# [EM] Improvement to Ranked Robin method

Richard, the VoteFair guy electionmethods at votefair.org
Wed Mar 30 21:58:30 PDT 2022

```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

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 ...

* 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
```