IRV Exhaustion

by Clay Shentrup & Warren D. Smith     skip to Moral at end

A major talking point from the Instant Runoff Voting community is that IRV "always elects a majority winner".

We already know that this cannot be true in the absolute sense, because of Condorcet cycles and IRV winner=loser pathologies.
It is also false because IRV can eliminate the true majority winner prior to the final round, as happened in Burlington 2009..

Here we consider another reason why IRV, in practice, can easily elect a candidate without majority support: ballot exhaustion.

San Francisco uses the "top 3 only" variant of IRV, which has ambiguously (and misleadingly) been called "Ranked Choice Voting." With this system, voters pick a first, second, and third choice, instead of ranking all the candidates. What can then happen is that, even in the final round, the winner still has less than 50% of the votes. In fact this is quite common: in San Francisco 2006 it happened in every race in which the winner had below 50% in the first round, i.e. in which a "runoff" was needed at all. Here are the two examples, from the official City & County of San Francisco government web site.

Notice that Ed Jew defeated Ron Dudum in the final round, with 8388 votes (38.2% of the 21985 total votes) to Dudum's 7587 (34.5%) – these figures after all vote "transfers" have been performed. If you remove the 2253 undervotes and 193 overvotes from the 21985 then Jew's 8388 is 42.9% of the 19539 total remaining ballots. Either way, Jew won with far fewer than 50% of the voters supporting him. (Nobody knows what more than 27% of the voters thought about the final Jew vs. Dudum match-up.)

Later note: In 2009 Ed Jew was sentenced to 64 months in prison after pleading guilty to extorting $80,000 in cash from local business owners.

SOURCE

A similar thing happened in District 6, where Chris Daly won with 8968 final-round votes out of 19915 cast, i.e. 45.0%. But if you remove the 2027 under- and 160 overvotes from the 19915, then as a fraction of the remaining 17728 votes, Daly's 8968 really was (just barely) a majority, 50.6%, although as a fraction of the 17941 ballots San Francisco considered "eligible" (i.e. used) for the purpose of first-round voting (i.e. used for the purpose of voting), Daly's final 8968 was (again just barely) not a majority.

SOURCE

What about 2004?

Was 2006 just a bad year for San Francisco? No – 2004 was even worse:

• In district 1, Jake McGoldrick won with 14011 ballots in the final round, i.e. 45.6% of the 30721 cast and 48.7% of the 28787 regarded as "eligible" and thus used in the election.
• In district 5, Ross Mirkarimi won with 13211 ballots in the final (19th!) round, i.e. 33.7% of the 39255 cast and 37.6% of the 35109 regarded as "eligible" and thus used in the election.
• In district 7, Sean R. Ellsbernd won with 13834 ballots in the final round, i.e. 39.6% of the 34905 cast and 43.9% of the 31639 regarded as "eligible" and thus used in the election.
• In district 11, Gerardo Sandoval won with 10679 ballots in the final round, i.e. 42.9% of the 24902 cast and 46.1% of the 23176 regarded as "eligible" and thus used in the election.

SOURCE

Again, in every single case where there was not an immediate first-round majority, the winner got less than a majority in the final round!

The Moral?

In all six cases in San Francisco 2006 and 2004 where there was not an immediate first-round majority, the winner got less than a majority in the final round. At least 20 IRV elections 2004-2011 featured non-majority winners.

Bastardized top-3 IRV is a popular variant pushed by IRV advocates who often proclaim that IRV will "always elect a candidate preferred by a majority of voters. " Ballot exhaustion is yet another reason why, at least for the San Franciscan "ranked choice" form, those claims are (very) false.

Return to main page