Thought about adding sortition (choose one person) but not sure if that is bending the rules a bit because the implication is what method is best for a single office of which sortition isn't meant for. It's meant for large legislative bodies with many seats where the randomness sort of cancels out to yield a proportional reflection of the electorate. Despite it only being intended for large legislative bodies as only a single person would be elected in each district it technically meets the description of being single seat voting method.

How is sortition better than the best proportional representation systems? I'm thinking of small-ish districts (electing on average ~10-12 representatives) and compensatory seats, at least ~1/4 of the total, allocated to effect nationwide proportionality but assigned to specific constituencies. Once this process determines how many seats each party wins in each district, you allocate seats to the most voted individual candidates, while also allowing voters to just vote for the party rather than a specific candidate.

With the possibile exception of STV, I think this is close to the best system humankind has developed. How is sortition better, especially for the same size of the legislature?

Yeah, sortition is the worst voting system possible if your goal is to elect the candidate preferred by the voters. Worse even than FPTP.

I think that's comparing apples to oranges. Sortition does not aim to be better than FPTP at the district level; it is fair to assume that, given a large enough legislature and proper procedures to perform the sortition, it would perform better than the median FPTP election in terms of proportionality, for example.

I think its disadvantages are more like in terms of MPs' experience and incentives, as well as the absence of a coherent party system.

it would perform better than the median FPTP election in terms of proportionality

By what metric?

Any measure of disproportionality, for example the Gallagher index: https://en.m.wikipedia.org/wiki/Gallagher_index

Gallagher index - Wikipedia

Hmmm I would suspect that sortition still does worse than FPTP and STV etc

It most certainly does for STV, not sure what you're including in that "etc" as STV is almost the opposite of FPTP.

Now, focusing only on FPTP, I'm curious as to how you think sortition can be more disproportional. Can you please walk me through the process of how that happens?

Here's the assumptions I'm making:

• access to registration as a "candidate" for random selection is equitable. This means "parties" end up have similar shares of their supporters registering. (This is based on whatever form "parties" take - we need something to base proportionality on.)

• candidate selection is properly random.

So, let's think of an example... let's say you have parties A, B, C and D with 38, 31, 19 and 12% support respectively. Let's say this is Great Britain, with 631 seats. With FPTP, D's support is more or less evenly spread across the country; they eke out maybe a handful of wins in their strongholds. C focuses their campaigning in places where the unpopular incumbent B is weakest and maybe gets like 10-12% of the seats (let's say, 68). B manages to holds on to about 20% (125), and A wins the rest (433) in a landslide.

Now suppose sortition. By assumption, the pool of candidates is proportional to the parties' support, and it is drawn from truly randomly. We'd expect the distribution of MPs selected to be similar to the distribution of candidates, that's how randomness works; statistical sample distributions are less likely the more they deviate from the population.

This is regardless of whether the sampling is taken nationally or at the level of the constituency. If you take a random set of 10 constituencies, it's quite likely they'll be 4:3:2:1 for these parties, give or take one, maybe two. Take 30 constituencies and the odds of proportionality only increase. Same for 100, 300 or all 631.

Now, of course countries like America wouldn't give parties equitable treatment, same as today, and people would find a way to screw with the randomness. But that's not a problem with sortition, it's a problem with these countries.

So, what am I missing?

Well in a multi-winner context FPTP becomes SNTV, but my general hunch is that sortition and SNTV only perform well at proportionality when averaged over many elections, because of their randomness:

For individual elections, their randomness (FPTP/SNTV's randomness comes from vote-splitting) means they don't do as well at proportionality as a system that's specifically designed to produce proportionality, leaving clumps of winners that over-represent some ideologies and under-represent others:

This paper doesn't simulate sortition, but I'm assuming it behaves similarly to SNTV. I might be wrong; I haven't thought it through.

Edit: Oh I previously said "worse than SNTV", not "similarly to SNTV". Well in that case, I guess I was thinking of single-winner elections, where sortition does worse than FPTP at things like Utilitarian Efficiency. Not sure if that carries through to PR. In PR context they might be equally random and equally bad.

I wonder if there is anything that fits all of the following:

• clearly desirable (e.g. life expectancy, low crime)

• measurable and measured in international rankings on an ~annual basis

• countries which elect their legislature via single-winner methods (US, UK, Canada, Australia, France...) consistently overperform multi-winner ones

• not tautological (not directly linked to being single-winner, like "you have one specific representative that lives near you")

IRV is the most well-known alternative system, but isn't actually particularly good.

