# Is there a version of IRV where eliminated candidates may come back if they gain enough votes?

In 2009 the Burlington mayoral election failed to elect the Condorcet winner while using IRV. Looking at the results table, there seems to be two simple modifications that could've changed the outcome:

1. Eliminate the second-ranking candidate too (Kurt Wright), transferring their votes to other candidates, including those who have already been eliminated
2. Tally the votes ignoring prior "eliminations", which would result in Andy Montroll winning due to Wright's secondary votes being transferred to him

Is there a version of IRV that does this? I've looked at the list of ranked choice and didn't see any that attempted to modify IRV this way.

• There are dozens (hundreds?) of ranked-choice voting systems. Which ones count as a "version of IRV" in your mind? Commented Nov 2, 2021 at 15:55

It's not clear what you consider "a version of IRV", but here are some candidates:

• Coombs's method is very similar to IRV, only changing the rule of who to eliminate in each round. (Eliminate the candidate ranked last by the largest number of voters, rather than the candidate ranked first by the fewest.)
• Baldwin's method is kind of similar to IRV, with an elimination rule based on tallying the rankings. (Sum all the rankings for each candidate and eliminate the candidate with the worst sum.)
• Nanson's method is similar to Baldwin's. (Eliminate all candidates whose ranking sums are worse than average.)
• Bottom-Two-Runoff IRV is a sort of contrived variation of IRV that ensures that a Condorcet winner remains in the race. Instead of eliminating the candidate ranked first by the fewest, hold a virtual runoff between the two least-favorited candidates and keep the winner. (At that point you might as well just use a full Condorcet method and do all the pairwise comparisons in one round, though.)
• Likewise, there are other Condorcet-IRV hybrids which seem like a waste of time to me, since you might as well just adopt a regular Condorcet method at that point:

All of these would have elected Montroll in Burlington, but don't really match what you've described.

If "version of IRV" just includes any voting system with ranked ballots, then just skip all that elimination stuff and adopt a plain Condorcet method like Tideman Ranked Pairs or Schulze method. These consider all voters' preferences simultaneously and find the candidate who would beat every other in a round-robin tournament.

• Hay, endolith. I finally got my paper about Burlington and IRV and Condorcet done to the point I don't think I'll add to it. Nicolaus Tideman is editing an special issue of Constitutional Political Economy on voting systems and has all-but-said that this paper is getting in that issue. Just thought you and others knowledgeable about RCV and Condorcet and Burlington might be interested. Commented Nov 30, 2021 at 6:06