AV 2.0: revision to the AV counting method

Further on the question of the counting method for AV elections, it occurs to me that there is a simple revision to the AV counting method that would remedy some of the main concerns about its fairness and complexity. For the still non-initiated, AV elections are conducted as follows:

  1. Voters list candidates in order of preference
  2. If a majority indicates one candidate as their first preference, that candidate is automatically elected
  3. If not, the candidate with the least first preferences is eliminated, and the second preferences of those who voted for him / her are redistributed to the remaining candidates
  4. If there is still no majority for any candidate, this process is repeated until one candidate does have a majority of the votes remaining in play, which may not be an absolute majority of all votes cast, as some voters will not indicate an exhaustive list of preferences, so their vote drops out.

One of the main problems with this procedure is that some voters – those who voted for candidates obtaining only a small total of first preferences – can in theory express multiple preferences as their vote is transferred from one candidate to another; while other voters’ second preferences – to say nothing of their subsequent preferences – aren’t counted at all because their first-preference candidate remains in the race. There are two problems with this:

  1. The result is determined by an inconsistent set of preferences: first preferences of a large number of voters, second preferences of a smaller set, third preferences of another set, and so on
  2. And it’s possible a ‘losing’ candidate may have a larger combined total of first and subsequent preferences than the ‘winner’, for the very reason that the second preferences of the two leading candidates (which could be for that losing candidate) aren’t counted. This works against parties at the centre of the political spectrum to the extent that the candidates eliminated early from the race are likely to be to the right and left of the Conservatives and Labour, so most of their votes are ultimately likely to be transferred to the Tories and Labour; whereas many of the second preferences of Conservative and Labour voters (not counted) will be for the Lib Dems.

The way you could remedy this would be as follows:

  1. If there is no majority of first preferences, eliminate all candidates that have no chance of winning, i.e. could not overtake the leading candidate under any conceivable preference-transfer scenario. This is easy to work out (see further below). In most English seats, this would leave only two candidates in the race, occasionally three and even more rarely four.
  2. Add to the totals of the remaining candidates any second preferences for them of voters whose first preference was one of the eliminated candidates. Ignore for the time being any third or subsequent preferences that are for the remaining candidates.
  3. If no candidate has yet obtained a majority, add to the total(s) of the other remaining candidate(s) the second preferences only (but not the subsequent preferences) of voters whose first preference was for the lowest-placed candidate still in the race. In other words, if there are three candidates left at this stage, the second preferences of voters whose first preference was the candidate in third position should be added as appropriate to the totals for the other two candidates left running. (If there are only two candidates left, the same applies: if any first-preference voter for the second-placed candidate has indicated the candidate in the lead as their second preference, that second preference should be added to the leading candidate’s total.)
  4. If this procedure still fails to produce a majority, then it should be repeated as many times as necessary. E.g. in a three-horse race, the next step would be to allocate the second preferences of voters for the second-placed candidate to the first- and third-ranked candidates as applies; or in a two-horse race, the next step is to allocate the second preferences of those whose first preference was the leading candidate to the candidate in second position (assuming any voters for the leading candidate did indicate the second-placed candidate as their second preference). You would also allocate the second preferences of voters for the leading candidate to the two other candidates in a three-horse race if redistributing the second preferences of voters for the third- and second-placed candidates had failed to produce a majority.
  5. If all of these steps continue not to break the deadlock, the process is repeated using third preferences; except this time, every single third-preference vote that was for any of the remaining candidates is added in a single step to their totals. If there is still no majority, the same procedure is carried out using fourth preferences, and so on until a majority is reached or there are no more preferences left to redistribute, in which case the candidate with the highest share of the vote (a plurality) wins.

This sounds complicated, and in some ways it is, as AV is an inherently complicated, convoluted system. However, in practice, this involves fewer redundant stages in the counting process than the present AV rules; and if you follow it step by step, it is logical and easily understood.

For a start, the number of counting stages is instantly reduced by eliminating all candidates that can’t win in one go in the event that no candidate has a majority of first preferences. The candidates who can’t win can easily be worked out. The last-placed candidate is automatically eliminated. If there are then, say, six candidates left, then if the combined first-preference total of the candidate in sixth position and the eliminated candidate is no greater than the fifth-placed candidate’s first preferences (i.e. if every single voter for the eliminated party gave the party in sixth their second preference), then that candidate is also eliminated. If, however, the sixth-placed candidate did overtake the candidate in fifth in this way, then you add the first-preference votes for the originally fifth-ranked candidate to their total; but if this in turn is no greater than the total of first preferences won by the fourth-placed candidate, then the originally sixth- and fifth-ranked candidates are eliminated. And so on up the chain.

Again, this sounds complicated, but in practice, in most seats, it could be worked out very quickly, simply by adding the first-preference totals for the third- to last-placed candidates, and seeing if this is greater than the total won by the candidate in second place. If so, then the third-placed candidate goes into the final race, and possibly the fourth-placed candidate does as well, depending on whether the total number of first preferences for the fourth- to last-placed candidates is greater than the number of first preferences won by the third-placed candidate alone. As I said, in most English seats, even the candidate in third position on first preferences would usually not overtake the second-placed candidate if you added the totals for all the lower-ranked candidates to their vote.

Thereafter, there is a logical sequence to the vote transfers: first, add the second preferences of voters for the eliminated candidates; then the second preferences of the lowest-ranked remaining candidate (giving the leading candidate(s) on first preferences a better chance of securing a strong majority); followed by the second preferences of the next-ranked and top-ranked candidates respectively; and then all the third preferences; and so on.

