By Anthony Gierzynski, Wes Hamilton, & Warren D. Smith, March 2009. (skip to summary) ( Brian Olson's independent analysis) (Return to main page)
Instant Runoff Voting (IRV) advocates, especially FairVote's Terrill G. Bouricius (who lives in Burlington, formerly served there as alderman, also formerly served as a Vermont state legislator, calls himself a "political scientist," was instrumental in making IRV happen in Burlington starting in 2006, is denoted a "senior analyst" by FairVote, and in 2005 received a contract to design Burlington's IRV voter education program), often hail Burlington's adoption of IRV for its mayoral election as a "great success." Bouricius has also contended in various online posts, print media, and interviews that IRV always elects a "majority winner." E.g.
1. Under instant runoff voting, if there is no majority winner, you're not done yet. You have a runoff. But instead of calling voters back to the polls, you just declare the bottom candidates defeated, look at those ballots, and transfer those ballots to those voters' second choice. So you determine which candidate is actually preferred by a majority of voters. – Terrill Bouricius, January 1999 published interview by Labor Party.
However, there are reasons to believe otherwise... We shall show by considering Burlingon's 2009 Mayor election that all the claims by Bouricius and FairVote in bold print above are false.
This was the second IRV election conducted in Burlington and it was won by Progressive Bob Kiss. (The other 4 candidates were Andy Montroll[Dem], James Simpson[Green], Dan Smith[Indpt], and Kurt Wright[Repub]. Kiss also won the first election, held in 2006; in that election Kiss had been both the plain-plurality and IRV winner, and almost certainly also a "beats-all" and Borda winner – won by a "landslide" – so there was little basis to dispute his enthronement.)
|Official Burlington Mayoral 2009 IRV race results (election held 3 March) from http://www.burlingtonvotes.org/20090303/. 8980 valid ballots (also 4 "invalid" ballots were left uncounted). Smith, Simpson, and Write-ins were eliminated immediately & simultaneously since their "defeat was mathematically inevitable." Then Montroll was dropped. That left Wright vs Kiss in the final round, which was won by Kiss.||Unofficial Burlington 2009 Mayoral race vote data. Votes counted by Juho Laatu. Also counted independently (pdf) by Univ. Vermont students in the Vermont Legislative Research Shop supervised by professor Anthony Gierzynski. (All 8980 ballots included in these counts, but candidates other than Kiss, Wright, and Montroll are ignored. Further data processing by W.D. Smith. There are disagreements among the Laatu, UVM, and official counts by up to 5 votes. )||
[Sample ballot (pdf)]
Pairwise-defeats matrix: entry says how many voters preferred canddt in that row over canddt in that column.
Remarks on the counts: Unfortunately, the Official, Laatu, and U.Vermont counts all disagree; but never by more than 5 votes (which is small enough that none of our conclusions below will be affected, no matter which count you trust). Laatu's count (done by software inputting official ballot files) is the most complete of the three and is the one we shall use below. The official count (which we downloaded various times, the latest on 27 March 2009 from Burlington's web site; it had not changed) was also done by computer using the same input files; but the U.Vermont count was done manually. We believe we understand the reason for the Laatu-vs-Official discrepancy: it is that the official count treated ballots involving equal-rankings in a stupid manner. Specifically, the official method apparently discarded the 4 ballots ranking their top-two candidates equal; but did not discard ballots ranking other candidate-pairs equal. This approach is a holdover from the olden pre-computer days when a ballot had to be put in one or the other pile. Since this election was counted by computer there was nothing stopping the computer from putting half of the vote in both piles. That, it seems to us, would have more-accurately reflected what the voter wanted (versus just discarding her vote entirely). This subpage gives full details about these discrepancies (as well as the full set of votes, plus many other calculations, e.g. full pairwise table).
1. According to the pairwise table, Democrat Andy Montroll was favored over Republican Kurt Wright 56% to 44% (930-vote margin) and over Progressive Bob Kiss 54% to 46% (590-vote margin) majorities in both cases. In other words, in voting terminology, Montroll was a "beats-all winner," also called a "Condorcet winner" – and a fairly convincing one.
However, in the IRV election, Montroll came in third! Kiss beat Wright in the final IRV round with 51.5% (252-vote official margin).
We repeat: According to the preferences stated by the voters on their ballots, if Montroll had gone head-to-head with either Kiss or Wright (or anybody else) in a two-man race, he would be mayor. This refutes Bouricius's claim that IRV "determines which candidate is actually preferred by a majority of voters."
