Voices & Choices

Understanding Condorcet Winners and Non-Monotonicity Through the Lens of Berkeley's District 2 City Council Race

Understanding Condorcet Winners and Non-Monotonicity Through the Lens of Berkeley's District 2 City Council Race

Berkeley’s District 2 City Council race was one of only two Bay Area ranked choice voting (RCV) races this year to feature a come from behind victory. Cheryl Davila, a local activist, won 31% of the first round vote, unseated incumbent Darryl Moore, who won 39% of the first round vote. The key to Davila’s victory in the final “instant runoff” was obtaining nearly three out of four votes from the third place finisher, Nanci Armstrong-Temple’s, after she was eliminated. Armstrong-Temple won 29% of the vote in the first round, and 73% of her voters ranked Davila second. Davila is now the only African American woman on the Berkeley city council. 

In a certain sense, this outcome is what RCV is all about: candidates with a combination of first choice support and broad support defeating candidates who might have large plurality support, but fall short of a majority coalition. Davila better represents the district when she wins the final head-to-head comparison against Moore.

But the close outcome raises a question for voting method analysts who like to get into the weeds of elections. Given the narrow tally for second (31% for winner Davila versus 29% for first-round loser Armstrong-Temple), was Davila truly the strongest candidate? By simulating a matchup against Armstrong-Temple using the ballot rankings already available, we can determine that Davila was the Condorcet winner: that is, she was the candidate most of the population would favor when matched against either one of her opponents, as shown below. FairVote has found that all RCV winners in every Bay Area contest with RCV so far have been Condorcet winners, and more information on this metric and its relative merits can be found in our recent blog post.


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A studious observer will notice one troubling consequence of these simulated pairwise matchups (that we include along with the actual Davila-Moore matchup). Moore beats Temple in a one-on-one matchup, despite Temple and Davila largely drawing from the same coalition. This is an artifact of slightly more Temple voters liking Davila than Davila voters liking Temple, and in and of itself it is not cause for concern. However, because the margins in these matchups are so small, and Davila’s first round vote share is very similar to Temple’s, it is easy to imagine very similar scenarios with very different results. Doing so will allow us to examine some of the more difficult facets of RCV (and also with traditional runoffs, which share the same property, but in fact are more prone to manipulation), but also why even close calls such as this District 2 race almost always fail to produce the most troubling possible outcomes.


Scenario 1: Non-monotonicity but no change in outcome

In this hypothetical scenario, suppose Moore had run a more energetic, but polarizing campaign. This allows him to draw in 184 voters who are ambivalent about their other choices, but scares away 92 Temple voters, who switch their second choice to Davila. On the surface not much has changed. Davila still wins by the same margin, Moore would still have beaten Temple in a hypothetical matchup, and Davila would still have beaten Temple as well, meaning that Davila is still the Condorcet winner. However, Moore’s margin over Temple has increased with some troubling implications. Moore’s margin over Temple is now large enough that then he could direct 130 of his votes to her, knocking Davila out of the race, and then still beaten Temple. In essence, this means that in this theoretical scenario, 130 of Moore’s 184 new voters would have actually hurt their candidate by ranking Moore first instead of Temple. This is known as non-monotonicity, and is explored further in Scenario 2.

It is important to note here that knowledge that this had even occurred or had the potential of occurring is only possible in hindsight. In a fairly low intensity local election, candidates like Moore who aren’t actively pursuing an RCV strategy are unlikely to know their supporters second or third preferences. Even when candidates do endorse one another, there are always voters who choose their own second or third rankings or only vote for their favorite candidate.


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Scenario 2: Non-monotonicity and Condorcet failure

Suppose that our 130 new Moore voters see scenario 1 coming (although in the real world this of course is not possible) and really do decide to vote for Temple in order to subvert the Davila coalition. In this scenario, Davila loses to Temple by one vote, becoming the first eliminated candidate, and then Moore beats Temple by one vote, winning the narrowest of victories.  Davila is still the Condorcet winner, she still beats Moore by 168 votes and Temple by 264, but she is no longer the winner due to finishing last in the first round. This scenario is why non-monotonicity in scenario 1 is troubling, but trying to illustrate how it would happen also demonstrates just how unlikely it is.

