Metrics for de-rigging elections
Two yardsticks for measuring the benefits of ranked-choice voting
Last week’s special election in Alaska de-rigged the voting system: it improved fairness and prevented a perverse outcome. It’s quite the opposite of what Senator Tom Cotton claimed.
One appeal of many alternative voting systems is that they are more likely to be majoritarian: the winner is supported in some way by a majority of voters. Given the current tensions in our democracy, this benefit could be quantified in two different ways: not just maximizing the good outcome, but also avoiding bad-faith manipulations. A possible step toward this goal uses two concepts that come up in science: true positives and false positives.
First, the downside. in any reform, bad actors will seek to manipulate the
rules to their advantage. I would define a false positive as an outcome where a candidate would lose to her major opponents one-on-one, but who finds a way to manipulate a more complicated situation to get herself elected. A good rule for determining the winner of an election should reduce false positives.
Sarah Palin would be such a false positive. In a head-to-head race, she lost to Mary Peltola by 3 points. This was the match that Palin should have wanted, since Peltola is a Democrat and farther from Palin than Nick Begich, the other Republican. We will not know for sure until cast-vote ballots are made publicly available, but it seems likely that Palin would have lost to Begich as well. It would be perverse for a candidate to be elected who loses both possible one-on-one contests. A good voting rule should minimize such outcomes.
In Alaska, even a first-past-the-post rule would have avoided the false-positive problem. Palin did not get the most votes in the first round. With a small number of candidates, first-past-the-post avoids false positives more often than not. The top-four (one of the four, Al Gross, dropped out) round that determined these three candidates set the stage.
Then there is a more basic desirable outcome: the winner should be preferred in a head-to-head contest with any other single opponent - the Condorcet winner criterion. Let’s call that a true positive. Now we have two criteria for a good voting system: identify the best winner (find the true positive) and don’t get hijacked by bad actors (avoid false positives).
Reformers often cite the problem that in a first-past-the-post system, it’s possible to win office without the support of a majority of votes. A ranked-choice rule reduces the risk by successively eliminating less-popular candidates. However, that process can fail. We don’t know whether Mary Peltola might have lost to Nick Begich in a one-on-one contest. After all, Begich is closer to Peltola ideologically, and Palin is viewed unfavorably by 60% of Alaskans.
To give you an idea of how likely the plurality winner is also a true positive, here are some results from a small simulation of 200 elections. (see the MATLAB code)
As the top first-choice finisher gets more votes, the more likely she/he is to win a ranked-choice election. (Note that the numbers here are approximate. For an exact relationship, one would start from real election data.)
A candidate can game the system, especially if voters are polarized. If an extreme candidate gets 50% of her supporters to list the opposite-extreme candidate as a second choice, she has a better chance against that candidate. Palin pursued a weaker version of this, discouraging her supporters from ranking Begich second.
In today’s simulations, here is how often an uplift-the-opposite strategy works:
In the French presidential race this year, extreme right candidate Marine Le Pen actually told her supporters to do exactly this - though not enough of them complied for it to work. That election began with a top-two primary, followed by a majority-vote runoff. Le Pen made it to the runoff, but then lost to centrist Emmanuel Macron. Le Pen had instructed her supporters to mark as their second choice the leftist candidate Jean-Luc Mélenchon. If he had made it to the runoff, surveys showed that she would have beaten him. Similarly, in California, which also uses a top-two primary, partisan strategists will attempt to game the rule by flooding the zone with weak candidates.
Such efforts can backfire. Sometimes an opposite-extreme candidate might end up winning!
The Alaska system attempts to reduce such game-playing by having not a top-two primary, but a top-four primary. To my knowledge, simulations have not been done to quantify whether four is the best number to avoid false-positive problems, reduce the cognitive burden on voters for the final election, and bring other benefits.
This brings me back to the reason that I’m writing about true positives and false positives in the first place. It’s not just an academic question! Right now, multiple reforms are being proposed. In addition to Top Four, other suggestions include approval voting, ranked-choice partisan primaries, and multimember districts. It would be helpful to know how these approaches stack up to one another, especially in different local and federal political environments. A true positive/false positive approach can help.
It’s likely that most or all the proposed reforms would be superior to the current first-past-the-post system. If so, rather than make fine distinctions about the merits of the various methods, it might be more constructive to acknowledge that any of them would be preferable to what we have now.
I look forward to hearing from passionate advocates of each reform. Also, if you have more ideas for metrics, I am interested in those as well.
I plan to develop this idea further and apply it to the other rules, of which there are at least a dozen. Stay tuned!
You might be interested in Levin and Nalebuff (1995) who compared different election systems using British Union election data. "An interesting feature of these British elections is that voters are required to rank the candidates. As a result, knowing the voter ranking, we can simulate elections under a variety of electoral systems. It is perhaps remarkable that among the 30 elections we examined, with the exception of plurality rule and single transferable vote, none of the other seven alternatives considered gave a different top choice (see later section). The systems differed in the rankings of the lower candidates. This empirical regularity suggests a connection to some recent theoretical work (Caplin and Nalebuff, 1988, 1991): when voter preferences are sufficiently similar, a variety of voting systems lead to similar choices, and these choices have desirable properties."
Recently, I've come to appreciate some of the advantages of ranked choice over approval voting (specifically the latter is susceptible to electoral ambushes by small but motivated slivers of the electorate). But we shouldn't lose sight of the empirical data suggesting that anything other than plurality voting will tend to give similar results.
In the news today we see Sarah Palin and Mark Begich going after each other on who would be the stronger opponent for Peltola ... if only we had the ranked-choice date on Begich vs Peltola ... sigh