Indeed, the electorate expressed a clear ordering among the candidates:
Montroll > Kiss > Wright > Smith > Simpsonwith a majority preferring every candidate higher in the ordering, over every candidate lower in it. And the "Montroll vs X" counts were
IRV elected Kiss, not Montroll, based on Kiss's "majority" (margin 250) versus Wright.
- Montroll was preferred vs Kiss by a voter Majority, 4067-3477, margin 590.
- Montroll was preferred vs Wright by a voter Majority, 4597-3668, margin 929.
- Montroll was preferred vs Smith by a voter Majority, 4573-2998, margin 1575.
- Montroll was preferred vs Simpson by a voter Majority,6267-591, margin 5676.
- Montroll was preferred vs All Write-Ins Combined by a voter Majority, 6658-104, margin 6554.
- There were no other candidates.
- Note that even Montroll's weakest margin (590 over Kiss) was 7.8% as a percentage, which is a pretty clear win. 7.8% was a greater victory margin than in 6 of the the 7 USA presidential elections 1988-2012.
Of course it was a huge success! No voting machines exploded or burst into flames. A majority of voters did not suffer from paper cuts.
(Montroll, incidentally, was endorsed by both former VT governor Howard Dean and the Burlington Free Press. It is possible in principle for IRV to yield even more dramatic thwarted-majority pathologies, e.g. X defeating every rival pairwise by 99:1 or larger majorities, yet still IRV eliminates X in its first round.)
2. Despite that, IRV still seems to have performed better in this election than plain plurality voting, which (based on top-preference votes) would have elected Wright. That would have been even worse, since Wright actually was a "lose-to-all loser" among the Big Three, i.e. would have lost head-to-head races versus either Kiss or Montroll.
Incidentally, plurality also elects Wright with reversed ballots (M,K,W only), i.e. paradoxically regards Wright as both the best winner and worst loser among the Big Three! IRV can also exhibit such "reversal failures" but did not in this particular race.
3. Also, in this IRV election, Wright was a "spoiler"; if Wright had not been in the race then Montroll would have won (which the Wright voters would have preferred: 1513 were for Montroll versus 495 for Kiss). Any voters who voted for Wright as their favorite "without any fear of inadvertently electing Kiss" were foolish to lack such fear, because, in fact, if they instead had "calculated" right, they could have strategically voted Montroll and thus avoided electing Kiss. (That's an example of "favorite-betrayal.") This refutes Bouricius's & FairVote's other claims shown in bold print.
4. Another problem with IRV is the fact that it cannot be counted in precincts because there is no such thing as a "precinct subtotal." That's bad because it forces centralized (or at least centrally-directed) counting, thus making the election more vulnerable to fraud and communication outages. This election also exhibited this kind of nonadditivity paradox. There were 7 wards. Apparently, the ward-winners (if IRV had been done in each ward independently) would have been
Let's just say that it is hard to infer from this that Kiss "should" be the overall IRV winner – most people would guess Wright or Montroll before guessing Kiss, especially if they knew that Wright voters expressed a preference for Montroll over Kiss by more than a 3:1 ratio.
It is possible in principle for IRV to yield more-dramatic such pathologies, for example X can be the IRV winner in every district, with Y the IRV winner in the whole country.
5. If we assume that the "W" voters who expressed no preference for K>M or M>K are regarded as (really) favoring one or the other with 50% chance – e.g. if "W"s are regarded as half W>M>K and half W>K>M (or any realistic ratio of W>K>M and W>M>K besides 50-50) – then this election also featured (what voting theorists call) a "no-show paradox." That is: If 753 Wright voters who favored Montroll over Kiss had simply stayed home and refused to vote, they would have gotten, in their view, a better election winner (Montroll) than they got by honestly voting. So for them, a better "calculation" than voting honestly, was not voting! (More details.)
6. Finally – and probably craziest of all – this election also featured non-monotonicity. If 753 of the W-voters (specifically, all 495 of the W>K>M voters plus 258 of the 1289 W-only voters) had instead decided to vote for K, then W would have been eliminated (not M) and then M would have beaten K in the final IRV round by 4067 to 3755. In other words, Kiss won, but if 753 Wright-voters had switched their vote to Kiss, that would have made Kiss lose!
With non-monotonicity we can be 100% certain that IRV must have delivered the "wrong winner" in either the election, or in the altered election got by changing the 753 votes (or both) – there is no way to contend both winners were sensible choices. (And the same sort of remark can also be made about no-show paradox elections.)
