Oakland California's 2010 Mayor Election

(IRV3 top3-only-restricted Instant Runoff Voting)

Election held: 2 Nov. 2010. The count (being IRV3) was difficult and it was not possible for Oakland to report official results until over 1 week later. (As of 10 Nov. we still are waiting. This page is based on a ballot file released by Oakland but not "certified" as final.) The initial reports led the press to state (wrongly) that Perata had (almost certainly) won.

11 Candidates: CANDELL, FIELDS, HARLAND, HODGE, KAPLAN, MACLEAY, PERATA, QUAN, TUMAN, YOUNG, and "WriteIn" (we have agglomerated all WriteIn votes into a "single 11th candidate," which is not really correct).

The votes: 97970 votes in all. 1150 vote-types. 1469 totally unusable "spoiled" ballots (plus more were partially spoiled and hence only partially usable).

Winners: Oakland's official winner computed via instant runoff voting (IRV3) was Quan. Quan also won under pseudoBorda count. Quan also was the unambiguous Condorcet ("beats-all") winner, if unranked candidates are regarded as ranked coequal last.

But if unranked candidates are regarded as – literally – unranked, then Perata was the unambiguous Condorcet ("beats-all") winner (a thwarted-majority paradox). Perata also was the plain-plurality winner (i.e. won IRV3's first round).

Participation-failure paradox: If 3135 new identical ballots of the form "KAPLAN>QUAN>...>PERATA" were added (which note, all rank Quan second and Perata dead last)... that (according to IRV) would make Perata win! (And make Quan lose.)

It is fortunate for them that those Perata-hating voters stayed home!

Verdict on IRV3: This election seems to be a success for IRV3: plain plurality would have elected Perata, but IRV3 successfully elected the Condorcet winner Quan. That is good in the sense the voters seem to have preferred Quan over Perata. Plain top-2 runoff (two rounds) presumably also would have elected Quan. However it is not possible to tell for sure if plain runoff would have elected Quan, nor whether the voters really preferred Quan over Perata, because over 7000 voters did not rank either. Depending on how those 7000+ voters felt about them relatively, a Quan-v-Perata head-to-head race could have gone either way (7000 was far more than required to swing it).

Despite the apparent success of IRV3, it is disturbing that it suffered a "participation paradox" (which also would have afflicted plain top-2 runoff): 3135 Perata-hating voters, by the act of not voting, caused Perata's defeat. (If they'd voted against him, Perata would have won.)

It also is disturbing that full IRV might well have returned a different result than the IRV3 process actually used. In other words, the rule forcing voters to rank at most three candidates, may have backfired and may have prevented the true IRV winner (who, e.g, might be Perata) from winning.

Approval & Score=Range voting: It is not possible to tell for sure from this data whom Approval and Score voting would have elected. But my current guess is Quan under both. Why?
First reason:

• Suppose every voter who ranked exactly 1 candidate, would have approved him alone.
• Suppose every voter who ranked exactly 2 candidates, would have approved either only her top choice, or both, with a fraction G of these votes doing the former and fraction 1-G the latter.
• Suppose every voter who ranked exactly 3 candidates (the maximum number Oakland permitted her to rank), would have approved either only her top 2, or all 3, with a fraction F of these votes doing the former and fraction 1-F the latter.

Then: Quan would have won an approval-voting election no matter what the values of F and G with 0≤F≤1 and 0≤G≤1.

Second reason: if the voters had realized the two most likely to win contenders were Quan & Perata, and hence to strategically make their votes have more "impact" always approved one and not the other, then (as far as can be told from the IRV3 ballots) Quan would have won.

Note that these two systems [Approval & Score/Range] can never suffer participation paradox – adding extra votes all rating A below B can never cause A to win and B to lose – and also cannot suffer thwarted majority paradox in the sense that if A beats B (with range or approval voting) with all the other candidates erased from all the ballots, then A will beat B, period. Unfortunately IRV can suffer both of those paradoxes, and it did in this election (although the second paradox was only suffered in Oakland 2010 if we regard unranked candidates as literally unranked).

Acknowledgments: I thank Juho Laatu for converting Oakland's ballot-image file to a sensible format and Rob LeGrand and Eric Gorr for software.

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