>Election Science is doing yeoman's work. And they just keep getting better.

They just need a billionaire patron and they could dramatically transform American politics for the better.

All those billionaires who give fat checks to political parties and candidates are doing it completely wrong. "Don't hate the player hate the game" -- but what if you could change the game?

The billionaires like the game—it gives them power!

Approval voting has been shown to increase voter satisfaction. I'll bet it would increase voter satisfaction for billionaires as well. They'd no longer be stuck with just a few bad candidates to support.

The counting must be coordinated, but doesn't have to be centralised. Though it always is so in practice

You could have each precinct count the first round, communicate the result to a coordinator then wait till everyone finished to count the second round etc

Alternatively you could have each precinct manually "digitise" each of their ballots into a computer representation and distribute these to a central location

> You could have each precinct count the first round

This is just centralized tallying with extra steps. You can't finish the first round without results from every precinct, that's the point. To finish the first round, you need to know who has the fewest first choice votes across the entire population, so each precinct would have to give the entire first choice votes distribution to the centralized location. But once a precinct knows the first choice distribution, by definition that means all the ballots have been cast and you also have all the second choice and lower ballot data as well, and eventually all the data will have to make its way to the centralized location so you may as well just give all the ballot data to the central location at one time (well, technically not all the ballot data is used because irv/ranked choice actually doesn't use all of it, but that's another discussion).

I don't understand how it is not possible for each precinct to not just count and transmit all of the unique combinations they receive. Ofc, with large number or choices and candidates this probably high number. But nothing prevents that.

At central location, combine the votes for unique combinations. And run the algorithm.

Great point.

> The gold standard for election integrity is casting paper ballets at poll sites, to be tabulated onsite the moment the polls close.

In essence this is a question of parallelization. Since cardinal systems (minor exception for STAR) your algorithm is argmax(reduce sum(ballots)). Your poll site would report their local reduce sum numbers to the central authority who would reduce sum across all areas and finally perform the argmax operation.

On the other hand, ordinal systems have to be much more coordinated as they are not trivial to parallelize. In essence they are doing an exhaustive search. We run many elections wherein we pop the argmin candidate each round. This has a lock because we cannot pop the argmin candidate from our local polling site until the central authority has collected all ballots and told everyone which candidate to pop.

This is a main motivation for my arguments into cardinal systems. There are other arguments (e.g. favorite betrayer, monotonicity, scalability, preference embedding) but when we are comparing methods and there are minutia to quibble over, algorithmic complexity is a big factor to be concerned with. In fact, I think it is an embarrassingly under discussed feature of extremely high importance. Just imagine how difficult all the recounts in the recent presidential election would have been under a ordinal system (and compare to a cardinal, which the cardinal we can also perform good statistical analysis while we are tallying votes and it is also good for random subset sampling. Also underappreciated features).

> On the other hand, ordinal systems have to be much more coordinated as they are not trivial to parallelize

I don't think this is true for all ordinal systems is it? Wouldn't most condorcet methods simply be tallied into a head-to-head table at each precinct and then combined centrally? It's mostly just IRV that has this issue since it's just iterated first past the post, and the order of elimination is important to know in each round before it can be continued. When all that's needed is a h2h table (no iteration) this isn't an issue.

Condorcet methods are frequently more computationally complex. Schultz is O(n3) and RP is O(n4).

We must note the categorical aspect here. Ordinal is a class of voting, not a specific one. Condorcet is a class of ordinal methods (that optimize the condorcet criteria) but not a specific method. You're right that this isn't true for all methods but I'm mentioning these specific methods because they are the ones that are better and commonly discussed. Unfortunately we can't just look at one aspect of a voting method to rule it in or out.

Ah when you mention parallelizing I was assuming you were referring to the issue of requiring that ballots all be centralized in order to tally them for IRV, rather than summing at each precinct individually. The data that has to be in a central location for a condorcet method would only be O(n2) since it's just computed from the h2h table, I was not trying to discuss the complexity of actually computing the final results.

Well cardinal methods could easily be calculated in a distributed manner. And complexity of computing the final results is quite important. It is an important part of what the entire thread is about.

Yes you're correct. but cardinal methods are just generally better all around.