A Farewell to Pass/Fail:
Why We Ditched Later No Harm
By Emily Dempsey - a Portland-based mathematician and computer scientist
During our search for the best voting system we could find, we learned a lot about the various criteria that are used to compare different systems. Unfortunately, it is impossible for a voting system to pass every single criterion out there, so we had to examine which criteria actually align with what we are trying to accomplish, and which do not. In picking apart Later No Harm in particular, we concluded that it actually works against our goals. Put simply:
We set out to fix The Spoiler Effect, and discovered that Later No Harm is actually one cause of the problem.
To explain, let’s start with a definition (1.):
Later No Harm (LNH) states that a voter honestly indicating their preference (or lack thereof) between two less-preferred candidates can not cause a more-preferred candidate to lose.
That certainly sounds good, but consider another criterion (2.):
The Favorite Betrayal Criterion (FB) states that a voter honestly indicating their preference (or lack thereof) between two more-preferred candidates can not cause a less-preferred candidate to win.
That also sounds good, right?
Well, unfortunately, satisfying both criteria is impossible without introducing other undesirable qualities (3.) to the voting system, so we we’re stuck having to fail one of them.
Let’s look at an example to explore the contradictory nature of these two criteria:
The Center Squeeze Scenario
Consider the following scenario with three candidates: Alice, Bob, and Carrie.
- 40% of voters love Alice, hate Bob, and like Carrie.
- 35% of voters love Bob, hate Alice, and like Carrie.
- 21% of voters love Carrie, hate Bob, and like Alice.
- 4% of voters love Carrie, hate Alice, and like Bob.
To put it another way:
- 61% like or love Alice.
- 39% like or love Bob.
- 100% like or love Carrie.
Who do you think should win in this election?
We think Carrie, for the following reasons:
- Many more voters like Carrie than like either Alice or Bob, and
- Alice and Bob are each hated by over a third of the electorate, while Carrie is hated by no one.
- As such, Carrie winning would maximize total satisfaction of the electorate overall.
Here are the kickers, though:
Any system that passes Later No Harm cannot elect Carrie unless voters lie. (4.)
Any system that passes the Favorite Betrayal Criterion must elect Carrie unless voters lie.
Let’s try to parse this out a bit.
Later No Harm
To conclude that Carrie should win, we rely on the facts that Alice voters prefer Carrie over Bob and that Bob voters prefer Carrie over Alice, but relying on either one of those facts directly violates Later No Harm: in either case, it means that Alice voters would cause their favorite candidate (Alice) to lose by honestly expressing their preference between two less-favored candidates (Bob and Carrie)(5.). Because of that, Alice voters might decide to lie and say that they hate Carrie just as much as Bob, or even that they like Bob more than Carrie, to prevent Carrie from beating Alice. This is a voting strategy known as Burying, (6.) which Later No Harm is aimed at preventing.
Avoiding strategic voting certainly sounds all well and good! So let’s make our system pass Later No Harm. To do so, we need to ignore the down-ballot preferences of both Alice and Bob voters... but, ignoring the down-ballot preferences of Bob voters directly violates The Favorite Betrayal Criterion: Bob voters would cause their least favorite candidate (Alice) to win by honestly expressing their preference between two more-favored candidates (Bob and Carrie), since their preference for Bob over Carrie obfuscates their preference for Carrie over Alice. Because of that, Bob voters might decide to lie and say that they love Carrie just as much as Bob, or even that they love Carrie more than Bob, to force the system to not ignore the fact that they prefer Carrie over Alice, and thus prevent Alice from beating Carrie. This is a voting strategy known as Favorite Betrayal, which (gasp) The Favorite Betrayal Criterion is aimed at preventing.
It’s a paradox:
Since we must fail one criterion or the other, we needed to make an informed choice on which to fail. To that end, we went back to what it is about our current voting system that we’re actually trying to fix, and examined which criterion would best help us reach that goal.
The Spoiler Effect
The main push behind all sorts of voting reform efforts presently underway is that our current system, Plurality voting, is objectively terrible.
One of the biggest reasons why Plurality is terrible is because it is extremely susceptible to a particularly nasty phenomenon called The Spoiler Effect. (7.)
The Spoiler Effect occurs when a third candidate entering a race splits votes with a similar candidate who would otherwise win, thus causing a candidate less-preferred by the electorate to win instead.
We’re all familiar with this phenomenon; it’s also known as Vote Splitting or The Nader Effect. This is what leads to heated arguments about whether it’s better to “vote your conscience”, or whether that’d be a waste and it’s actually better to settle for “the lesser of two evils”. This is what entrenches the two-party system, and causes voters to feel like they are powerless to express their true opinions.
This is the thing we set out to fix.
And as it turns out, any system that passes Later No Harm is extremely susceptible to The Spoiler Effect.
The main issue goes back to the scenario described in the previous section, in which a (deterministic) voting system that passes Later No Harm necessarily fails The Favorite Betrayal Criterion. In such a system, voters who love Bob and hate Alice are forced to choose between honestly voting for Bob, or strategically voting against Alice. This is exactly the conundrum voters face in Plurality elections with a Spoiler Effect.
Whether they’ve realized it or not, folks who tout Later No Harm as the holy grail of voting systems criteria are actually saying that The Spoiler Effect is not a problem they think is important to fix. We respectfully disagree, and thus said goodbye to Later No Harm.
What Does This Mean For STAR Voting?
Now, the astute voting systems enthusiast may note that STAR Voting actually fails both Later No Harm and The Favorite Betrayal Criterion - but hear us out! This is actually also desirable.
