This blog collects perspectives on the election you won't find anywhere else, by political experts, based in the School of Politics and International Relations at The University of Nottingham.

Tuesday, 11 May 2010

The Alternative Vote, why bother?

The campaign for and the outcome of the General Election has put electoral reform firmly on the political agenda. Somewhat surprisingly the alternative vote (AV) has become the most discussed option for replacing the current first-past-the-post system (FPTP), embraced by Labour, and even allowed by the Conservatives to be voted upon in a referendum. This potential acceptance by the two major parties is understandable, as AV is for them the safest option, and least likely to break their joint hegemony over British politics.

When thinking about the different ways in which elections can be organised, the first question to be answered is whether one wants each constituency electing only a single MP, or multi-member constituencies.

Elections for single member constituencies can be organised in three fashions: first-past-the-post, alternative vote, and approval voting. But irrespective of which of these is used, all single member constituency systems are prone to disproportional outcomes, which means that the shares of votes and shares of seats can diverge widely.

AV thus does not solve the problem of dis-proportionality that lays at the root of many demands for electoral reform. It may even turn out less proportional than FPTP. In other words, it is also likely to yield parliaments where a vote share of only 35% yields 55% of the seats (as was the case for Labour in the previous parliament). because Labour and the Conservatives are most likely to be in a position to benefit from this, it is quite understandable that they favour AV if the call for electoral reform cannot be stifled any more.

What is ‘solved’ by AV is a ‘problem’ that hardly anyone cared about, namely that an individual MP be elected with fewer than 50% of the votes in his/her constituency. AV changes this by asking voters to rank their preferences for the candidates. If no candidate has an absolute majority of first preferences, then the one with the fewest first preference votes is eliminated, and his/her votes are allocated to the other candidates on the basis of the 2nd preferences on those ballots. Applying this, if necessary repeatedly, will guarantee that the eventual winner will have been supported by a majority in the constituency (a ‘majority’ that then consists of a mixture of 1st preferences, plus added 2nd preferences, possibly 3rd preferences, and so on). But this does not do anything to diminish the discrepancy between vote shares and seat shares across the country as a whole, and which motivates much of the support for electoral reform.

AV may even prevent a party that is more preferred than any of its competitors from winning in a constituency. Take, for example, a constituency with three candidates on the ballot, let’s call them Harriet, Chris and William. Voters are asked to rank their preferences for these on their ballot papers. A possible outcome would be the following:

40 % of the voters give 1st preference to Harriet, 2nd preference to Chris, and 3rd to William.;

35 % give 1st preference to William, 2nd preference to Chris, and 3rd to Harriet;

25 % give 1st preference to Chris, 2nd preference to William, and 3rd to Harriet.

Because none of the candidates has more than 50% of the 1st preferences, Chris is eliminated because he got the smallest number of 1st preferences. The 25% of the ballots which ranked Chris first are now allocated to William and Harriet, depending on the second preferences. In the example above, everyone who ranked Chris first ranked William second, so all these votes are transferred to William, who thus obtains a comfortable majority of 60% (35% + 25%) and wins the seat.

But actually, Chris, who was eliminated, was more preferred than either Harriet or William! 65 % of the voters prefer Chris over William (40% + 25%), while 60% prefer Chris over Harriet (35% + 25%). All that this shows is that the ‘majority’ with which William would be elected under the AV system, is an artificial one.

All in all, AV does not solve the biggest problem that leads to the call for electoral reform. It does not yield more proportional outcomes than the current FPTP system, which is exactly why both Labour and Conservatives can conceivably live with it without giving up their dreams of an absolute majority of the seats. And finally, AV can easily lead to the elimination of a candidates who is more preferred than any of his or her competitors.

In a next contribution to this blog more about other alternatives to FPTP.

Professor Cees van der Eijk


  1. Delbert Wilkins11 May 2010 at 10:24

    You touch on the question that no-one (let alone the shrill proponents of PR) is apparently asking - how do we want to be represented? It has nothing to do with which party would benefit and everything to do with how we want our interests to be represented in Parliament. If we choose to retain a single-member constituency link (which I suspect (but don't know for sure) that most people would want) then PR is simply not applicable. If anything, it is those in favour of PR who are acting on narrow party interest, not those who oppose it.

    This whole debate has been fatuous in the extreme.

  2. Suppose I have an election between candidates (A,B,C,D) and the voting system (VS), say, elects B. In my opinion a good VS should satisfy these counter-factual conditions:
    * If any candidate apart from B had decided not to stand, then B would still have won.
    * If an additional candidate, E, had also decided to stand, then the VS could have elected only B or E.

    FPTP fails both of these consistency tests, whereas AV passes. I think the answer to "why bother with AV?" is that FPTP is so absolutely dreadful.