It is marketed using claims like "It fixes the spoiler effect", "It makes it safe to vote honestly for your true favorite without wasting your vote", etc. But these are not actually true.

It only counts first-choice rankings in each round, which means it suffers from the same type of vote-splitting as FPTP, and can eliminate the most-preferred, highest-approved candidates prematurely.

Its Condorcet Efficiency and Social Utility Efficiency are mediocre, and it suffers from center-squeeze, causing it to be increasingly biased against the most-representative candidates the more there are on the ballot.

What voting system will be used for the poll?

@PlasmaBallin I'm inclined to use native Manifold voting features available at market close (Currently, that looks like a poll, which forces FPTP I guess). If Manifold supports a better voting method in 2030, as measured by this market, then we'll use that.

@kenakofer So if Manifold introduced, e.g., checkbox polls, then you would use that, since according to this market's probability, approval voting is better than plurality?

@PlasmaBallin Exactly

@kenakofer will this market N/A if Manifold concludes (correctly, IMO) that all non-proportional single-winner methods (like those in the polls) are inferior to proportional ones, preferably multi-winner?

@BrunoParga this market is about single winner methods, so I'm not sure how a proportional method could be eligible for the running.

I would certainly be interested in a generalization of this market, so please make it and link it if you want!

@kenakofer If manifold still has only a choose 1 poll by the time this closes, perhaps an interesting alternative you could do a runoff poll where you ask people to choose between the two options with the highest probability of winning according to this market. Though if manifold does add approval polls or some other non-plurality polling method I agree that that is probably what should be used.

For making questions in this top 2 style manner it's good to have the rules be that all questions get resolved to n/a except the top 2 (of which the winner would resolve yes and the runner up no) so you just get the probability if it would win given it is in the top two though this market was not set up that way. That way any option people believe to be a Condorcet winner would naturally rise to the top as it would win the head to head. You can't change this market but that might be a good setup for future markets when you are trying to determine the most popular outcome.

Top-2 runoff does not necessarily select the Condorcet winner.

@BrunoParga o Top 2 runoff uses an initial round of plurality to choose the top 2. I am instead recommending chooseing the top 2 based off of the market. If there is a consensusin the market that an option is a condorcet winner it's corresponding manifold market should be the highest and thus if you select the top 2 from the market your selection will include the Condorcet winner whom will bet the runner up in the poll so it should be a lot better at electing a Cond. winner then a top 2 runoff.

Though this still has limitations, if there is no consensus on what option the condorcet winner is but there is consensus that the condorcet winner exists among a group of options those options could still split their probilities and thus not make it into the top 2, which is why I suggested having the market be on whether each option would win if selected from the top 2 with the highest share price and resolving the non top 2 as n/a. If there is then a market consensus that the condorcet winner exists among a group of options all the above options will have higher share prices then options outside of that group allowing the market to apply more scrutiny to the options in that group until a new consensus is formed among a smaller subset of that group.

If there is a consensusin the market that an option is a condorcet winner

You cannot determine the Condorcet winner without all voters either ranking or scoring the candidates. I don't think the market does that in a way that's comparable to ranked or scored voting methods.

if you select the top 2 from the market your selection will include the Condorcet winner whom will bet the runner up in the poll

Yes, that is likely but not guaranteed.

Ultimately, I don't put too much stock on the Condorcet criterion. There can be situations where candidate A beats all others by a very narrow margin and B beats everyone else (besides A) by huge margins. It is not obvious to me that A is the "rightful" winner.

I think any single-winner election suffers from unsurmountable problems; there should be no single-winner elections at all.

A Condorcet-compliant ranked-choice system

Wait, does this one count? It describes multiple voting algorithms, but they are also all so similar that it would seem weird not to group them together.

@PlasmaBallin Yeah, see the comments below. I'm open to suggestions if you can think of a better operationalization for sets of voting methods.

Here is a detailed nested debate about various systems:

https://www.kialo.com/the-us-should-adopt-a-better-voting-system-for-single-winner-elections-4650

@Snarflak Currently the ranking on Kialo is:

1. STAR voting

2. Approval voting

3. Score voting

4. Condorcet

5. Instant runoff/Ranked Choice

6. Two-round system

7. First-past-the-post

8. Borda Count