# [EM] Improvement to Ranked Robin method

Colin Champion colin.champion at routemaster.app
Thu Mar 31 11:55:30 PDT 2022

```Richard – there are two ways of using a Borda tiebreak, sometimes
written "Llull//Borda" and "Llull,Borda". It sounds like you understood
me to be attributing "Llull,Borda" to you while you were actually
advocating "Llull//Borda". (I have no idea which of these was Dasgupta
and Maskin’s preference – I don’t think they were clear.) Certainly
Llull//Borda reduces to a plurality choice between two tied candidates.
Other tiebreaks (eg. minimax) can be used in the same two ways,
which is why a fairly general notation exists. I can't say I like it as
a notation, since it's far from self-explanatory.
Colin

On 31/03/2022 18:10, Richard, the VoteFair guy wrote:
> On 3/30/2022 11:51 PM, Colin Champion wrote:
> > ... is the candidate with the highest support count not the
> > candidate with the highest Borda score? Have you not reinvented
>
> Borda count is a positional voting method:
>
> https://en.wikipedia.org/wiki/Positional_voting
>
> As a tie breaker, only the candidates who are tied are considered in
> this count.
>
> When the tie is between just two candidates, the Borda count would
> still use the (positional) numbers assigned by the voters.
>
> In contrast, I'm recommending a counting method that disregards which
> position contains the mark being counted.  So a two-candidate tie
> becomes simple plurality counting.
>
> To repeat, I'm suggesting breaking a tie by using pairwise support
> counts.  On one ballot the pairwise support count is the number of
> candidates who are ranked lower than the candidate getting the support
> count.  Those counts are added across all the ballots to yield that
> candidate's pairwise support count.
>
> A big advantage is that it can be counted directly from the ballots,
> without first creating a pairwise matrix.  Although software would use
> the pairwise matrix approach, voters and the legal description and the
> tabulated results would not mention the pairwise matrix.
>
> Richard Fobes
> The VoteFair guy
>
>
> On 3/30/2022 11:51 PM, Colin Champion wrote:
>> Richard – is the candidate with the highest support count not the
>> candidate with the highest Borda score? Have you not reinvented
>>    Colin
>>
>>
>> On 31/03/2022 05:58, Richard, the VoteFair guy wrote:
>>> 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
>>>
>>>   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
>>> ----
>>> Election-Methods mailing list - see https://electorama.com/em for list
>>> info
>>

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