Some voting-system geeks (something I am proud to call myself!) would object that counting the second preferences of voters whose first-preference candidates are still in contention violates the ‘later no harm’ rule. This states that by indicating a lesser preference, voters shouldn’t be able to harm their higher-preference candidates’ chances. However, it depends how you look at it. On the First Past the Post view of the world, if a candidate, say, is in second place on first preferences, they have already lost. Therefore, if you allow the second preferences of that candidate’s voters to be added as appropriate to the total of the candidate in the lead, that’s not really ‘harming’ the second-placed candidate, since (s)he’s already lost. On the contrary, this is giving to voters whose candidate hasn’t won the chance to help determine the eventual winner via their second preferences: something which AV as currently constituted denies those voters but does allow voters for less successful candidates to do. If those second preferences still do not produce a majority for the leading candidate, then the second-placed candidate can benefit from the second preferences of voters for the leading candidate.

So in fact, by allowing vote transfers from candidates still in the race, my amendment to AV can actually improve the prospects of some lower-ranked candidates as well as ‘harming’ them, so long as there is no majority of first and second preferences across the whole electorate for the candidate who won the most first-preference votes, who would be the clear and deserving winner. What you’d have to do is explain to voters that by indicating second and subsequent preferences, they might help those candidates to win ahead of their first-preference candidates in some circumstances. But if they still indicated second preferences for candidates with a strong prospect of beating their first choice, then they can’t reasonably complain if that’s the eventual outcome.

My revision to the AV rules addresses both of the main deficiencies of the AV counting method listed above:

  1. The result is determined by a consistent set of preferences: if not on first preferences alone, then on the first preferences of potential winners + the second preferences of losing candidates – whether those candidates are definitely out of the race or have ‘lost’ according to FPTP principles (as discussed above). And if that’s not decisive, the third preferences of all voters are added, then the fourth preferences of all voters, and so on.
  2. It’s unlikely that the winner, in my version of AV, could gain fewer first + preference votes than one of the losers; and if they did so, it would still constitute a stronger majority in that it would be based on more first and second preferences, and fewer lower preferences, than AV majorities.

Of course, it’s unlikely that this revision to AV will ever be adopted, whether next month’s referendum results in a victory for AV or not. But that doesn’t mean rational thought shouldn’t be directed towards making a bad system a little better, whether politicians and voters are interested or not. Up to my readers to decide whether my version is better.

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4 Responses

  1. Brilliant post. I have a question that a voting-system geek like yourself should be able to answer for me. Imagine Constituency X under AV with four candidates and the following vote distribution:

    Cand. 1: 45%
    Cand. 2: 39%
    Cand. 3: 10%
    Cand. 4: 6%

    Since result is not >50% the votes for Candidate 4 are now distributed over the top three candidates. Let’s assume that at least some of the 2nd preferences were for Candidate 3 and that not Candidate 1 did not gain enough 2nd pref. votes to gain a >50% majority. Then the votes for Candidate 3 + the votes for Candidate 4 that had Candidate 3 as 2nd preference are to be redistributed.

    My question comes in two parts: Firstly, is the ‘whole pile’ of votes redistributed or are the votes redistributed by randomly drawing from the Cand. 3 votes? Secondly, does the ‘small print’ of AV stipulate that the 1st preference votes for Candidate 3 are to be redistributed PRIOR TO the votes for Candidate 4 that had Candidate 3 as 2nd preference?

    • Thanks, Tico. My understanding is that the whole pile of candidate 3’s votes (including second preferences deriving from candidate 4) are redistributed en bloc to the other two candidates or recorded as ‘exhausted’ if voters haven’t indicated a preference for either candidate 1 or 2. So no distinction is made between the original candidate-4 and candidate-3 votes.

      In essence, it doesn’t make any difference to the eventual winner which order the votes are counted in, as only one candidate can by definition obtain over 50% of the vote at each stage of the count. However, returning officers are obliged to continue counting beyond the point at which the winner is known (i.e. once a candidate has passed the threshold of 50% of votes still in play) because they have to record the full tallies for each candidate along with the record of the vote transfers. What won’t be recorded separately is the break-down of the vote transfers from candidate 3; i.e. which ones were candidate-3 first preferences, and which were candidate-3 second preferences.

  2. ok thanks! By the way, did you see Nick Clegg on BBC Breakfast this morning? He twice dodged the, in my opinion relevant and interesting, question why the referendum is on AV and not a more proportionate voting system. What is your take on that? Is he not willing to admit that that was the best the LibDems managed to negotiate with the Conservatives or is there another reason? I somewhere read, but unfortunately forgot to bookmark, that the LibDems themselves are to blame for AV being on offer and not STV or AV+.

    • My view is that the Lib Dems had decided before the election that they probably wouldn’t be in a position to insist on STV as a condition for entering a coalition with either the Tories or Labour. You can tell this by reading between the lines in their manifesto. At the front, they put four key policies that were the lines in the sand for a coalition deal (various Lib Dem spokespersons have said as much since the coalition was formed). Though electoral reform was one of them, STV wasn’t, and they merely said later in the manifesto that STV was their preferred option, without saying they’d insist on it.

      When it came to the talks, I think the Tories must have made it clear there was no way they could sell STV to their MPs and membership, especially as they were committed to re-drawing the existing single-member constituencies. But there was already a strategy on the part of the electoral reform movement (such as the Electoral Reform Society) to accept AV as a compromise if it was on offer (they were prepared to go along with Gordon Brown’s offer of AV in the event of a Labour government) in the hope that this could be evolved to either AV+ or STV subsequently. So the willingness to do a deal was there on all sides: a classic backroom-politics compromise.

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