Australia's 2007 elections – IRV pathologies undermine its success

by Warren D. Smith, Dec. 2007. Skip to conclusion. (Executive summary)

IRV advocate Rob Richie recently hailed the Australian house elections (held 24 November 2007) as a "big success" for Instant Runoff Voting (IRV). These elections threw out both Prime Minister John W. Howard and his party, the NatLibs, enthroning Kevin Rudd and giving his Labour Party majority control.

But was this really a big success for IRV? We'll examine that here using data from the Australian Electoral Commission web site. (Warning: All this is based on data we got from the AEC on 30 November 2007, which was not in final form. However, it turned out the same seat counts ultimately arose, in the final say, as we tabulated.) The conclusions of that examination are as follows:

1. If Australian house elections had been held with plain plurality voting rather than IRV then (assuming every voter would have voted for the same candidate they top-ranked with IRV) the results of 9 of the 150 House races would have changed. In all 9 cases, plurality voting would have elected the NatLib candidate instead of the Labour candidate who actually won with IRV. More realistically, with plurality probably some third-party voters would have been more-afraid to vote third party and would have voted for the top-two party candidates. If so, then fewer than "9" races would alter (perhaps only 7 or 8?). That would decrease the importance of IRV in one way (fewer results changed) but in another sense (improved voter honesty) would increase it back.
2. Labour and Rudd still would have won majority control with plain plurality voting, just a smaller majority (77 out of 150 seats, versus what they got with IRV, which was 85 out of 150).
3. In view of this, we agree with Rob Richie that these elections were at least a "success" (albeit perhaps not a "big success") for IRV. But we contend approval and range voting would have been an even bigger success, as we'll now explain.
4. If Australia had employed approval, range, or Condorcet voting instead of IRV, then we believe the same result would have happened, i.e. exactly the same 9 races would have swung toward Labour – or perhaps only 7 or 8 with range and approval if the third-party voters did not approve Labour enough or score it highly enough; and also the Greens might have won some races with Range and/or Approval – but either way then range & approval would arguably have made a better call than IRV in those cases.
5. All 9 IRV-swinging races displayed a pathology called "participation failure" or "no-show paradox." That is, in every case, adding some number of extra Green>Labour>NatLib voters, would have caused the IRV winner to become NatLib. That is bad, because:
   1. These extra voters, by voting honestly, would have made the election result worse in their view.
   2. They would have been better off not voting at all (as, in fact, they didn't).
   3. They also would have been better off voting dishonestly; and with these extra Green voters, some of the Labour voters also would have been better off voting dishonestly.
   4. All 9 losing Natlib candidates have the following valid gripe, enabling them to attack the legitimacy of IRV:
      1. I lost to Labour with IRV,
      2. But if extra voters, all of whom ranked me dead last and preferred Labour over me, entered the picture, then I would have won,
      3. So, since I would have won and defeated Labour even with this handicap, why the heck did I lose without the handicap?
         ∴ My defeat was bogus or the election system (IRV) is bogus, or both.

   But that whole conclusion and gripe can be avoided, but the way out involves admitting that there was a different pathology ("failure to elect Condorcet winner") which occurred even more frequently. In each case where this alternate pathology occurred, the Green loser would have the following valid gripe, enabling them to attack the legitimacy of IRV:

   1. I would have defeated the Labour candidate if it had been just me versus him.
   2. I also would have defeated the NatLib if it had been just me versus him.
   3. So why did they win and not me?!

   ∴ This IRV election system and my defeat are both bogus!

   Note: there is a 2-way choice here – at least one of these two pathologies (and hence gripes) is valid in each election, but the incomplete data released by the AEC is insufficient to tell which. I suspect, however, that the second problem (the Green gripe) is the one that is correct in the vast majority of cases.

6. Approval and Range cannot exhibit the first sort of pathology and probably did not exhibit the latter either; hence apparently no candidate in any of the 150 races would have had any such valid gripe enabling attacking the legitimacy of range & approval voting.
7. The myth that IRV pathologies are "extremely rare" is totally refuted. The claim that IRV improved on plain plurality voting is undermined because the two systems delivered exactly the same winners in every case, except for cases in which the legitimacy of IRV can validly be questioned.
8. Australia is still counting and recounting all the close IRV elections 1 week 2 weeks later and warn that it is not clear that Labour really has 85 seats, etc (those results are subject to change). Update 6 Dec 2007: the AEC still considers 9 of the 150 seats to be "doubtful," i.e. insufficiently clear who won, 12 days after the election. Later update: As of 11 Dec, improvement! Now only 7 seats are unclear, but the AEC is closing for Xmas holidays so we cannot know any more for quite a while... Final update: As of 28 Dec, over 1 month after the (24 Nov) elections, the AEC now considers the matter finalized and is awarding Labour 83 seats. The outcomes of our 9 flagged races, did not change. That is because IRV is a difficult system to count, and ties and near-ties even between "no hoper" candidates, can change the winner. Australia's numbers of invalid "spoiled" ballots were easily large enough to change the winner in many of the 150 races. (And, incidentally, spoilage rates are lower with range and approval voting but higher under IRV.) Approval (or even range) voting are simpler to count and less subject to tie-crises. They would have been counted sooner with fewer worries, less effort, and less cost, and could have been counted in precincts leading to greater transparency and credibility.

