[EM] RCIPE version 2

[VoteFair]

Version 2 of the Ranked Choice Including Pairwise Elimination (RCIPE) 
voting method is now coded.

Here's a link to the scatter plot that shows its Clone Independence and 
IIA (Independence of Irrelevant Alternatives) success rates compared to 
other single-winner methods:

   https://www.rankedchoiceoregon.org/img/clone_iia_success_rates.jpg

Based on Kristofer's feedback on the scatter plot, I've moved the IRV 
(instant-runoff voting) data points to the top to show that IRV has a 
zero Clone Independence failure rate.  (The CI measurements yield a 
non-zero CI failure rate because IRV does not specify a tie breaker 
method and there are lots of lower-level ties in these "stress test" 
measurements.)  I've removed the IRV-BTR data because it's so similar to 
IRV.

Here is how RCIPE version 2 is counted:

* Eliminate the "pairwise losing candidate" (Condorcet loser) when there 
is one.

* Calculate a "pairwise support count" for each candidate.  Each ballot 
contributes to that count the number of remaining(!) candidates who are 
ranked lower than the specified candidate.

* Eliminate the candidate who has the smallest pairwise support count.

* Repeat the loop to eliminate the next candidate.  The last candidate 
remaining is the winner.

* If there is a tie for the smallest pairwise support count, use IRV 
(instant-runoff voting) as the tie-breaker.  Specifically, eliminate the 
tied(!) candidate who is ranked highest -- compared to the other tied 
candidates -- on the fewest ballots.

* If there is still a tie, eliminate the candidate who has the smallest 
one-on-one pairwise count against any other tied candidate. (This 
addition is based on recent suggestions here.)

That's it!

The change from RCIPE v1 to v2 consists of:

* Reversing the order of the "IRV" step and the tie-breaker step that 
involves the pairwise support counts

* Ignoring the pairwise opposition counts

This RCIPE version 2 method "fails" lots of fairness criteria.  However, 
the success rates for the most important criteria are high, and similar 
to -- and for CI even better than -- the Condorcet-Kemeny method.  For 
example, where C-K indicates the Condorcet-Kemeny method, and IPE 
indicates Instant Pairwise Elimination:

Condorcet compliance
Method, 2 choices, 6 choices, 9 choices
C-K, 100, 100, 100
IPE, 100, 100, 100
RCIPEv2, 100, 100, 99.6
RCIPEv1, 100, 99.1, 96.5

Clone Independence
Method, 2 choices, 6 choices, 9 choices
C-K, 100, 94.2, 94.4
IPE, 100, 94.7, 93.7
RCIPEv2, 100, 98.4, 97.3
RCIPEv1, 100, 99.8, 99.6

Independence of Irrelevant Alternatives
Method, 6 choices, 9 choices
C-K, 83.7, 78.2
IPE, 83, 76.9
RCIPEv2, 78.5, 70.7
RCIPEv1, 77.5, 69.2

In other words, as is well-known, getting smaller failure rates for one 
criterion requires accepting larger failure rates for other criteria.

This method is a nice compromise regarding failure rates.

The big advantages are:

* Simple for voters to understand how the counting is done.  Whereas 
STAR voting gets a candidate's score from the ballot's column heading, 
RCIPE v2 gets a candidate's "score" from the ballot by counting how many 
remaining candidates are ranked lower than that candidate.

* Pairwise losing candidates are identified using the same pairwise counts.

* Eliminates one candidate at a time, which many voters find to be 
easier to understand and trust.

* Avoids using fractions or decimal numbers to allow two or more 
candidates to be ranked at the same preference level, which was needed 
for RCIPE v1.

* Is precinct summable!

As a bonus, the ballots can be counted manually.  Or the calculations 
can be done using a calculator and paper and pen.

Is there anything I'm overlooking?  If not, I'll update the RCIPE 
article on Electowiki.  Of course I'll move the version 1 description to 
the history section.

Thanks for any feedback.

Richard Fobes
The VoteFair guy