[EM] Revised: Instant Pairwise Elimination (IPE)
VoteFair
electionmethods at votefair.org
Sun Jan 12 17:44:27 PST 2020
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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