  3. Chaps,

    A useful post would be a practical (ie journo's) summary of Arrow's paradox, and an explanation of how any voting system is inconsistent in some sense. A lot of the debate about voting systems at the moment is predicated on the notion that there is a perfect voting system, not on the trade-offs that are made in any particular system. And bum up approval voting a bit, it deserves it: it's the simplest adaption of the current system but is substantially fairer. It also addresses the argument that votes for losers in safe seats are wasted.

  4. I think a (relatively) simple change to AV that makes it much fairer is to eliminate the candidate with the highest mean ranking rather than the candidate with the lowest count of 1st rankings.

    In this example the mean rankings would be:

    Chris: 25% @ 1, 75% @ 2 (mean 1.75)
    William: 35% @ 1, 25% @ 2, 40% @ 3 (mean 2.05)
    Harriet: 40% @ 1, 60% @ 3 (mean 2.2)

    Leading to Harriet being eliminated in the first round rather than Chris.

    When the 40% of preference 2 votes from Harriet is added to Chris's 25%, Chris wins with the support of 65% of voters.

  5. I think it is also important that a voting system should lead to the same result no matter which order the votes are counted. STV can vary greatly in result depending on the order the votes are counted.

  6. You mention the advantage of AV that it ensures the elected candidate has some support of over 50% of the electorate, and (I think rightly) state that it's a goal that few are worried about.

    However the other problem it goes a long way to address is that of the need for tactical voting*. Let's take as an example of real political parties, and assume that we can rank them from left to right as Green, Labour, Lib Dems, Conservative, UKIP, BNP. Assuming a constituency that is viewed to be a Labour/Conservative battleground, then tactical voting would call for Greens to fall in behind Labour and BNP/UKIP supporters to vote Conservatives, with Lib Dems individually deciding whether they'd rather nudge a bit to the left or to the right. Under AV, Greens can vote Greens 1, Labour 2, Lib Dem 3; BNP supporters can vote BNP 1, UKIP 2, Conservative 3... and so on - each voter can honestly express their preference, with a reasonable expectation that their vote will end up helping someone they favour over someone they don't.

    * I appreciate that AV doesn't completely prevent tactical voting, but it does help a lot.

  7. As Lloyd George said: There is nothing more dangerous than to leap a chasm in two jumps

  8. There is also French (cough! cough!) ballotage system. If any candidate get more than 50%, the first two candidates face each other again. With just two candidates, the winner will always have more than 50%.

    In order to avoid two elections, the AV option could work as a "ballotage", instead of eliminating the last, eliminate all but the first two.

    P.S.: Don't forget that what matters in the first count is the main vote. What really matter in your example is that 75% didn't want Chris as their first option.

  9. Cees van der Eijk13 May 2010 at 01:56

    Reply to some of the comments

    Thanks to all who have commented.

    Delbert Wilkins comment is spot on: one of the key questions is how we want to be represented. The basic choice here is between on the one hand representation of localities and, on the other of party preferences as they exist in the country as a whole. Local representation in its extreme form requires single member constituencies. Representation of party preferences in the country leads to PR with the entire country acting as a single constituency (as exists in, e.g., the Netherlands and Israel). But there are many options in between these two extremes, which either involve mult-member constituencies, or some form of mixed representation. I will discuss these in a separate blog post. The question which of these options is actually preferred by most people can only be answered by surveys (or referendums).

    Peter Conlon suggests some criteria that should be realised by an electoral system. These are sensible, but there are many more that one can think of (see for more extensive discussion of all such kinds of criteria Colomer, Josep M. (2004). Handbook of Electoral System Choice. London and New York: Palgrave Macmillan; and
    Farrell, David M. (2001). Electoral Systems: A Comparative Introduction. New York: St. Martin's Press.) Maybe a topic for another blog post, later (just as Anonymous' request for a simple explanation of Arrow's paradox).

    Russell Heiling's suggestion to eliminate candidates in AV not on numbers of smallest number of 1st preferences but on highest mean ranking is excellent and would solve some of the problems of the more common form of AV. Of course, it does make a strong assumption, namely that the ranks of preferences are the same as the strengths of those preferences, as it would not make sense otherwise to calculate a mean. As an example: if strength of preference (referred to by economists as 'utility') could be measured on a scale of, say, 0 to 10, then 3 voters could have the following preferences :
    Chris: 100, Harriet: 69, William: 68
    Chris: 100, Harriet: 0, William: 70
    Chris: 100, Harriet: 3, William: 0.
    Who is least preferred? Russell would suggest William, as he ranks 3, 2, 3, while Harriet ranks 2, 3 and 2. Yet, in terms of strengths of preferences William (average 46) is clearly preferred over Harriet (averages 23).
    This example is not meant to belittle Russell's creative suggestion, but to highlight its implicit assumptions.

    Anonymous' comment on tactical voting is another insightful one. Yet, AV is not immune aginst tactical voting (albeit under different circumstances than sketched in this comment).

    Thanks to all! Without doubt we'll see more posts on electoral reform inthe future.


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