Do minor modifications to IRV prevent 2PD?

If our efforts to get a cardinal system in place nationwide fail, I was wondering if some modification of IRV could be sold.
In particular, I was think about a rule where you take the bottom two candidates, and eliminate the one not majority-preferred to the other.
Does this (or some other small modification to IRV) break two party domination?

Good to keep in mind any evidence saying Condorcet leads to two-party domination:

Generally, if it fails Favorite Betrayal, and voters strategically exploit that, it maintains two-party domination. Does BTR-IRV do that with Naive Exaggeration (rank one frontrunner top, one bottom)?

I submit Instant Pairwise Elimination, Check-IRV (not largest majorities), or Condorcet with the plurality Smith set candidate winning as ordinal options.

My view is that cardinal systems, barring court strikedown, or some kind of barring of ballot measures and implementation thereof, will eventually triumph. Anyone can see through real results that they’ll break two-party domination.

I am not a big fan of BTR-IRV. Here is a case where I think it could go wrong (I have the Brazilian presidential election in mind, although I simplified it to 3 candidates in a way that helps my argument).
Suppose the sincere preferences are:
48%: A>B>C
7%: B>A>C
10%: B>C>A
35%: C>B>A
With regular IRV, B gets center-squeezed. BTR-IRV could solve it, because B beats C in the BTR, but B is extremely dependent on the A preferences to win this runoff. A is essentially assured victory if they draw C as their opponent for the final runoff, as they lead pairwise by 10 points, but are unlikely to win a final runoff against B. Thus the A supporters have every incentive to vote A>C>B. The only strategy non-A supporters have to counter this is for the C supporters to vote for B instead, but that (1) suggests BTR-IRV does indeed have a spoiler problem, and (2) although this would be the correct strategy in BTR-IRV, normal IRV, and the top-two method that the actual election was conducted under, the voters in the real election voted for the spoiler anyway.

This is kind of complicated (which defeats the point, I know), but here is a modification of Minimax that has some Approval-like properties.
You rank the candidates, and put them above or below a threshold. In each pairwise matchup, A vs B, the number of ballots counting against candidate A includes (1) ballots that rank B>A, and (2) ballots that rank A=B below the threshold. A ballot cast A=B=C|D=E=F… behaves exactly like an approval vote for A, B, and C.

It should be possible, with the use of a checkbox, to let the voter simply not rank candidates with the understanding that they’re disapproved.

Typically unranked candidates are assumed to be coequal last.

OK, now I started thinking of “Approval-IRV”: you cast a rank-order ballot with equalities allowed. All the candidates ranked 1 get one full vote. If all your #1 candidates are eliminated, then your vote moves down to the next tier that still has candidates in the running.

It satisfies a weaker version of LNH. You can vote as in Approval or IRV.

It still fails precinct summability, though.

But you’ve still got to deal with the “Rank-3” limitation.

What is that and why is it a problem?

Most ranked ballots only allow ranking 3 candidates, due to complexity/space limitations. That may reduce the value of Approval-IRV.

If you are limited to ranking 3 candidates, vote splitting is inevitable. The only way around that is delegation, but then you’ve left the realm of “minor” modifications.
Although I don’t know if I’d say “most” IRV implementations limit you to 3 rankings. For example, Maine allows complete rankings.

Optional Delegation could be considered a minor modification.

I reply to this question at!topic/electionscience/BjoXS26L-dw

Doesn’t it really just come down to Favorite Betrayal? As long as any variant of IRV fails that, it’d probably be farcical or complicated in order to end two-party domination under that variant.

After thinking about it for a while, I am not even convinced that Approval-IRV (which fails Favorite Betrayal) truly breaks 2PD… although it is better than plain IRV.

I thought for a while Asset might break two-party domination despite failing Favorite Betrayal, but I then realized that because it’s a Condorcet method for candidates (weighted by voters’ votes), it fails Favorite Betrayal in the same way that WDS describes Condorcet’s failing to end two-party domination. The only way to really work in some kind of modification to IRV that’s minor but allows it to better satisfy Favorite Betrayal might be Optional Delegation, but even that’s tricky.

Edit: From further study of WDS’s examples, my guess is that Condorcet and thus Asset may not be subject to Favorite Betrayal leading to two-party domination quite so strictly, simply because it requires the voters to betray the consensus in society and think strategically more than I imagine they would. Also, a lot of these examples require contrived Condorcet cycles or rank-equalities hurting a frontrunner; but this doesn’t mean these methods are entirely off the hook.

#48%: A>B>C
#7%: B>A>C
#10%: B>C>A
#35%: C>B>A

b 48 1 2 3
b 7 2 1 3
b 10 2 3 1
b 35 3 2 1

When I checked out your sample data (copy above to the clipboard to paste) here, B won Condorset, STAR, and approval while A won RCV.

Check out IRV with candidate withdrawal. Basically, an outcome like Burlington can be avoided by the spoiler candidate dropping out after the election, allowing a Condorcet winner to win. u/curiouslefty on has written more.