[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
> > perfectly adequate.
> >
> > -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
> >> > Dasgupta-Maskin?
> >>
> >> 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
> >>> Dasgupta-Maskin?
> >>> 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
> >>>> 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
> >>>> ----
> >>>> Election-Methods mailing list - see https://electorama.com/em
> >>>> for list
> >>>> info
> >>>
> >
> > ----
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> >
> >
> >
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