Details

• Zero house seats were won by 3rd party members (as usual, same as the preceding Australian election in 2004 and the one before that in 2001). But a couple of "independents" all of whom were former major-party members, hold and held seats.
• According to one 6 December count, there was 93% (another page said 92%; the figure changes with time and which AEC web page you look at) turnout for House races out of 13,645,073 enrolled voters (despite "compulsory" voting which "should" have yielded 100% turnout); 7% of voters presumably will pay fines.
• 1054 candidates ran for the 150 house seats which is 7.03 candidates per seat average.
• Every race was contested by at least 3 candidates.
• But it appears there were no "genuine" 3-way races, i.e. the 3rd-placer was always far behind the top 2 in all 150 races, at least reckoned by top-preference votes. For that reason, there was no example of a favorite-betrayal or nonmonotonic IRV race because it was always basically just a 2-man race.

9 "Participation failure" or "Condorcet failure" pathologies

There were by our count exactly 9 races (of the 150 total races) where the plurality and IRV winners disagreed. (You can re-examine the 150 races here: http://vtr.aec.gov.au/HouseDivisionMenu-13745-NAT.htm. We initially counted 8 but Malcolm MacKerras pointed out there were actually 9 such races and we have now added the 9th: Bass.) In all 9 cases, the Labour candidate did not win the "plurality election" (IRV round #1) but did win the IRV election. Here are the 9:

SWUNG RACE #1: VIC DIVISION - CORANGAMITE
McArthur(lib) was the plurality winner but Cheeseman(Labour) was
the IRV winner:
name            plur-total IRV-total
McArthur(liberal)    37438 41260
Cheeseman(labor)     35394 42418
Fiona Nelson(Green)   6319
[We have listed only the top 3 candidates. Fuller data here:
http://vtr.aec.gov.au/HouseDivisionFirstPrefs-13745-207.htm]

SWUNG RACE #2: NSW DIVISION - BENNELONG
name                   plur-total IRV-total
John W Howard(liberal PM!)  38545 41159
Maxine McKew(labor)         38181 43272
Lindsay Peters(Green)        4652
[We have listed only the top 3 candidates. Fuller data here:
http://vtr.aec.gov.au/HouseDivisionFirstPrefs-13745-105.htm]

SWUNG RACE #3: TAS DIVISION - BRADDON
name            plur-total IRV-total
Mark Baker(liberal)  28307 31231
Sidebottom(labor)    28185 33062
O'Halloran(Green)     5112
[We have listed only the top 3 candidates. Fuller data here:
http://vtr.aec.gov.au/HouseDivisionFirstPrefs-13745-193.htm]

SWUNG RACE #4: VIC DIVISION - DEAKIN
name         plur-total IRV-total
Barresi(liberal)  33488 36518
Symon(labor)      31732 38727
Pemberton(Green)   6146
[We have listed only the top 3 candidates. Fuller data here:
http://vtr.aec.gov.au/HouseDivisionFirstPrefs-13745-193.htm]

SWUNG RACE #5: WA DIVISION - HASLUCK
name         plur-total IRV-total
Henry(liberal)    29488 33275
Jackson(labor)    28429 34771
Bremmer(Green)     5706
[We have listed only the top 3 candidates. Fuller data here:
http://vtr.aec.gov.au/HouseDivisionFirstPrefs-13745-193.htm]

SWUNG RACE #6: NSW DIVISION - PAGE
name             plur-total IRV-total
Gulaptis(nationals)   32480 35912
Safin(labor)          31790 39563
Jongen(Green)          5917
[We have listed only the top 3 candidates. Fuller data here:
http://vtr.aec.gov.au/HouseDivisionFirstPrefs-13745-138.htm]

SWUNG RACE #7: NSW DIVISION - ROBERTSON
name            plur-total IRV-total
Jim Lloyd(liberal)   36702 40048
Belinda Neal(labor)  34743 40344
Wroblewski(Green)     5600
[We have listed only the top 3 candidates. Fuller data here:
http://vtr.aec.gov.au/HouseDivisionFirstPrefs-13745-146.htm]

SWUNG RACE #8: NT DIVISION - SOLOMON
name              plur-total IRV-total
David Tollner(CLP)     22495 23882
Damian Hale(labor)     20227 24144
Debbie Hudson(Green)    4308
[We have listed only the top 3 candidates. Fuller data here:
http://vtr.aec.gov.au/HouseDivisionFirstPrefs-13745-307.htm]