Note how difficult the scenario would be to actually carry out. That is, not only would Moore have had to earn more votes in order to win, he then somehow would have had to known that it was strategically smart to ask a very precise number of them to vote for another candidate - perhaps fun to map out on a chalkboard, but utterly unrealistic in the real world of politics.

Even if the Moore camp could coordinate this kind of manipulation, estimating their support or Temple’s wrong by even a few votes would cause their least favorite candidate, Temple, to win. The fact that RCV and traditional runoffs can hypothetically allow the Condorcet winner to lose troubles some,  but as we will see in scenario 3, Condorcet failure can happen independent of any RCV mechanism.


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Scenario 3: No Condorcet winner, everyone can claim they should have won

Adjusting Moore voters’ second ranking preferences so that his voters split between Davila and Temple equally, demonstrates another reason why issues of election procedure can become so thorny. Sometimes there is no Condorcet winner. By having 133 Moore voters change their second choice from Davila to Temple, we can create a scenario in which Moore wins against Temple, Davila wins against Moore, and Temple wins against Davila. In essence we have taken the electoral preferences of 7322 people and created a very elaborate game of rock-paper-scissors.

Who ought to win here? Davila still has the largest margin in her victory scenario, Temple can claim that since she would have beaten Davila she should win, Moore can claim that since he had the largest base he should win. There is no consistent alternative criterion with which to adjudicate between these claims. Moore’s win would likely lead some activists to cry foul, and some who were unhappy with the results might even blame RCV for leading to such a complicated outcome, but RCV does not actually create scenarios like this. Rather, because it allows voters to say more about their views than a single-vote system, it just gives us the tools to assess whether these scenarios have occurred.

Runoff elections also provide opportunities to create these sorts of comparisons,  and we have found significant evidence that the problem of non-Condorcet winners is far more dangerous in low turnout runoffs than it is for RCV elections.  One example that RCV would have avoided is the 2016 state treasurer race in Washington State’s “Top Two Primary, where a majority of voters in the primary voted for Democrats, but two Republicans advanced. We also know from our Bay Area study that at least two RCV & Condorcet winner would have failed to qualify for a runoff (they were in third place or lower in the initial count). 

We have no way of knowing how many of our plurality elections have Condorcet winners who lost, because plurality elections do not produce evidence of deeper voter preferences (such as second choices) that can be analyzed later. However, we do know from our study of Bay Area RCV races that, if voters had voted the same way in plurality as they did with their first choice in RCV (something of course we can’t know to be true), seven so far would have been lost by the Condorcet winner had their municipality used a plurality system. On the national level, there is evidence, particularly in areas of the country that regularly see three major contenders for certain offices, such as Maine, that these sorts of outcomes happen fairly often.


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What can we learn from our near miss with the absurd world of election irregularities? For one thing, while these situations worry some academics who study election systems, we have little evidence that they happen in practice. FairVote has conducted detailed analysis of RCV election results in the Bay Area, and has yet to find any evidence of a non-condorcet winner winning an RCV election. While FairVote has found that RCV elections increase competition, the fact of the matter is that most local elections are still not all that competitive. For situations like those outlined above to occur, several candidates have to have very similar vote totals, and their supporters need to split their second or third choices roughly evenly among the remaining candidates. Even more importantly, the issue  has  not strategic relevance -- that is, it would be folly to ever try to get voters to change their votes based on some theory that it would help in such  a scenario. There are just far too many unknowns in an election relating to voter turnout and certainty of voter preference.

FairVote is planning on conducting a serious investigation into issues involving alleged voter paradoxes within the next year. Whatever we find, it is important to note that no system for translating the nebulous preferences of the public into specific candidates and policies is perfect, but that RCV performs far better than the plurality and plurality runoff systems that most of the US uses now.

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