IRV versus Top-2-Runoff – T2R "flips" more winners

(perhaps explaining why IRV yields 2-party domination while T2R doesn't)

By Jim Riley & Warren D. Smith, Sept. 2009. (Skip to conclusion.)

We examine the hypothesis that IRV (Instant Runoff) and T2R (ordinary top-2-runoff voting; 2-round elections, 2nd round undertaken if no candidate gets over 50% of the votes in the first round) behave rather differently in practice, despite the fact that naively speaking, they might seem similar. We and others (e.g. Taagapera & Shugart) had previously noted (see also comparison and evidence and possible reasons) that IRV apparently always causes a country to devolve into (≤2)-party dominated ("duopoly") status (at least, in IRV seats), while top-2-runoff usually doesn't.

The question is why. One possible hypothesis is that with IRV, the same winner nearly always wins (in practice in the real world) as the one who would have won with plain plurality voting. And it is well known ("Duverger's law") that the latter causes duopoly, with the top reason being that voters fear "spoilers" and strategically alter votes in effort to avoid them; this causes "third parties" to weaken and die. Meanwhile (the hypothesis continues) it is significantly less frequent that T2R and Plurality elect the same winner.

Suppose IRV voters tend to vote one major-party-candidate top (and the other bottom or nearly) in a naive effort to "increase the impact" of their vote. THEOREM: If over 1/3 of IRV voters rank each major-party candidate top (and there are two major parties) then a third-party candidate can never win. ANOTHER THEOREM: If over 75% of the voters vote in one of the two forms "A>almost all others>B" or "B>almost all others>A" then either A or B will always win. It appears these 66.67% and 75% threshholds are comfortably exceeded in Australia – exactly why in its three House election cycles 2001-2007 (comprising 450 individual IRV elections) there were a grand total of zero third-party winners. This also presumably explains the heavy agreement between IRV and plain plurality voting's winners. (NESD property.)

If so, it would be logical that IRV would behave highly similarly to plurality and, over time, fatally weaken third-parties and thus force duopoly. But T2R would behave differently-enough from plurality that third parties could stay strong enough usually to prevent duopoly. (Both empirically happen.)

And there may be a nonlinear "tipping point" positive-feedback effect such that if third parties are too weak, they get weaker (leading to death), while if strong enough, they can stay that way. (This is the same principle that makes nonlinear bistable "flip-flop" electric circuits work.)

Our purpose here is to examine the veracity of that hypothesis. We shall end up confirming it.

Data tabulating number of elections with same or different winner than plain plurality's

T2R Country, State, or CitySameDifferent
France (Presidency 1965-2007) [summary]0+53
Louisiana-USA (Governor 1975-2007)5+31
Los Angeles (Mayor 1961-2009) [summary table]2+92
San Francisco (19 Municipal Elections 2000-2003) 6+85
Presidents of Brazil 1998-2006, Mexico 2000-2006, Iran 2001-2009, Poland 1990-2005, Argentina 1999-2007, Finland 1994-2006, Austria 1998-2004, Chile 1989-2006, Portugal 1996-2006, Sierra Leone 2002-2007, & Ghana 1992-2004312
Georgia-USA (Senator 2008) and Arizona-USA (Governor 1991)0+20
Texas House Primaries 1990-2008; only the 148 cases with ≥3 candidates, which led to 95=69+26 runoffs53+6926
Total19239 (17%)

Some of the above "same winner" data is split ("53+69") into the cases where there was no runoff since the plurality winner had over 50% (or occasionally due to one of the runoff-contenders withdrawing), versus cases where the first round winner re-won the second round. Evidently runoffs are needed about 2/3 of the time.

