Final-Five Voting

clay shentrup
4 min readOct 14, 2021

Final-Five Voting is a deeply mathematically flawed idea, for a few reasons that I think are fairly obvious. But I’ll spell them out here. To start, let’s look at a random candidate distribution in two-dimensional “issue space”, representing political ideology.

I’ll start by demonstrating the concept via my Political Compass test results.

I’m as neoliberal as they come. Taco trucks on every corner, NOW!

Now let’s imagine a random distribution of candidates for public office, like so. Each colored dot represents a candidate, and the background is painted to match the closest candidate.

Now suppose we want to have a winnowing process to advance some subset of these candidates to the general election, giving voters another month to focus on a small tractable set of candidates, see them debate, and so on, so that their understanding of these candidates is more substantial than a mere sound bite or two. How many candidates should we choose, and who should we choose?

Well let’s suppose Lime (center) is the “best” candidate — the one who makes the most voters the most satisfied. In that case, logically, the 2nd best candidate must be the Teal (or is it Pine Green?) candidate just to her right. The 3rd best appears to be Turquoise. Then Royal Blue 4th, then Brown 5th.

Who?

It would be irrational to argue that Lime is best but, say, Yellow or Pink is 2nd best. By definition, the “best” candidates must be highly similar, since they’re the ones closest to the policy platform that maximizes human welfare. Thus the most important consideration for our voting method is that it avoids vote splitting, and tends to find the consensus view. This is where the score voting family of methods happens to excel, including approval voting and STAR voting.

How many?

Next we need to ask how many candidates should make the general. The benefit of more candidates is that they invigorate the debate and help point out flaws in the other candidates for us. The downside is that too many candidates gets us right back to the problem of ignorance. Our limited attention means we’re just not going to become experts on all the candidates, and so the public benefits from having a reasonably small number of options in the final pass.

But further there’s just the practical matter of statistics. A 3rd place (or worse) finisher is very unlikely to come from behind to victory in the general. An analysis of ranked choice voting puts it succinctly:

in the 1362 IRV elections I’ve personally looked into:

- 1263 went to the person who was in first on the first round of counting
- 98 went to the person who was in second on the first round of counting
- 4 went to the person who was in third on the first round of counting
- none went to anyone who was worse than third on the first round of counting

Do we really need to advance more than two finalists when one of the top two wins more than 99.7% of the time?

This is even more true when we consider the strategic benefit: that a two-candidate election is the only case where voting is completely sincere and strategy-free, and thus has no need for anything more complex than the traditional choose-one ballot.

In the March 2021 St Louis primary, for instance (which produced a top two general in April), the first-round winner won the runoff in 16 of 18 elections. But in all cases, there was a top two general election resulting in an incontrovertible mandate across the board. And all without the need for any complex ranking process.

Approval voting advanced two progressive women — by far the two most ideological similar of the four primary candidates — to the April general, making for a more nuanced contest focused on specifics rather than broad ideological labels.

Final-Five Is Three Too Many

The Final-Five proposal is not only flawed in how many candidates it advances to the general—five instead of just two—but it also uses plurality voting (the world’s worst voting method) for the primary.

Conclusion

The Institute for Political Innovation should use approval voting instead of plurality voting in their primary. There’s no benefit to crowding the general with unpopular candidates. And they should reduce the number of finalists down to two. There may be a reasonable argument for up to three candidates, or even four, but then you have to worry about strategic voting.

And guess what? This system (approval voting plus top two runoff) is exactly what St Louis uses.

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clay shentrup

advocate of score voting and approval voting. software engineer.