SWUNG RACE #9: TAS DIVISION - BASS
name              plur-total IRV-total
Jodie Campbell(labor)  23764 32553
M.Ferguson(liberal)    27769 31282
Tom Millen(Green)       9745
[We have listed only the top 3 candidates. Fuller data here:
http://vtr.aec.gov.au/HouseDivisionFirstPrefs-13745-192.htm]

Since the Australian Election Commission ignored my request for more data (and keeps the full IRV results secret, only distributing simplified election summaries which are not enough information to reconstruct the ballots) we are forced to analyse these elections somewhat simplistically. So let us disregard the other candidates in 4th, 5th, etc place and assume Green voters prefer Labour over NatLib, while Labour voters do not, on average, have an especially noticeable Green-over-Natlib preference, i.e. either would prefer NatLibs or would split about 50-50. (Note: every other party was well behind the Greens so these assumptions are plausibly OK.)

How realistic are those assumptions, and how much does it matter? It is definitely correct that a big majority among Greens prefered Labour over the NatLibs; this is evident both from party stances and more importantly from the elections themselves, which involved many cases where Green vote-transfers made the Labour candidate win. However it is not at all clear that the Labour voters were neutral, or NatLib-favoring, about NatLib versus Green. There is no way to tell how the Labour voters ranked the others from the AEC's simplified election summaries, but we can say that the Labour Party's pre-made "above the line" vote ranked the Greens #2 and the NatLibs second-to-last, which at least suggests Labour voters prefered Greens>NatLibs. We are nevertheless going to proceed under this assumption to see what consequences would follow. Then later, we shall reconsider what happens if we drop this assumption in favor of the opposite view that they prefer Green>NatLib. Actually we shall consider 3 cases: [c1] the Labour voters prefer Green>NatLib, [c2] prefer NatLib>Green, or [c3] do not care. In all 3 cases we will see there had to be a pathology in the election, it is just that we do not always find the same pathology. We shall begin with cases c2 & c3 now, and the "reconsideration" will later handle c1 [which is the one I consider most likely to be actually correct]. We proceed:

[c2 and c3]: All nine of these examples are pathological in the sense that if we add an appropriate number (respectively 30200, 33700, 23100, 26500, 23200, 26200, 30100, 17050, and 15000) of extra Green>Labour>NatLib voters, then those voters, by casting their honest vote, would cause the result to worsen (their most-hated NatLib would win in both cases). In other words we have a "participation failure" or "no-show paradox" or "spoiler" scenario (all 9 examples have the same structure and all 3 of these epithets are simultaneously valid in every case) where adding extra identical honest Green votes would worsen the election winner in the view of these new voters.

These extra Greenies would be better off dishonestly betraying their favorite by ranking him/her below top (IRV doesn't care how far below); they also would be better off not voting (which is in fact what happened). That's the "paradox."

So the picture is fairly clear based on my hopefully-exhaustive examination of all 150 Australian 2007 House races. Exactly two things happened:

1. IRV and plurality winners agree – IRV was no improvement versus plurality – 141 out of 150 cases.
2. They disagree – but in 9 out of 9 cases where that happened, there was a "participation failure" paradox/pathology allowing the defeated NatLib a valid gripe against the legitimacy of both his defeat and the IRV voting system.

Reconsideration – you can wriggle out of that, but then... meet "Condorcet-failure"!

If the Labour voters all preferred Green>NatLib, then our analysis above finding "participation failure" pathology in all 9 IRV-swung elections, is invalidated. However, we warn IRV-proponents not to be relieved about that. That's because this new opposed assumption doesn't "save" them so much as "throw them out of the frying pan into the fire."

[c1]: The official pre-made party line vote-recommendations in Australia 2007 were as follows (restricted to Labour,NatLib,Green only and ignoring other parties):

Suppose all the Labour, NatLib, and Green voters indeed voted this way. In that case, Green was the "Condorcet winner," i.e. would have beaten both rivals in a head-to-head contest, in every race in which neither the Labour or NatLib won an outright majority – i.e. in all 9 of the IRV-swung races, plus plausibly a lot more races too.

In all these races, IRV refused to elect that Condorcet winner! The Green candidate would have had the very legitimate gripe "I would have defeated every rival head-to-head, so I should have won"! That's arguably an even worse "pathology" being exhibited by IRV, and whether or not it was "worse," it definitely occurred more often.

Range and Approval voting would have outperformed IRV in these elections.

Analogous look at Irish presidential (IRV) elections

Puzzle 55d: the presumed underlying theoretical reason this pathology is so common

IRV "paradox probabilities" calculations in 3 probabilistic models

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