# [EM] Improvement to Ranked Robin method

Richard, the VoteFair guy electionmethods at votefair.org
Thu Apr 7 14:46:20 PDT 2022

```On 4/5/2022 9:03 PM, Forest Simmons wrote:
> Recursion?  Who said recursion? Where did you get that impression?
> Where is the recursion in ...
>
> ... elect the candidate that, on the fewest number of ballots,
> is pairwise defeated by the ballot favorite ....

Forest, thank you for clarifying that your word "best" refers to "the
ballot favorite."

However, I still don't yet understand how the counting works.  How can
any ballot yield a defeat of the candidate who is ranked highest on that
ballot?

For example, suppose there is a ballot:

A > B > C

How would this one ballot be counted?

Specifically, who is "pairwise defeated by the ballot favorite"?

Thanks!

Richard Fobes
The VoteFair guy

On 4/5/2022 9:03 PM, Forest Simmons wrote:
>
>
> El sáb., 2 de abr. de 2022 9:41 p. m., Richard, the VoteFair guy
> <electionmethods at votefair.org <mailto:electionmethods at votefair.org>>
> escribió:
>
>     On 4/1/2022 6:24 PM, Forest Simmons wrote:
>      > ...
>      > Here are two versions of decloned Copeland that are not prone to
>     ties:
>      >
>      > 1.Elect the candidate that, on the greatest number of ballots,
>      > pairwise defeats the candidate designated "worst."
>      > ...
>      > 2. Elect the candidate that, on the fewest number of ballots, is
>      > pairwise defeated by the candidate designated "best."
>
>     Both of these ways of resolving Copeland ties are more difficult to
>     understand -- for most voters -- than the current version.
>
>
> These are not ways of resolving Copeland ties ... rather they are two
> succinctly stated complete versions of Copeland that only vanishingly
> rarely require any tie breaker at all, let alone one as elaborate as you
> are suggesting.
>
>
>     As a further barrier to understanding, these definitions involve
>     recursion.
>
>
> Recursion?  Who said recursion? Where did you get that impression? Where
> is the recursion in ...
>
> ... elect the candidate that, on the fewest number of ballots,
> is pairwise defeated by the ballot favorite ....
>
> To spell it out in complete detail ... just open each ballot B and,
> after identifying the first preference X on each ballot B, give a
> demerit to each candidate Y defeated pairwise by candidate X.
>
> After tallying all of the ballots in this same fashion, elect the
> candidate with the fewest demerits.
>
> [That's all there is ... don't try reading something complicated into it
> ;-)
> If another method seems simpler, it's only because you are more familiar
> with it.]
>
> A Condorcet candidate will have no demerits because, by definition a
> Condorcet candidate is not defeated pairwise.
>
> The key to clone independence is focusing on defeats incurred by the
> ballot favorites, rather than giving all pairwise defeats equal weight.
>
>
>       That's even more difficult to procedurally understand than a
>     pairwise matrix.
>
>
>     The goal of the Ranked Robin method (according to the description on
>     Electowiki) is to provide a method that is reasonably easy to
>     understand, yet uses ranked choice ballots and yields reasonably fair
>     results.
>
>     As I said, I'm proposing that the method be made even easier to
>     understand by using pairwise support counts, which are directly
>     countable from the ballots, without involving a pairwise matrix.
>
>     Regarding your desire to protect against clone failures, those are just
>     one special kind of "irrelevant alternative," as in IIA
>     (independence of
>     irrelevant alternatives).  Personally I'm more concerned about reducing
>     all kinds of irrelevant alternatives.  In this case I'm concerned that
>     attempts to fully eliminate clone independence failures might have the
>     side effect of increasing the rates of other kinds of IIA failures.
>
>     Richard Fobes
>     The VoteFair guy
>
>
>     On 4/1/2022 6:24 PM, Forest Simmons wrote:
>     > Besides being prone to ties, Copeland also suffers from Clone
>     > Dependence, which makes it inferior to IRV in that regard.
>     >
>     > Here are two versions of decloned Copeland that are not prone to ties:
>     >
>     > 1.Elect the candidate that, on the greatest number of ballots,
>     pairwise
>     > defeats the candidate designated "worst."
>     >
>     > That is the burial resistant version of decloned Copeland.
>     >
>     > The other version, that may be more appealing to some people, is this:
>     >
>     > 2. Elect the candidate that, on the fewest number of ballots, is
>     > pairwise defeated by the candidate designated "best."
>     >
>     > Both of these methods are monotonic, clone free, and "Round Robin
>     > Efficient."
>     >
>     > It is practically impossible for either method to yield a tied
>     result in
>     > an actual political election involving hundreds of ballots.
>     >
>     > Because of that fact, the obligatory tie breaker does not need the
>     > special scrutiny that is so important for ordinary clone dependent
>     Copeland.
>     >
>     > Random Favorite would be the simplest ... and perfectly adequate tie
>     > breaker.
>     >
>     > At the other end of the spectrum, method one could serve as the tie
>     > breaker for method two, and vice-versa.
>     >
>     > Between those possibilities there are many others that are also
>     >
>     > -Forest
>     >
>     >
>     >
>     >
>     > El jue., 31 de mar. de 2022 12:04 p. m., Colin Champion
>     > <colin.champion at routemaster.app
>     <mailto:colin.champion at routemaster.app>
>     <mailto:colin.champion at routemaster.app
>     <mailto:colin.champion at routemaster.app>>>
>     > escribió:
>     >
>     >     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
>     >>>>
>     >>>>       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
>     >>>>     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
>     >>>>
>     >>>>     * 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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>     >     list info
>     >
>     >
>     >
>     > ----
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>     list info
>     >
>     ----
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>
```