The two-party preferred fallacy

Back in the 1970s, when the idea of analyzing voting and poll results in terms of the “two-party preferred vote, it was a major advance. Even though Australia has had preferential voting since (I think) 1921, it was poorly understood, to the point that when a candidate or party with plurality of votes lost on preferences, it was seen as a source of justified grievance (not helped by the fact that both the DLP and the Australian Democrats were splitoffs from a major party that aligned mostly with the other major party).

But that was in the days when Parliaments (or at least Lower Houses) were almost invariably made up solely of members of the major parties. Just as in the 1970s, the facts have changed but concepts haven’t caught up with it. Even though it’s now very common for the government to have a minority of seats, and such governments have worked very well, pundits still treat this outcome as an aberration, a “hung Parliament”. This is reflected in the continued use of the two-party preferred measure, which presumes that the last two candidates in any electorate, after preferences are distributed, will be those of the major parties. So, for example, Green votes for Adam Bandt are allocated between Labor and Liberal parties and used to forecast the election outcome, even though Bandt’s preferences will never be distributed.

There are various ways this could be fixed. The ideal one, in my view, would be to replaced “two-party preferred” with a seat-by-seat allocation of votes to “two most preferred”. That would need big samples to be reliable, but there are a variety of techniques that could be used to mitigate the problem.

The big benefit of this is that we could then see whether or not the poll was predicting an outright majority for one party. Assuming equal luck in marginal seats, a poll giving more than 50 per cent of the “two most preferred” vote to one party would imply a majority of seats for that party.

My reading is that most of the current polling yields a deliberative (or, as our pundits persist in describing it, “hung”) parliament as the central estimate, with enough error to allow either side the chance of majority. Given the likely alignment of independents and Greens a deliberative parliament would probably allow the formation of a Labor minority government. That raises the thorny question of the relationship between Labor and the Greens, which I will deal with in another post if I get time.

17 thoughts on “The two-party preferred fallacy

  1. Not only do our pollsters do this, but even the Queensland Electoral Commission buys into the same fallacy. When I scrutineered vote counting in the recent Brisbane City Council election, Jonathan Sri, the Greens candidate, was in a clear second place in my booth. Nevertheless the ECQ staff didn’t entertain the prospect of counting Labor preferences in a notional two party count. This was despite the fact that at the previous election the booth had more or less reflected the way votes went across the whole ward. Of course the notional count doesn’t affect the final result, but it does give the impression that preferences have enabled the Greens to “steal” the seat from Labor when it is reported in the media on the night.

  2. Two-party-preferred is definitely still relevant IMHO.

    As of the last election only 11 of the 150 Lower House seats were not ALP vs Coalition for the final two candidates. Of those eleven, three were Greens vs Labor and another three were Liberal vs National.

    All of those eleven seats had large two-party-preferred margins; only in Denison and Indi was the margin below 10% (in both cases, about 9%).

    If we get substantially more Green vs Coalition contests (results that might run counter to 2PP), or Xenophon makes a major Lower House impact (centrists), that will reduce the relevance of 2PP.

    The electoral commissions do publish ‘two-candidate-preferred’ breakdowns for those seats which require it (although they will usually default to 2PP and switch to the correct breakdown later on).

  3. @Robertito

    The booth two party preferred is done on two basis, the first is to give a useful measure on the night and the second is to give a meaningful electorate wide figure.

    You have to choose two candidates before the night, same for all booths, so they choose two assuming this election like the last one. In any case it doesn’t really matter in the end as the final result is done on a full preference distribution and will give the correct winning and runner-up candidate, you just have to wait longer for he right result.

  4. I do not follow. Why would Adam Brandt’s preferences never be distributed?

    Is this merely because he was the winner?

    The two party preferences still operate, and have value, but with different parties.

    The two-party thing is not only a Lib-Lab construct.

  5. My reading is that most of the current polling yields a deliberative (or, as our pundits persist in describing it, “hung”) parliament as the central estimate, with enough error to allow either side the chance of majority.

    Yes, that’s also my reading. The lastest Fairfax-Ipsos poll gives a 2PP of 51-49 to the Coalition of voters allocate preferences as they did in 2013, or 50-50 if voters allocate preference as they say they intend to this time around. I can see no reason to assume that the former disposition of voters is more likely than what they say their disposition currently is.

  6. Antony Green has been making this point, that classic 2pp is meaningless, for some time, specifically about NSW, but Cth is probably at the tipping point now.

    Robertito, the 2CP ‘throw’ at the booth count is decided in advance by the ECQ (or the AEC). After close of polls, a sealed envelope is opened which contains the names of the two candidates to whom preferences are to be distributed in the booth count. If you think about it, there’s no other way to get timely 2CP results out, and the electoral authority’s guesstimate is correct 95+% of the time.

    Paul, history has shown that the previous election’s distribution is a more reliable indicator of Election Day performance than respondent allocation. That relationship might not hold any more if we’ve moved into a new era of voter behaviour. Or the last couple of elections might be aberrations.

    Ivor, no one will ever officially know what Bandt voters preferences are, unless he finishes third or lower. They are never examined, except by scrutineers as his first prefs are counted.


  7. I think 2pp is preferred by pollsters and media as they can extrapolate a national result from a small sample. As Antony Green points out, pollsters only ask for 1st preference before calculating the 2pp.

  8. Another way of estimating the distribution of votes is to use computational models. I don’t know if anyone has done this. It would be worth trying.

    From previous elections we have questions and answers and the actual result. We build a model that simulates an election where the way votes cast are estimated from the answers to questions. We run many elections and distribute the votes. We optimise parameters in the model using search algorithms to get the best fit between the model and the actual result. We do this for every seat. This calibrates the model and shows it works.

    We then do our polling and simulate many elections using the answers to questions and voting intentions as input. This gives a distribution of results for each seat.

    Example algorithms are tabu search and ant algorithms.

  9. The notion of two-party preferred is an obvious nonsense in the Senate.

    It will still have relevance until the greens win a few more seats and make coalitions with labour are more likely than not scenario if labour were to win

  10. current odds on Betfair indicate a Trump presidency more likely than Shorten Prime Ministership. Sobering.

  11. Wouldn’t the main attraction of 2pp to polsters be that it is cheap? There would be considerably more effort needed if they were to identify seats where the ALP of the coalition might not win, and then poll enough people in those seats to get a reasonable idea of the final result.

    Still, they should give it a try. Laziness or lack of drive is not really an excuse to not do the job properly.

  12. @John Brookes

    As I mentioned earlier, in a bit over 90% of seats 2PP is entirely relevant because it correctly assumes the final two candidates. And in most of the non-classic seats the 2PP margin is very high anyway; on a Left vs Right basis the seat is still predictable.

    To a large extent we can easily identify seats where the (ALP or Coalition) might not win — simply look for those seats where one of them finished third (or lower!) on primary vote.

    Respondent-allocated preferences are usually no more accurate than as-at-previous-election preferences, so it’s even possible in some non-classic seats to predict the two-candidate-preferred result.

  13. The question that came to mind when reading JQs comments was ‘Does it Matter?’. The only poll of interest to me is the one on election night and I would like to see a system that more fairly represented the voters. I suggest that in addition to the representation by constituency additional seats are allocated on the basis of the overall number of votes cast for each party such that the representation in the lower house reflects the proportion of votes cast for each party.

  14. @John Turner
    Yes, mixed-member proportional is a good system. It would be particularly good here in Queensland, what with our lack of upper house and all.

    (I hasten to add that preferential voting can be retained for the constituency seats aspect).

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