[EM] Revised: Instant Pairwise Elimination (IPE)

[C.Benham]

I missed the earlier discussion on this.

So what if an elimination round /does /have a "pairwise-losing 
candidate", what then?

And what exactly is a "pairwise-losing candidate"?

Just curious.

Chris Benham

On 13/01/2020 12:14 pm, VoteFair wrote:
> Based on a suggestion from a user on Reddit, I have revised the 
> definition of the Instant Pairwise Elimination method that previously 
> I published at Democracy Chronicles and then discussed here.
>
> The method still successively eliminates pairwise (Condorcet) losers.
>
> Now, instead of resolving Condorcet (rock-paper-scissors) cycles using 
> an "upside-down" version of instant-runoff voting (IRV), it uses 
> pairwise counts as described here:
>
> "If an elimination round has no pairwise-losing candidate, then the 
> method eliminates the candidate with the largest pairwise opposition 
> count, which is determined by counting on each ballot the number of 
> not-yet-eliminated candidates who are ranked above that candidate, and 
> adding those numbers across all the ballots. If there is a tie for the 
> largest pairwise opposition count, the method eliminates the candidate 
> with the smallest pairwise support count, which similarly counts 
> support rather than opposition. If there is also a tie for the 
> smallest pairwise support count, then those candidates are tied and 
> all those tied candidates are eliminated in the same elimination round."
>
> Below are my guesses for which fairness criteria it fails and passes. 
> Please tell me which guesses are not correct.
>
>   Condorcet: fail
>   Condorcet loser: pass
>   Ranks equal: pass
>   Ranks greater than 2: pass
>   Polytime: pass
>   Resolvable: pass
>   Majority: fail
>   Majority loser: fail
>   Mutual majority: fail
>   Smith/ISDA: fail
>   LIIA: fail
>   IIA: fail
>   Cloneproof: fail
>   Monotone: fail
>   Consistency: fail
>   Reversal symmetry: fail
>   Later no harm: fail
>   Later no help: fail
>   Burying: fail
>   Participation: fail ?
>   No favorite betrayal: fail ?
>   Summable: O(N!) ?
>
> As I've said many times, it's the frequency with which the failures 
> occur that is much, much more important than simply counting how many 
> criteria it fails. I suspect that its frequencies of failure will be 
> quite low compared to most other single-winner methods, and may 
> approach the low frequencies that I believe characterize the 
> Condorcet-Kemeny method.
>
> I've created a page for this method on Electowiki. You are welcome to 
> edit that page with any corrections.
>
> BTW, I realize that it's possible that the alternate elimination 
> method always identifies the pairwise/Condorcet loser (if there is 
> one). If so, this would mean that the description could be 
> "simplified" to a single step (actually two steps in case there is a 
> tie). However, for the benefit of most voters who are not comfortable 
> with mathematics it's important to explicitly state that the first 
> priority is to eliminate the pairwise loser.
>
> Of course software that implements the method would do the 
> calculations using a much faster method than the counting method 
> described above. The description above is written to be understandable 
> to people who are not already familiar with pairwise counting.
>
> In advance, thank you for any feedback.
>
> Richard Fobes
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