Vote-counting: election-system analysis

[lpetrich]

Winners of RCV Races - FairVote

I'd posted earlier on Every RCV Election in the Bay Area So Far Has Produced Condorcet Winners - FairVote but this work is more recent, mentioning some work that was published in 2019.

• Since 1992, 49 senators from 27 states have been elected with less than 50 percent support.
• Primary elections are also often decided with small pluralities. The chart below shows plurality wins in primary elections for U.S. House of Representatives races in 2018. In some highly-contested races, winners received as little as 22% of the vote -- meaning 78% of people voted against them.
• There have been 204 single-winner ranked choice elections in the U.S. which included at least 3 candidates. In 96 of these (or 47%), a majority winner was identified in the first round. The remaining 108 races went into the instant runoff before declaring a winner.
• Sometimes, the winner of a single-winner RCV election does not have a majority of total votes cast in the first round. A winner is declared when a candidate has a majority of votes which are active in that round of counting, which excludes ballots which have become exhausted. This has occurred in 63 single-winner RCV elections in the U.S. As noted by Burnett and Kogan, ballot exhaustion is sometimes due to jurisdiction limiting the maximum number of rankings to three. 53 out of 63 elections in which the winner had fewer than 50% of first-round votes occurred in elections which limited voters to three rankings. You can learn more about the majority criterion with RCV in our FAQ.

Of the 353 single-winner RCV races in the US since 2004, 15 were won by a candidate who was not first place in the first round. Of these, 14 were in second place, and 1 in third place.

Of these, 322 of them have enough available info to judge whether the race had a Condorcet winner. Every one of them did, and in all but one case, the Condorcet winner was the IRV winner. The exception: the 2009 Burlington VT mayoral election.

 

[lpetrich]

"Monotonicity in ranked voting means that ranking a candidate lower can never help them, and ranking a candidate higher can never hurt them."

Every system where the votes are counted in rounds has a risk of a non-monotonic outcome, including top-two and IRV.

We have not identified any RCV election in which any group of voters has attempted to exploit the possibility of non-monotonicity for strategic purposes. Doing so successfully would both require a highly unusual set of circumstances, and a detailed and accurate understanding of how the electorate will rank the candidates. Because this is prohibitively difficult, the issue of monotonicity under RCV is largely academic - it has never had any impact on any RCV campaign and is unlikely to have any impact in the future.

There is only one election with a possibly non-monotonic outcome: Burlington 2009.

Montroll was the Condorcet winner, but was third in the top-preference. So when the count was down to three candidates, he was dropped, and since more of his votes were transferred to Kiss rather than to Wright, Kiss won.

Whether this election constitutes a non-monotonic outcome depends on how strictly the criterion is defined. There was no candidate that could have won merely by voters ranking him lower. However, if between 367 and 589 Wright voters had instead ranked Kiss first (without changing any other ballots), Wright would have been eliminated instead of Montroll, and Montroll would then beat Kiss. In other words, there is a group of voters that could have caused Kiss to lose by ranking him higher. However, this would be Wright voters helping to elect Montroll. No group of voters could have elected their own preferred candidate by ranking that candidate lower.

Seems like some very careful strategy was needed here, strategy that needed precise knowledge of what the other voters would be doing.

 

[lpetrich]

Caucus Rules | Who We Are | House Democrats in the US House, adopted on July 6, 2020

I decided to look through how its internal elections work.

Its single-seat elections are done with the exhaustive vote, a multi-round procedure. Whoever gets a majority is elected. But if no candidate gets a majority, then the one with the fewest votes is dropped from the count and another round of counting is done. Essentially a separate-round version of IRV.

Its multiseat elections are done with the bloc vote, approval voting limited to the number of seats.