The only statewide election ever held using IRV in the USA (up to 2013)

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North Carolina's Omnibus Voting bill passed in 2006 created both a voluntary IRV (instant runoff voting) pilot program for local and county elections from 2007-2009 and also created mandatory IRV for certain judicial elections from that point on. The pilot was extended one more year through 2010, but then expired. Judicial IRV remained, but they canceled it in another omnibus election bill (which includes voter ID – passed by both houses of the General Assembly, and finally signed by Governor Pat McCrory on 12 August 2013).

And so it was that on 2 Nov. 2010 North Carolina held an election for Court of Appeals Judge using a version of IRV3. The winner was to serve an 8-year term. The rules: each ballot was a rank-ordering of the top three choices by that voter – or fewer if that voter chose to give only 1 or 2 choices. The winner then was to be selected from the two candidates with the top two totals; for that purpose each ballot counts as a vote for whichever of the two final candidates is ranked highest by the voter.

These rules were described by Gary D. Robertson: Concession after N.C. Court of Appeals recount widens lead, Associated Press 20 Dec. 2010 (which also claims "the ranking concept hadn't been used in a statewide race anywhere in at least 70 years"); and a (better) official description was in section b1.2 of NC state statute 163329. A good article on this is Nelda Holder: Instant-runoff voting debuts in state, county elections, 2 Sept. 2010 Mountain Express.

There also were, at the same time, 3 superior court vacancies also filled using an instant runoff process. Those other races each had 3 candidates. However, NC superior court judges are not elected statewide, but rather are contested within districts.

This race is of interest since it apparently is the only statewide election ever conducted in USA history in any state using an instant-runoff style process (up to 2013). Specifically, an NC bar association report Race For Wynn's Seat Will Require Instant Runoff Voting by Russell Rawlings (31 Aug. 2010) quotes Damon Circosta, executive director of the NC Center for Voter Education, as claiming this race was "the first time the instant runoff procedure has been used nationally in a statewide race"; and NC never did it again and abandoned the system in 2013.

The reason that NC adopted this system was a bad experience in 2004 when 8 people ran for a NC Supreme Court judgeship, and the winner Paul M. Newby was elected with only 23% of the vote. Since the seat had not opened until well after the date (May) in which primaries were normally held, there was no possibility of a runoff. This 23% victory was considered questionably democratic, and "Instant Runoff" was enacted to cure any future instance of this problem. The first test of that came in 2010 when Judge James A. Wynn was suddenly raised in August 2010 to the Federal Bench, leaving his old NC Court of Appeals seat empty with no time for the usual 2-election (including runoff) process.

There were 13 candidates and 2700383 ballots cast (official turnout=43.75%). However, of those 2.70 million ballots, only 1.94 million (72%) successfully cast at least a first-choice vote in the Court of Appeals race, so we shall count this as only 1943771 voters, which is 31.49% turnout.

In the table, the first-round results were announced to the press as "unofficial" by the NC state board of elections. As you can see, they gave Thigpen a nearly 100000-vote lead over his nearest rival McCullough. Their final results were computed by considering the second- and third-choices (if any) of the voters who chose one of the 11 eliminated candidates as their first choice (as well as, presumably, re-counting the first round results more carefully). These final results were not announced until far later (5 January of the next year, 2011) and state only the final-round totals, and only for McCullough and Thigpen – the other 11 candidates and the genuine turnout ≈1943771 were not even mentioned. (However Thigpen conceded on 20 December 2010, based on incomplete recounts; this was "only" 48 days after the election. The recount and the original count differed by about 100 votes.) Also missing: any hint of how many spoiled ballots there were. That by itself was quite remarkable. This is probably the worst official election result announcement (in terms of information provided) that I have ever seen – as well as one of the slowest counts in modern USA history.

1. Was McCullough's victory correct under the official voting rules used in this election?
2. And was it democratically correct?

(i) It is difficult to answer this, because the final margin of 6655 votes (0.34%) was so small, since the election observers were unable to satisfactorily observe the very prolonged counting, and finally since this was the first time the state had ever used IRV (making mistakes likely).

The actual vote-counting process used employed unvalidated software and hence was, technically, illegal under NC state law. According to anecdotal reports the number of "spoiled ballots" due to confused voters exceeded the usual number by a factor of about 5-7.

(ii) The "democracy" of this election is cast into doubt by the following self-contradiction, called a no-show paradox:

Suppose an additional 230000 voters – each ranking (say) Sullivan top, McCullough 2nd, Dillon 3rd, and (therefore) Thigpen and all others thus co-equally bottom – had shown up. Since McCullough officially won, you might naively imagine that adding this huge set of extra ballots, all of which ranked McCullough second and Thigpen dead last, could not have helped Thigpen win. But if you imagined that, you'd be wrong. Those extra "we hate Thigpen" votes would have made Thigpen the official winner!
    Therefore these 230000 no-show voters were very wise not to vote. If they had honestly voted their opinion that Thigpen was the worst, that would have made him win. They cleverly did not vote at all, keeping their hatred for Thigpen secret, which caused him to lose.

