.

Surely, first preferences ought to carry more weight than second or subsequent preferences, if only by reference to what first preferences are supposed to mean: a voter’s considered, deliberate selection of a candidate as the best person for the job (i.e. a wholly or mainly positive choice) – as opposed to a mere second best, or the candidate most likely to defeat the person a voter doesn’t want to win, or even the least-bad candidate (more negative choices).

Putting this another way, if you calculated the ‘aggregate preference’ for each candidate as an average of each voter’s ranking of them, then it’s quite likely that Miliband Sr will have obtained a score nearer to one (i.e. highest preference across the electoral constituency overall) than his younger brother. We’ll never actually know this, unless the Labour Party responds to my request for a break-down of the vote giving the number of first, second, third, fourth and fifth preferences received by each candidate. But I’m not holding my breath.

The point is, if Ed Miliband’s leadership credentials are being challenged ostensibly because of his victory’s reliance on the union vote, then this will also be playing on nagging doubts about whether he was a worthy winner across all three colleges, precisely because his victory was dependent on winning more lower-preference and fewer higher-preference votes than his brother.

‘But’, I hear you say, ‘at least Ed Miliband won an overall majority in the fourth round, based on the AV system’. Well, actually, he didn’t, because the vote wasn’t counted correctly – or at least, it wasn’t counted in the way AV ballots will be counted in UK-parliamentary elections if AV wins out in the referendum next May. That is to say, at each round in the leadership count, the percentages were calculated on the basis of the number of votes still in play rather than as a share of the total number of votes cast. In other words, at each round, some of the ballots were ‘exhausted’: voters did not list any subsequent preferences. In AV as it is proposed to implement it for parliamentary elections, these exhausted ballots would still be used to calculate the overall shares of the vote; but they were ignored in the Labour-leadership count.

This means that – and don’t worry double-checking, I’ve done the maths – the true percentages for each candidate across the three electoral colleges, taking into account the exhausted ballots, were as follows:

Candidate                 Ed Miliband           David Miliband
MPs / MEPs                  15.288                         17.544
Party members              14.711                         17.554
Unions                           18.842                         12.666
Total                               48.841                         47.764

So in fact, this election is another illustration of how AV can produce no overall majority for any candidate. In reality, however, both candidates probably enjoyed some degree of support from a majority of the party. That’s because the second and subsequent preferences that weren’t counted were those of voters who chose either David or Ed as their first preference. It’s quite likely that enough David voters would have indicated Ed as their second preference to give Ed a higher majority of all first and second preferences than that which would have been obtained by David – or vice-versa: David could have won a higher majority than Ed thanks to a greater willingness on the part of Ed voters to put David down as their second choice. But we won’t know that, if indeed we ever will, until the Labour Party gives us the full facts.

Meanwhile, doubts will persist as to whether Ed was a worthy winner and the considered choice of the Labour Party. And AV plays a major part in that uncertainty.