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Comment by dragonwriter | Hacker News Reader

Without going through whole way to Condorcet methods, you can eliminate the problems associated with IRV's elimination step by just dropping the elimination step; set the election quota as the the smallest integer greater than half the ballots cast, if no one reaches the quota with just first preference votes, then add in second preference votes and see if there is a winner, and so on until someone wins.

This also has (compared to both Condorcet methods and base IRV) relative simplicity of tallying ballots and processing them to get a result.

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Alternatively, why not just go full Condorcet? The Schulze Method has a significant backing: https://en.wikipedia.org/wiki/Schulze_method#Users

If you really want simplicity though, I suppose you could use IRV as your tie breaker amongst the Schwartz set.

While I think the argument that voters won't understand how winners are chosen for IRV is a bit overstated, I think it'd be completely true with the Schulze method -- its safe to say that the average voter doesn't have a strong understanding of graph theory.

Which isn't to say it isn't a good system; but its definitely a draw back. Supporting IRV seems like a good first step in which we don't let perfect be the enemy of good.

Barring edge cases, Condorcet methods can be described like single-elimination tournaments which pretty much everyone is familiar with.

Yes, graph theory comes into play for tie breaking (assuming we can agree that cyclic Condorcet paradoxes are ties of sorts), but the core of the idea is already understood by an overwhelming majority in concept if not by name.

Condorcet methods are more like a particular method of choosing the winner of a round-robin tournament; they don't really map naturally to a single-elimination tournament.

Of course, if you assume consistent relative performance, then any single winner tournament that you construct among the candidates in a Condorcet election would choose the Condorcet winner of one exists, and some member of the Smith set in any case (though different initial bracket structure can choose different Smith set members in the absence of a Condorcet winner.)

Simplicity for voters is one example concern, but administrative/tallying simplicity is important for large elections with potentials for challenges of election counts and gear, and the potential need to fallback to humans in a distributed network of locations tallying votes.

A method which is summable for k=1 is good for this, one which is summable for some k>1 is less good, and a nonsummable method (like IRV) is, to me, unacceptable. [0]

[0] http://wiki.electorama.com/wiki/Summability_criterion

Is that a problem in practice, though? If I were conducting a count under a cardinal voting system (such as range voting or approval voting) I would count one candidate after another. This would really slow down a count involving a large number of candidates, which is bad for a system aiming to increase voter choice. However, under IRV/RCV I would literally put the ballot papers in piles (one for each candidate) and count each pile. It's possible (and, I believe, typical) that less counting is required under IRV/RCV than under any of the other voting systems mentioned on the page you linked to (with the exception of plurality voting).

Is this modification described or analyzed anywhere more thoroughly?

With variations on whether (and at what ranks) you allow (and how you apply) equal rank votes, and how you resolve majorities that occur on the same round, it's corresponds roughly to the family of Bucklin [0] and Majority Choice Approval [1] methods.

[0] http://wiki.electorama.com/wiki/Bucklin_voting

[1] http://wiki.electorama.com/wiki/Majority_Choice_Approval

Bucklin seems worse than IRV on every property except monotonicity:

https://en.m.wikipedia.org/wiki/Single-member_district

Well, it's actually identical on most criteria listed on that page (it's worse on Condorcet Loser and Clone Independence, which I'd argue are less important than Monotonicity, while still agreeing that Clone Independence is a real and practical concern; Condorcet Loser less so), but Bucklin's also not the best of the Bucklin/MCA family. Go back to the link I provided upthread and look at the analysis of the MCA variants (which Wikipedia doesn't include); most versions of MCA also satisfy Clone Independence.

Bucklin and most MCA variants are also summable (mostly k=1, some k=2), while IRV is not summable [0]; this is an important trait for verifiable large elections which Wikipedia'so table omits.

[0] http://wiki.electorama.com/wiki/Summability_criterion

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