The thing is, not only did we say goodbye to passing Later No Harm specifically, but we also said goodbye to taking a binary pass/fail approach to evaluating voting systems on any criteria. This is because voting systems criteria really describe extremes; to unequivocally pass one criterion is to unequivocally fail another - as we illustrated above with Later No Harm and The Favorite Betrayal Criterion. (8.)
This is a situation where perfection is the enemy of good. We believe it is better for a system to balance and maximize two opposing criteria and in doing so mitigate the ways in which it fails both, rather than to pass one criterion and in doing so exaggerate the ways in which it fails the other.
For instance, Plurality passes Later No Harm so voters will never Bury, but they are incentivized to Favorite Betray in a huge range of situations that are extremely likely to happen and very easy to predict. This is why “vote your conscience” vs “vote the lesser of two evils” is such a prolific debate in our society: the vast majority of voters have been in that exact situation and very aware of it - or at least know someone for whom that’s the case - excruciatingly often.
Meanwhile, STAR Voting reduces the incentive to Favorite Betray to only situations that are very rare in real life and extremely difficult to predict. (9.) The expressive range of scores available and the existence of an automatic runoff in STAR Voting also reduce the viability of Burying significantly. (10.) Because of this, voting honestly in STAR Voting really is a voter’s safest bet, and thus the best “strategy”. (11.) This is really what we set out to accomplish, and why we chose STAR Voting for our cause.
While this article was in the works, Jameson Quinn of The Center for Election Science published an excellent voting theory primer. He expands on many of the ideas we scratched the surface on here, and we highly recommend giving his article a read if you’d like to learn more.
This article was sited in a presentation by Sara Wolk to Sightline Institute, which goes more in depth on where to go from here in a post-binary voting science era. Equal Vote and other groups are now advocating a new lens to compare voting systems using five pillars of a just voting system: Equality, Accuracy, Honesty, Expressiveness, and Simplicity.
About the Author:
Emily Dempsey graduated from Truman State University with a BA in Mathematics and a BS in computer science. Her curiosity about voting reform was piqued after coming across C.G.P. Grey's series on voting in the animal kingdom, and became inspired to get tangibly involved in voting reform after seeing news about Maine's ballot measure in 2016. She has been working with what would become Equal Vote PDX ever since.
1. Several definitions have been used for Later No Harm in various conversations about voting systems. We believe the definition presented in this post was the best definition to use for the issues we are discussing here.
2. Similarly, The Favorite Betrayal Criterion also has various definitions that have been used in different conversations; we have defined it here in a way we believe is most useful for the discussion at hand.
3. Namely, in order to satisfy both LNH and FB as defined in this post, a voting system would have to be non-deterministic, or fail to reliably elect a majority winner between only 2 candidates. For example, Random Ballot passes both, but is not deterministic. See also: Independence of Irrelevant Alternatives.
4. By some alternative definitions of LNH, Minimax Pairwise Opposition passes LNH and yet elects C in the presented scenario with honest votes, but Minimax Pairwise Opposition fails the definition of LNH that we are discussing in this post, since changing a vote from B > C > A to B > A > C (or B > A = C) could cause B to lose to A.
5. Ignoring Bob voters’ down-ballot preferences is just as important in this situation as ignoring Alice voters’ down-ballot preferences. A formal proof doesn’t really fit here; the gist is that 1) only ignoring Alice voters’ down-ballot preferences fails LNH due to Carrie voters’ down-ballot preferences causing Carrie to lose to Alice, and 2) a system that would only ignore Alice and Carrie voters’ down-ballot preferences can be gamed by Alice voters lying about their preferences between Bob and Carrie to cause Alice to win (by causing Bob voters’ down-ballot preferences to be ignored instead of Carrie voters’), thus failing LNH.
6. Burying and Bullet Voting are two related strategies that were both described in this paragraph, but we kept it simple by just naming one. They are distinct strategies, but are in essence two implementations of the same general case of lying about down-ballot preferences. You can read more about this and other strategies at https://www.equal.vote/strategic-star.
7. As ever, multiple definitions of The Spoiler Effect have been used in various conversations about voting systems; we selected the definition that most accurately captured the phenomenon we are aiming to prevent.
8. And as has been proven by Arrow, Gibbard, and Satterthwaite.
9. Specifically, STAR Voting only incentivizes Favorite Betrayal when there is a Condorcet Cycle. Not much is known about how likely Condorcet Cycles are in real-world elections, but they are certainly less likely (and, I would wager, much more difficult for a voter to predict) than other problematic phenomena such as Vote Splitting and Center Squeeze Scenarios, in which many other voting systems incentivize Favorite Betrayal and STAR Voting does not.
10. Burying is extremely likely to backfire on voters in STAR Voting. The likelihood that the voter will keep their second-favorite candidate out of the runoff by Burying them is pretty low compared to the likelihood that either 1) their favorite and least-favorite candidates were both going to make the runoff regardless and Burying didn’t matter, or 2) their second-favorite and least-favorite candidates both make the runoff (possibly thanks to this voter!), and Burying resulted in the voter giving their least-favorite candidate their vote!
11. This is backed up by the Voter Satisfaction Efficiency simulations run by Jameson Quinn of The Center for Election Science, in which STAR Voting performs extremely well overall, and at its very best when all voters are completely honest. This is starkly contrasted with Plurality, which performs at its best when all voters are strategic, and even then still falls short of STAR Voting’s very worst performance.
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