[EM] Revised: Instant Pairwise Elimination (IPE)

[VoteFair]

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