IRV Country (or city)SameDifferent
Ireland (Presidency up to 2008) [summary table]7+21
San Francisco (14 Municipal Elections 2004-2009) 7+70
Australia (House 24 Nov 2007); every race had ≥3 and on average 7.03 candidates75+669
Australia (House 9 Oct 2004) on average 7.27 candidates per race 89+538
Australia (House Nov 2001) with 6.9 candidates per race on average1455
Total45123 (5%)

Similarly some of the IRV-table's "same-winner" numbers has been split into races "decided on first preferences" and those "where a distribution of preferences was necessary to determine the elected candidate" (according to the AEC). Evidently the latter happens about 45% of the time.

Later note: Antony Green provided a table of many more years of Australian House-IRV elections, which we have not verified. Green's table finds an average (over the 24 election cycles 1949-2007) plurality→IRV winner "flip rate" of 5.4% and the percentage of races where a pseudo-runoff was required was, on average, 35.5%.

IRV Notes: Voting (and full rank-ordering) is theoretically compulsory in (most of) Australia, although about 6% break the law and do not vote and of the ones that do vote, about 5% fail to cast a valid ballot. I think in 100% of the Australian IRV races tabulated, there were at least 3 candidates. However, of the 10 Irish presidential races, there were only 3 cases with ≥3 candidates (1945:3, 1990:3, and 1997:5) – i.e. in the other 7 cases (five with 1 candidate, two with 2) the use of "instant runoff" voting was illusory. Irish turnout was 48% for the 1997 election. In 1990, over 99% of the ballots were valid but about 10% of them failed to give a full rank-ordering of the three candidates.

T2R Notes: Factors leading us to use Texas include: large number of elections (150 districts contested every two years) with relatively large electorates (around 140,000 persons per district in 2000; note Texas has about 15% greater population than Australia). In addition, there is a quasi-non-partisan nature to the primaries. Texas does not have party registration; you simply choose your party on election day. (Texas used to have one-party domination by the Democrats – so the primary effectively was the real election – which is the historical reason there is a runoff.) In many areas, if you want to vote for your local county officials, you have to vote in the Democratic or Republican primary. Voter turnout (as a fraction of adult population; these numbers would be higher as a fraction of registered voters) in competed TX house primaries appears to range from about 4% to 50%, averaging about 14%. The reason we restricted attention to the Texas races with ≥3 candidates is those were the only ones where a runoff was even a possibility. Most Texas House primaries have 0 or 1 candidates – i.e. are not elections at all! – and the majority of the genuine elections involve fewer than 3 candidates making a runoff impossible. E.g. in the 1992 Democratic Primary (150 districts), only 28 had ≥2 candidates, only 13 had ≥3, of which there were 9 runoffs:

   35  No Candidate (causing Republican to be unopposed in general election)
   84  1 Candidate (i.e. primary was not necessary)
   15  2 Candidates
   11  3 Candidates (7 with runoff, 4 without).
    3  4 Candidates (3 with runoff).
    1  5 Candidate race (led to runoff).
    1  7 Candidate race (led to runoff).
Incidentally, the fact that only 3.5% of the 2700 primaries over the 18-year span needed a runoff suggests that arguments against runoffs based on cost savings may be largely irrelevant.


This data has been criticized as not a truly-fair comparison of T2R versus IRV, because, e.g.

  1. Low-turnout-Texans psychologically differ from high-turnout Australians – so ours is an "apples to oranges" not "apples to apples" comparison. (One could also attack Ghana, Ireland, etc as not being "apples," but since the data is dominated by Australia and Texas, that matters little.)
  2. Usually candidates only run if they think they have a chance to win. Therefore by employing only the Texas races with ≥3 candidates, we created a "selection bias" towards "less clear" races.
  3. Apple: Australia in IRV seats (house) has 2-party domination (although not in its non-IRV senate seats). Oranges: Texas also has 2-party "duopoly," but in primary elections this is not terribly relevant because every candidate is from one party, which has no particularly-organized subparties. And most of the T2R countries are not duopolies.
  4. When computing the statistical error bars (see conclusion) we assumed all the IRV elections were independent of each other. (Ditto for the T2R elections.) In fact, there are dependencies, since, e.g, a similar race might occur next election in the same district. Therefore, the error bars ought to be greater than we said.