In terms of the frequency of non-monotonicity in real-world elections: there is no evidence that this has ever played a role in any IRV election – not the IRV presidential elections in Ireland, nor the literally thousands of hotly contested IRV federal elections that have taken place for generations in Australia, nor in any of the IRV elections in the United States... Monotonicity has little if any real world impact. – FairVote web page on "monotonicity" downloaded 15 March 2009 and again Feb. 2011 (still makes this claim).
|Method||Winner (full vote set)||Winner (M,K,W only)|
|Nanson-Baldwin, Black, BTR-IRV, Raynaud, Schulze-beatpaths, Simpson-Kramer minmax, Tideman-ranked-pairs, WBS-IRV, Copeland, Heitzig-River, Arrow-Raynaud, Borda (if combine all write-in canddts into "one" or omit them), Dodgson, Keener-Eigenvector, Brian Olson's IRNR method, Sinkhorn, Bucklin, and (probably) Range & Approval||MONTROLL||MONTROLL|
|AntiPlurality and Coombs||?||MONTROLL|
Notes: There really is no sensible way to run Borda, Coombs, or AntiPlurality elections if there are write-in candidates.
We do not know who Range & Approval voting would have elected because we only have rank-order ballot data – depending on how the voters chose their "approval thresholds" or numerical range-vote scores, they could have made any of the Big Three win (also Smith). However it seems likely they would have elected Montroll. Here's an analysis supporting that view: Suppose we assume that voters who ranked exactly one candidate among the big three would have approved him alone; voters who ranked exactly two would have approved both, and voters who ranked all three would have approved the top-two a fraction X of the time (otherwise approve top-one alone). The point of this analysis, suggested by Stephen Unger, is that voters were allowed to vote "A>B," which while mathematically equivalent to "A>B>C" among the three candidates A,B,C, was psychologically different; by "ranking" a candidate versus "leaving him unranked" those voters in some sense were providing an "approval threshhold." Then the total approval counts would be
Note that Montroll is the most-approved (and Wright the least-approved) regardless of the value of X for all X with 0≤X≤1.
Hence: pretty much every voting method mankind ever invented would elect MONTROLL – making this a pretty easy election to call – except that IRV elects KISS and plurality elects WRIGHT. This election thus singles out IRV & plurality as nearly-uniquely bad performers.
Another way of looking at it is: among the Big Three, all these voting methods, including IRV, unanimously agree that Wright is the worst choice, i.e, they all would elect Wright using reversed ballots. (The exceptions: AntiPlurality would select Montroll and Coombs would select Kiss as "worst.") If we agree Wright is clearly worst, then it comes down to Kiss vs Montroll. And the voters prefer MONTROLL over Kiss by 4067 to 3477.
Our observation is that IRV-propagandists generally follow this 4-step procedure.
(When with a new audience, they revert back to step 1.)
(Update 27 March 2009) IRV propagandists indeed responded roughly as predicted above: Extensive discussion & compressed summary.
(Update: March 2010 and 2011) Burlington by referendum voted to repeal IRV. Unfortunately the only choices the referendum provided were (a) IRV or (b) a plurality+runoff scheme; no particularly good voting-system choice (c) was available. A year later still, Mayor Kiss attempted to bring back IRV by a "backdoor" method – or his critics interpreted it that way – but this attempt was rejected by Burlington's voters by a 58-42 margin [Burlington voters decisively defeat two key proposals backed by Mayor Bob Kiss, Burlington Free Press article by John Briggs 1 March 2011].
As shown in this election, IRV does not "solve the spoiler problem," does not "allow voters to vote their true preference without fear of inadvertently electing a candidate they cannot stand," and it does not elect candidates "actually preferred by a majority." These and other (e.g. non-monotonicity) pathologies are not rare. IRV in this election did not serve as a "bulwark of democracy" – rather the opposite. Our belief is that range voting, also known as "score voting," (and probably also approval voting) would not have exhibited any of these problems and in the present example would have elected Montroll, with Kiss second. (Indeed range voting never exhibits non-monotonicity or spoilers, and it is rare that it refuses to elect beats-all winners.) Kiss would probably have done better (relatively speaking) with range than with approval, though – based on general principles. Specifically, we can simplistically regard Kiss as "leftist," Montroll as "centrist," and Wright as "rightist" in this election. IRV tends to favor extremists while approval voting tends to favor centrists; but range voting has little or no built-in favortism for or against either.
Anthony Quas: Anomalous Outcomes in Preferential Voting, Stochastics and Dynamics 4,1 (2004) 95-105;
William H. Riker & Peter C. Ordeshook: An Introduction to Positive Political Theory (Englewood Cliffs, NJ: Prentice-Hall, Inc., 1973);
Peter Fishburn & Steven Brams: Paradoxes of Preferential Voting: What Can Go Wrong with Sophisticated Voting Systems Designed to Remedy Problems of Simpler Systems, Mathematics Magazine 56,4 (September 1983) 207-214.
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