[EM] Improvement to Ranked Robin method

[Richard, the VoteFair guy]

Here I'm suggesting a way to improve the recently (fall 2021) created 
"Ranked Robin" method, which is described at Electowiki at this link:

   https://electowiki.org/wiki/Ranked_Robin

The improvement is to replace the first-level tie breaker -- which looks 
at margins calculated from the pairwise matrix -- with "pairwise support 
counts" -- which are easily described without using any numbers from the 
pairwise matrix.

Starting from the beginning ...

Currently the Ranked Robin method is described this way:

"Elect the candidate who pairwise beats the greatest number of candidates."

That's the method described by Ramon Llull (in 1299).

According to Electowiki that's been improved to become the Copeland 
method, which elects "the candidate with the most (pairwise victories 
minus pairwise defeats)."

According to Wikipedia the Copeland method doesn't do the subtraction 
and instead adds "half the number of candidates with whom he or she has 
a preference tie."

All of these Copeland method variations produce lots of ties.

So of course the Ranked Robin method needs tie breakers.  Here's the 
first-level tie breaker as it's currently specified:

"For each finalist, subtract the number of votes preferring each other 
finalist from the number of votes preferring them over each other 
finalist. The finalist with the greatest total difference is elected."

A big disadvantage of this Ranked Robin tie breaker is that it uses 
numbers from the pairwise matrix.  Yet one of the stated goals of the 
Ranked Robin method is to avoid confusing voters with the pairwise matrix.

Therefore I suggest replacing this tie-breaker method with the use of 
"pairwise support counts."  These counts are part of the "Instant 
Pairwise Elimination" (IPE) method, which is described at Electowiki at 
this link:

   https://electowiki.org/wiki/Instant_Pairwise_Elimination

It says:

"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. ..."

Of course the second-level tie-breaker would be to use pairwise 
opposition counts.  (The pairwise support counts and pairwise opposition 
counts are not always symmetrical.)

Notice that the numbers in the pairwise matrix do not need to be mentioned.

Yes, the software will calculate the pairwise support counts from the 
numbers in the pairwise matrix.  But that fact doesn't need to be 
mentioned -- to the voters, or in the legal description.

The resulting improved Ranked Robin method can be described as follows:

"The [improved] Ranked Robin method elects the candidate who has the 
most number of one-on-one wins against every other candidate plus half 
the number of one-on-one ties. [*]  If more than one candidate has the 
same largest number, the method elects from those tied candidates the 
candidate with the highest pairwise support count.  The pairwise support 
count for each of the tied candidates is the sum, across all the 
ballots, of the number of tied [**] candidates who are ranked lower than 
the candidate whose pairwise support count is being counted."

[*] The wording can be adjusted depending on which Copeland variation is 
desired.  Adding the words "minus the number of one-on-one losses" would 
specify the other variation.

[**] Importantly, the ballot marks for the non-tied candidates must be 
ignored when resolving the tie.

When the election results are displayed, they might look something like 
this, where the names are from the Ranked Robin article, and the numbers 
don't apply to any particular case:


     Matchup win and loss counts:

     Ava: 4 wins (against ...) and 2 losses (to ...)

     Bianca: 4 wins (against ...) and 2 losses (to ...)

     Cedric: 3 wins (against ...) and 3 losses (to ...)

     Deegan: 3 wins (against ...) and 3 losses (to ...)

     Eli: 2 wins (against ...) and 4 losses (to ...)

     Fabio: 0 wins and 6 losses


     The result is a tie between Ava and Bianca because they each have 4 
wins, and that's more than any other candidate.  Considering just these 
tied candidates, their pairwise support counts are:

     Ava: 213

     Bianca: 123

     So Ava wins!


Notice there's no need to show a pairwise matrix!

To prevent a potential source of confusion, the Wikipedia article about 
the Borda count begins with the words "The Borda count is a family of 
positional voting rules which gives each candidate, for each ballot, a 
number of points corresponding to the number of candidates ranked 
lower."  The last portion of this sentence describes pairwise support 
counts, but it has nothing to do with the Borda count.  The Wikipedia 
article for "positional voting" correctly says:  "Positional voting is a 
ranked voting electoral system in which the options or candidates 
receive points based on their rank position on each ballot and the one 
with the most points overall wins."  The remainder of Wikipedia's Borda 
count article correctly specifies positional voting in the descriptions 
and examples.  The Borda count article at Electowiki does not include 
this first-sentence mistake.  I'm going to let someone else figure out 
how the first sentence in Wikipedia should be worded.  (I'd rather fight 
other battles.)

I'm calling attention to this difference between pairwise support counts 
and the Borda count because this issue has previously caused confusion 
in this forum.

Getting back to the Ranked Robin method, this improved version is not 
likely to significantly increase the failure rates of the most important 
failure criteria, and it's likely to reduce some failure rates.

Currently the Ranked Robin article claims that the method passes some 
fairness criteria that it actually doesn't pass.  When the Ranked Robin 
article is improved to include a concise description of the method 
(which should be near the beginning), some experts here can identify 
which of the listed "pass" criteria need to be moved to the listed 
"fail" criteria.

Interestingly, the Ranked Robin method and its name were created by 
people who have previously promoted only STAR voting.  I'm pleased that 
they are finally recognizing that STAR ballots are not going to replace 
ranked choice ballots throughout the US.  And that they recognize the 
need to promote a method that takes advantage of the Forward Party's 
recommendation of "ranked choice voting."

Looking at the broader perspective ...

The current version of Ranked Robin already has these advantages:

* Uses pairwise vote counting, which looks deeper into the ballot 
preferences compared to instant-runoff voting.

* Is precinct summable.

* Allows voters to mark more than one candidate at the same ranking level.

I suggest making it even easier to understand by using pairwise support 
counts.  This improvement will eliminate the need to educate voters 
about the pairwise matrix.  And I believe this change will still provide 
a similar level of fairness.

Certainly, in multiple ways, it's much better than instant-runoff voting.

Richard Fobes
The VoteFair guy