Does AV mean higher or lower effective number of parties?

There may be a conventional wisdom among people who study comparative electoral systems that the Alternative Vote (also known as Instant Runoff or Majority Preferential) tends to suppress the effective number of parties, compared to plurality (First Past the Post, or FPTP). Or maybe it is just me, but I will admit to having such a notion. After all, Australia is a pretty strict two-party system, isn’t it?

The correct way to approach the question of whether AV means a higher or lower effective number of parties (N) than FPTP is to ask: What we should expect N to be, given the country’s seat product?

As explained by Taagepera (2007) and further elaborated and tested by Li and Shugart (2016), the seat product is a country’s mean district magnitude (M), times its assembly size (S). The Seat Product Model says that the effective number of seat-winning parties (Ns) tends to be the sixth root of this product: Ns=(MS)1/6.

The model is logical, not a mere product of empirical regression work, although regression tests confirm it almost precisely (Li and Shugart, 2016).

When all districts elect just one member, thus M=1, the Seat Product is just the assembly size, S. Hence we take the sixth root of S to get an expectation for Ns. What if we do this for Australia’s House of Representatives? We get an expectation of 2.31.

The actual Ns for Australia’s elections since 1984, the year S was increased from 125 to 148 (subsequently it has increased to 150, a minor change) is… 2.53. However, I believe that figure (I am using Gallagher’s Election Indices) treats the Coalition parties as one in elections before 2010.

In the two most recent elections, Ns has been 2.92 and 3.23. The notes to Gallagher’s Election Indices indicate that for these elections the Liberal Party, the Nationals, and the Liberal National Party of Queensland are treated as separate parties. In my opinion they should be so treated, although I suppose one could have a debate about that.

The actual mean is thus above the expectation for a hypothetical FPTP of the same size assembly. If we use the figure of 2.53, it is obviously not much higher than 2.31 (the ratio is 1.10). However, if we consider the value, at least in recent elections, to be around 3.0, it is about 1.30 times the expectation value.

Contrast this with the UK, where elections of the same period (1987-2010) have a mean Ns=2.30. This is just what we expect for FPTP, right? Not much over 2.0. Not so fast! The UK has a huge assembly, and with S=650 (aprpox., as it varies over the period), we should expect Ns=2.94. The UK actually has one of the more under-fragmented assemblies, according to the Seat Product Model, with this recent-period average being only 78% of expectation.

So how about Canada, where AV is one of the potential reforms being considered? Over a similar period (1984-2011) we get Ns=2.63. With S around 300 during this time, we should get Ns=2.59. So Canada pretty much nails the expectation of the model.

So, should we expect Ns to go down if Canada were to adopt AV, as (what I characterized as) the conventional wisdom would have it? Or should we expect it to go up?

I would not be inclined to say ‘down’. I will just leave it at that for now.

16 thoughts on “Does AV mean higher or lower effective number of parties?

  1. One can get further insight from the larger Australian states. Maybe. New South Wales, Queensland, and Victoria all have assemblies with sizes around 90. So we should expect Ns around 2.1. Over elections since 2000 (gleaned from Adam Carr), we have:

    NSW, Ns=2.64
    Qsld., Ns=1.87
    VIc., Ns=2.22

    Well, that does not help answer the question so much!


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  3. I suspect CPV tends to create a duopoly in a way that OPV would not. Among other things, the duopolistic parties have a habit of pointing to the 2PP while neglecting to mention that number is purely an artefact of CPV.


  4. If Canada had adopted AV at the same time that Australia did, the Conservative/ Liberal two party monopoly would have been preserved, much as the Liberal/ Labour one was in Australia. However, now there are too many ridings that are effectively contests between one of the big two and some other party, usually NDP (and CCF earlier) but also one of the Quebecois and Western protest parties that arise periodically.

    One caveat is that its clear to me in following Canadian politics that there are tons of low information Canadian voters who see Canadian politics as purely a contest between the Liberals and Conservatives. They are influenced no doubt by exposure to American media, but also Canadian news media which has a fairly obvious (to me) bias against the NDP. However, this effect is not strong enough to secure both the #1 and #2 spots in every riding for the Liberals and Conservatives.

    One check on the Australian electoral history is that of France. Like Australia, France uses what in practice amount to single member majority (SMM) districts. Unlike Australia, France doesn’t use AV but instead holds a later run-off election, allowing voters to learn the results of the initial round (which they often respond to by abstaining in the second round) and also give more scope for political parties to make deals. It is instructive to compare the results of what are, again, essentially single member majority electoral systems with a difference in how the elections are conducted.


    • The Liberal Party of Australia was not founded until 1945, long after the introduction of preferential voting in 1918. The period 1917-45 not only saw a succession of parties of resistance (National Labor Party, Commonwealth Liberal Party, Nationalist Party, Country Party of Australia, United Australia Party) but for much of that time there were competing parties of movement (Australian Labor Party, no less than three successive Lang Labor parties and the Hughes and Scullin splits) as well. I am not completely sure that the period can be characterised as a triumph of duopoly.


    • Ed, France has *plurality* runoff, with candidates admitted to the second round if they have a number of votes equivalent to 12.5% of registered voters in the first round. This results in many three-way contests in the second round; traditionally, the centre-right/centre-left candidate with fewer votes would back out of the race if the Front National candidate made it into the second round. Is that really similar enough to AV?