This tells us that either the official election result was (democratically speaking) wrong or the same IRV3 process in this new election would have been wrong (or both). It is not possible to contend that McCullough really should have beaten Thigpen and contend that with 230000 extra voters rating McCullough second and Thigpen dead last, that Thigpen really should have won.

Also, there almost certainly was a spoiler/vote-spitting problem:

There were 6 candidates from Raleigh who probably "split the vote" with each other, thus explaining why Thigpen got much fewer 2nd- and 3rd-preferences than McCullough, allowing the latter to pull ahead. If so, then had enough of the Raleigh candidates not run that (paradoxically) would have caused one of the remaining Raleigh candidates to win. Thigpen only needed a tiny 7000 extra to hold off McCullough, which almost certainly would have happened if the Raleigh vote-splitting had been eliminated by one (or several) Raleigh candidates dropping out before election day. (However, they probably had heard false propaganda that IRV3 "eliminates the vote-split and spoiler problems," so they kept on running.)
    A different vote-splitting possibility arose since of the 13 candidates, 6 were Democratic Party (including Thigpen), 4 were Republican (including McCullough), and the remaining 3 were unaffiliated. Again, this would have worked against Thigpen. The Republican Party predicted that and instructed voters to vote McCullough top, or if not, then second; while the Democratic Party had no comparable strategy-advice focus-on-one campaign.

Finally, there may have been a non-monotonicity paradox:

Suppose 94000 "Thigpen-top, Dillon-2nd" voters both (a) existed, and (b) decided to lower Thigpen to "worst." In that case, the two top finishers in the 1st round would instead have been Thigpen (301619) versus Dillon (295870) and then after the 2nd and 3rd choices were considered, quite likely Thigpen would have won. If so, then paradoxically, 94000 voters by lowering Thigpen from top to bottom on their ballot would have made Thigpen win.
    Did 94000 such voters really exist? (I am unsure, but probably at least 10000 did.) As a simplified mathematical model, assume the votes were maximally and independently random subject to the 39 totals in the 3×13 table below. In that case we would expect there to be 43167=395218×179917/(1810007-162797) such voters. This is not a proof (for that we would need to inspect the raw ballot data, which I do not have) but at least makes it mildly plausible (perhaps a 20% chance), that non-monotonicity happened. In order for it to have happened it is necessary that the Thigpen voters had at least about twice the usual propensity to rank Dillon second. To see that this level of deviation from the random model is plausible, simply consider the (other) very large deviation that we know happened – among ballots ranking both McCullough and Thigpen, far more than expected ranked McCullough ahead. Specifically, if we may ignore "spoiled" ballots, there had to be 81406 ballots ranking both but with Thigpen ranked ahead, and 180717 ranking both but with McCullough ranked ahead. The latter greatly exceeds the expectations of the random model.

More generally, McCullough's official winning plurality of 28% was well short of a majority. That meant it was mathematically possible that somebody like Dillon could have been the one with the most votes if the 2nd and 3rd preferences of the Thigpen and McCullough voters had been counted (except, of course, these were never counted). If that indeed happened, then certainly this election was a failure democratically speaking.

Also, had 4th preferences been provided and counted (which, of course, they were not) that too could easily have changed the winner.

It also is interesting to consider a different vote-counting method than the one used: let each top-rank vote for a candidate contribute 1 to his score; each second-rank vote contribute S to his score; and each third-rank vote contribute T, for some pre-agreed constants S and T with 0≤T≤S≤1. Joyce McCloy and Douglas G. Clark (editor of Greensboro News and Record) obtained the following data from the NC state board of elections on 23 December 2010 (her raw data in Microsoft excel format and county-level results converted to plain ASCII) where I have summed over counties:

(EASY) THEOREM: Thigpen's score under this system 395218+162797S+160027T exceeds McCullough's score 295620+157309S+165802T by at least 99000 for every possible pair of real numbers (S,T) with 0≤T≤S≤1. And this is true not only for McCullough, but indeed for every rival of Thigpen.

This strikes me as devastating for McCullough and indeed for everybody not named Thigpen.

Since both Thigpen and McCullough took public campaign finance money, they unfortunately had nothing left over to pay for a forensic audit of the vote and the finance laws forbade them from raising more money for that purpose – something not foreseen when the IRV law was passed.

Conclusion

I have to conclude that this IRV3 voting system yielded a miscarriage of democracy in this, the only statewide election ever conducted using it. The NC state legislature may have agreed: In 2010-2013, they both terminated the IRV pilot program and forbade IRV in North Carolina.

I thank Joyce McCloy & Chris Telesca for helpful information.

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