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.

 

 Race and Candidate Pass 1 Pass 2 Pass 3 Pass 4  

Pre-RCV
Count

Pre-RCV Diff.

 MEMBER, BOARD OF SUPERVISORS DIST. 4
 RON DUDUM

5,134

5,521

6,305

7,587

 

 

5,072

62

 ED JEW (Winner)

5,184

5,441

6,455

8,388

 

 

5,125

59

 JAYNRY MAK

4,569

5,012

5,851*

 

 

 

4,504

65

 DOUG CHAN

3,236

3,414*

 

 

 

 

3,192

44

 HOUSTON ZHENG

234*

 

 

 

 

 

225

9

 DAVID FERGUSON

1,455*

 

 

 

 

 

1,419

36

 WRITE-IN

2*

 

 

 

 

 

2

0

 Eligible Ballots 

19,814

19,388

18,611

15,975

 

Undervotes

2,253

 

 Exhausted Ballots 

2,171

2,597

3,374

6,010

 

Overvotes

193

 

 Total Ballots 

21,985

21,985

21,985

21,985

 

Total

21,985

 

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.

 

Race and Candidate Pass 1 Pass 2 Pass 3 Pass 4 Pass 5  

Pre-RCV
Count

Pre-RCV Diff.

 MEMBER, BOARD OF SUPERVISORS DIST. 6
 VILIAM DUGOVIC

340

348

358*

 

 

 

 

330

10

 GEORGE DIAS

230

231*

 

 

 

 

 

222

8

 MATT DRAKE

679

688

725

830

869

 

 

669

10

 CHRIS DALY (Winner)

8,746

8,763

8,803

8,871

8,968

 

 

8,654

92

 DAVY JONES

389

402

421

463

506

 

 

372

17

 ROBERT JORDAN

125*

 

 

 

 

 

 

119

6

 MANUEL JIMENEZ, JR.

317

328

375

399*

 

 

 

311

6

 ROB BLACK

7,115

7,134

7,173

7,215

7,303

 

 

7,051

64

 WRITE-IN

*

 

 

 

 

 

 

0

0

 Eligible Ballots 

17,941

17,894

17,855

17,778

17,646

 

Undervotes

2,027

 

 Exhausted Ballots 

1,974

2,021

2,060

2,137

2,269

 

Overvotes

160

 

 Total Ballots 

19,915

19,915

19,915

19,915

19,915

 

Total

19,915

 

SOURCE

What about 2004?

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

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.


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