      • “Is that really similar enough to AV?”

        For practical purposes it is because most of the second round contests wind up being between two candidates.


      • I would not want to lump AV and majority-plurality into one category. They really are fundamentally different (even if, in practice, most French runoffs have had two candidates). I don’t think I’d lump majority-runoff (top two) with AV, either, although they do at least share the feature of whittling the contest down to two. But the mechanisms are just too different to pool them into one category.


  5. “The notes to Gallagher’s Election Indices indicate that for these elections the Liberal Party, the Nationals, and the Liberal National Party of Queensland are treated as separate parties. In my opinion they should be so treated, although I suppose one could have a debate about that.”

    The Liberal National Party of Queensland is a merger party and a fairly recent one at that. It shouldn’t really be treated as a *third* entity. LNP federal MPs will caucus with either their Liberal or National counterparts, and should be thought of in that regard.

    Treating the Coalition (in states where the Liberals and Nationals are organisationally separate) as one party or two for analysis can be problematic even to Aussies, considering that the two parties only nowadays run against each other in rural areas where neither has the sitting (or outgoing) member, and that public policy disagreements are rare. (They usually run combined Upper House tickets too). To talk of them as “one-and-a-half parties” would not raise eyebrows. The exception is WA, where they’re definitely separate parties.

    My opinion (for federal-level analysis): NSW & Vic Liberals = one party, NSW & Vic Nationals = one party, for other Coalition MPs and candidates, look at who they (would) caucus with and assign membership accordingly.


    • Sure, LNP MHRs and Senators, once elected, go to Canberra and sit with either the Liberal or the National caucus. But they are elected as LNP candidates. There is no federal division or State district within Queensland where a voter can decide between Liberal and National candidates. (In theory, they could still do it for the Senate, by deciding between “sits with the Liberals LNP” and “sits with the Nationals LNP” candidates on the LNP ticket, with the promise of a re-run such as the Brandis versus Barnaby Joyce intra-party contest in 2004.)
      To really complicate things, the federal National Party caucus consists of:
      1. Those MHRs and Senators from Queensland who were elected as LNP but who self-identify as Nationals once their plane touches down at Canberra airport.
      2. MHRs and Senators from WA and Victoria who were elected as Nationals.
      3. One of the two or three, or two of the three, MHRs/ Senators from the Northern Territory who was/were elected as “Country Liberals.” By convention, the CLP NT Senator (there always being exactly one of the two, with PR-STV) sits with the Nats while the CLP MHRs (the number varying from zero to two, depending how many seats the NT got and how many Labor won) sits with the Libs. Thus at one point Nigel Scullion, the Nationals’ federal Senate leader, hadn’t even been elected as a “National.”
      4. Finally, Nationals from WA who are members of the State affiliate of the federal National Party even though the WA State party is not always automatically in a standing coalition with the Liberals in either Federal or State Parliaments.
      The Nationals have never elected anyone from or in Tasmania (due to the island State’s system of first-past-the-post voting in single-seat electorates, which keeps out minor parties) and only seems to ever win one or two State seats in South Australia, where its sole Assembly MHA ended up in a coalition Cabinet with Labor.
      I agree with AlexJ about “one and a half [mainstream conservative] parties” as an average across this wide brown continent, but there are significant regional variations – I’d score the jurisdictions numerically as 1.0 parties in Queensland, 1.2 in NSW (where intra-Coalition relations are historically excellent), 1.5 in Victoria (where intra-coalition relations have historically been stormier and, I believe, the first-ever official Lib/ Nat coalition government was not actually formed until 1992), and 1.8 or 1.9 in WA (this would rise to 2.1 if the WA Nats ever did actually carry out their threat to one day co-ally with Labor).


      • “There is no federal division or State district within Queensland where a voter can decide between Liberal and National candidates.”

        Nor in about 90% of any state except WA, and even then only when neither is the incumbent (unless the Victorian Nats have gotten antsy again?).

        “The Nationals have never elected anyone from or in Tasmania (due to the island State’s system of first-past-the-post voting in single-seat electorates, which keeps out minor parties)”

        I can only assume you’re speaking *very* historically in that regard? To my knowledge, Tasmania is now single-seat for only: (a) Federal lower house, (b) State upper house, and (c) local government mayor/deputy; in any event all of those are IRV.


      • About Tasmania, perhaps FPTP killed off the Nats early on? I don’t know the history, myself. Come to think of it I wonder why I’ve never considered it. I think I did know there were no Nationals on Australia’s second island, but I’ve never reflected on it.


      • Is that FPTP Tasmania comment a joke or did I seriously miss something here? (Or is its just too early?) Tasmania has been electing the House of Assembly by STV since 1909, before the Liberal or National parties existed (technically)

        And…the Country Party was founded by a Tasmanian sitting in a Tasmanian seat.


      • Okay, sorry, I was being sarcastic about Tasmania… (-;

        Founded by a Tasmanian who was elected in 1903 “as a Revenue Tariffist supporting the Free Trade Party on most economic issues” and who didn’t become an actual Countryite untril 1920. So I yield to the gentleman on that question. I’d only been looking at election results since 1906, when Tasmania started using STV-PR for State elections. My bad.


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