Burlington Vermont 2009 IRV mayor election

Thwarted-majority, non-monotonicity & other failures (oops)

By Anthony Gierzynski, Wes Hamilton, & Warren D. Smith, March 2009.    (skip to summary)    ( Brian Olson's independent analysis)    (Return to main page)

The Propaganda

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.

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.

The votes

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.)

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).

The pathologies

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 > Simpson with a majority preferring every candidate higher in the ordering, over every candidate lower in it. And the "Montroll vs X" counts were

• 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.

IRV elected Kiss, not Montroll, based on Kiss's "majority" (margin 250) versus Wright.

(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.)

Was that "hypothetical" and depending on "cooked data"? No. Unfortunately some have acquired that mis-impression, either due to IRV-propagandists attacking me and trying to muddy the waters, and/or my failure to write clearly enough. So let me now re-state the situation more clearly. The no-show paradox in Burlington was viewable as follows:

1. All votes were of these 9 forms M>K>W, M>W>K, M>K=W, W>M>K, W>K>M, W>M=K, K>W>M, K>M>W, K>M=W if restricted to Burlington's top-3 candidates {W,K,M} only.
2. If we modify that election to remove some ballots of form W>M=K as well as some ballots of form W>M>K (note all of these ballots ranked K either sole bottom or coequal bottom): that causes K to stop winning and M to win.
3. That was a paradox. Nothing hypothetical needed: just use the actual, entirely un-hypothetical, ballots.
4. Now we optionally can go further by hypothesizing that the W>M=K ballots really were W>M>K and/or W>K>M secret preferences, and that there were enough of the former so that all the removed ballots really did rank K sole-bottom either explicitly or secretly. That hypothesis strikes me as very plausible, and if true arguably would make this paradox a bit "worse." But if you don't like hypothesizing, then fine – just get rid of it entirely and we still have a genuine bottom-remove kind of paradox.

I hope that clarifies this. And the same unhypotheticalness applies to the non-monotonicity paradox we are about to explain. And there was no need to "restrict to Burlington's top-3 candidates {W,K,M} only"; you can also redo all that with the full ballots, including candidates Smith & Simpson too, but I will not give the full details of that since they would be too voluminous.

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.)

Who would other voting methods have elected?

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.

How will the IRV-propagandists respond?

Our observation is that IRV-propagandists generally follow this 4-step procedure.

1. Contend IRV is the most amazing, best-possible voting method in all sorts of (unfortunately demonstrably false) ways. This tends to impress those who think about it for ≤3 minutes or know little about voting theory.
2. When confronted with counterexamples to their claims, sneer those were mere "semantics" of interest only to "mathematicians." (Unfortunately, as we've just seen, these counterexamples have very real democracy-denying consequences.)
3. When that doesn't work (because now they're talking to somebody who actually knows something), contend such counterexamples, while admittedly making IRV look bad, only arise incredibly rarely. (E.g. FairVote "senior analyst" Stephen Hill, quoted in W.Poundstone's book Gaming the Vote, compared the rate of occurrence of IRV pathologies like non-monotonicity to that of a "major meteorite strike.") Hill must be amazed how not only non-monotonicity, but 5 other pathologies as well, all managed to occur in only the second IRV election Burlington ever tried! What an incredible fluke! This must be like the annihilation of the entire galaxy! The amazingness increases to even greater astronomical levels when you realize the number of times such phenomena have already been seen when surveying the Louisiana governor runoff elections (such as the notorious "Lizard vs. Wizard" race), or the Australia 2007 IRV races; and in the (also continually touted by these same IRV propagandists as a "great success" – as usual they never mention its pathologies when they do that) 1990 Irish presidential election, Frome 2009, ...
4. When that too has fallen to the ground, they generally claim the pathology actually was no problem, e.g. it was just great that Kiss won this election, and they see no problem with any of the vast number of pathologies here (course, they'd perceived problems back when it was a "rare" artificial election example in step 3, but that was then); or contend that better and simpler voting systems such as range or approval are somehow bad and/or unobtainable for mysterious reasons that only they possess, but which cannot be divulged or clearly explained; or falsely contend that somehow Arrow's theorem means that nothing can avoid these problems, so IRV is doing as well as anything could; or flail around trying to distract attention with some red herring.

(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) 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 (March 2011), 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. There were several Burlington Free Press articles on this repeal by John Briggs.

The truth

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.

Some references

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