Our responses:

  1. No matter what we had done, we could be attacked for this reason. The fact is, there are not very many large IRV and T2R elections in the world, and one has to use the limited data that is available. We did. If you want to study an unreal artificial world in which the T2R and IRV elections are conducted in exactly-alike settings, then use a computer simulation study. (We've done those too. What generally happens is, critics complain about computer studies since they are "not the real world" and complain about real-world studies since they are "not in a perfect jewel-like setting like a computer-simulation study would have been." Sorry.) So far, our critics on this score have not suggested better data sources. Further, a factor>3 alteration in flip rate, is so large it is difficult to credibly ascribe to such psychological differences.
  2. One could counter-argue that every Australian race had ≥3 candidates, and Australian races usually have more candidates than in Texas – so that, if anything, the bias operated in the other direction! Indeed, this would seem to mean that Australia should, a priori, expect more chance of "flips" than Texas, but in fact they get a factor of 3.3 fewer, which strengthens our main conclusion that T2R flips more races (not weakens it). [But it could be counter-counter-argued that in Australia, many of the contenders were running merely to "carry the flag" for various Australian third-parties, not because they had a reasonable expectation of winning; while in Texas most thought they had a chance to win – different candidate psychologies, therefore more selection bias in Texas. One then could counter3 that in Texas, unanointed candidates could select a race to try to win, but in Australia third parties won zero out of 450 seats and hence they could not even try to be selective since no matter what they tried, they always lost – thus proving Australia's comparative lack of democracy versus Texas, due to IRV versus T2R.]
  3. True. But that reinforces our point: IRV leads to duopoly, T2R mainly does not. You can criticize our study for such differences, but one of the points of making a real-world study is to detect and observe such differences! They really exist. Duopoly is a self-strengthening feedback loop; it is not just that (a) IRV's election results yield duopoly; duopoly also (b) creates a setting in which IRV's election results are affected, yielding... duopoly. In the real world (a) and (b) both happen and cannot be disentangled. (One could try to disentangle them by using recently-created countries like Fiji which have not yet had time to develop full duopoly. However, there is less data of that sort, and if we had done this we would have been – justly – criticized for using "atypical" and "irrelevant" election data from dubious infant/proto-democracies!)
  4. These dependencies don't amount to much. E.g. in Australia, the 9 flipping districts in 2007, were entirely different from the 8 in 2004, which in turn were entirely different from the 5 in 2001. In Texas, the 148 runoff-possible races were scattered so rarely among the 2700 total primaries that again, little dependency could happen; even the top three most-competitive districts (#28, #47 and #75) each only had 4 races during the 18-year (10-primary) span with ≥3 candidates each, and of the 11 runoffs that resulted, none repeated both contenders and only two repeated one contender.

To sum up: I think we've done this study nearly as well as could have been reasonably expected given the limitations forced upon us by operating in the real world. The conclusions are pretty clear. Which are:



Based on the data here, real-world IRV elections yield a (4.86±0.99)% "flipping" rate (i.e. rate of changing the winner away from the plain-plurality winner). But T2R elections lead to (16.36±2.49)% flip rate. [We have provided "mean±1σ" error bars viewing all exemplars of each election-type as i.i.d. Bernoullis.] We therefore have over 4.29σ worth of confidence, i.e. over 99.999% confidence, that T2R elections really do yield a greater flip rate than IRV elections. (In fact, the ratio is 3.37±0.93.) Hypothesis confirmed!

Of course, the underlying reason why TTR has over 3× greater flip rate, is a separate question which this data does not directly address. See the reasons page for our guesses. But just the fact that it does, regardless of why, is probably a big reason for further effects like IRV 2-party-domination dysfunction.

One also could argue, based on this, that by campaigning to change true-runoff elections to instant in the USA, that the voting-"reform" group "FairVote" has actually been reducing democracy.

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