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<font face="Helvetica, Arial, sans-serif">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. <br>
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.<br>
Colin<br>
</font><br>
<div class="moz-cite-prefix">On 31/03/2022 18:10, Richard, the
VoteFair guy wrote:<br>
</div>
<blockquote type="cite"
cite="mid:e3f4bdb7-5b06-5171-04b9-39c12b1e737a@votefair.org">On
3/30/2022 11:51 PM, Colin Champion wrote:
<br>
> ... is the candidate with the highest support count not the
<br>
> candidate with the highest Borda score? Have you not
reinvented
<br>
> Dasgupta-Maskin?
<br>
<br>
Borda count is a positional voting method:
<br>
<br>
<a class="moz-txt-link-freetext" href="https://en.wikipedia.org/wiki/Positional_voting">https://en.wikipedia.org/wiki/Positional_voting</a>
<br>
<br>
As a tie breaker, only the candidates who are tied are considered
in this count.
<br>
<br>
When the tie is between just two candidates, the Borda count would
still use the (positional) numbers assigned by the voters.
<br>
<br>
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.
<br>
<br>
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.
<br>
<br>
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.
<br>
<br>
Richard Fobes
<br>
The VoteFair guy
<br>
<br>
<br>
On 3/30/2022 11:51 PM, Colin Champion wrote:
<br>
<blockquote type="cite">Richard – is the candidate with the
highest support count not the
<br>
candidate with the highest Borda score? Have you not reinvented
<br>
Dasgupta-Maskin?
<br>
Colin
<br>
<br>
<br>
On 31/03/2022 05:58, Richard, the VoteFair guy wrote:
<br>
<blockquote type="cite">Here I'm suggesting a way to improve the
recently (fall 2021) created
<br>
"Ranked Robin" method, which is described at Electowiki at
this link:
<br>
<br>
<a class="moz-txt-link-freetext" href="https://electowiki.org/wiki/Ranked_Robin">https://electowiki.org/wiki/Ranked_Robin</a>
<br>
<br>
The improvement is to replace the first-level tie breaker --
which
<br>
looks at margins calculated from the pairwise matrix -- with
"pairwise
<br>
support counts" -- which are easily described without using
any
<br>
numbers from the pairwise matrix.
<br>
<br>
Starting from the beginning ...
<br>
<br>
Currently the Ranked Robin method is described this way:
<br>
<br>
"Elect the candidate who pairwise beats the greatest number of
<br>
candidates."
<br>
<br>
That's the method described by Ramon Llull (in 1299).
<br>
<br>
According to Electowiki that's been improved to become the
Copeland
<br>
method, which elects "the candidate with the most (pairwise
victories
<br>
minus pairwise defeats)."
<br>
<br>
According to Wikipedia the Copeland method doesn't do the
subtraction
<br>
and instead adds "half the number of candidates with whom he
or she
<br>
has a preference tie."
<br>
<br>
All of these Copeland method variations produce lots of ties.
<br>
<br>
So of course the Ranked Robin method needs tie breakers.
Here's the
<br>
first-level tie breaker as it's currently specified:
<br>
<br>
"For each finalist, subtract the number of votes preferring
each other
<br>
finalist from the number of votes preferring them over each
other
<br>
finalist. The finalist with the greatest total difference is
elected."
<br>
<br>
A big disadvantage of this Ranked Robin tie breaker is that it
uses
<br>
numbers from the pairwise matrix. Yet one of the stated goals
of the
<br>
Ranked Robin method is to avoid confusing voters with the
pairwise
<br>
matrix.
<br>
<br>
Therefore I suggest replacing this tie-breaker method with the
use of
<br>
"pairwise support counts." These counts are part of the
"Instant
<br>
Pairwise Elimination" (IPE) method, which is described at
Electowiki
<br>
at this link:
<br>
<br>
<a class="moz-txt-link-freetext" href="https://electowiki.org/wiki/Instant_Pairwise_Elimination">https://electowiki.org/wiki/Instant_Pairwise_Elimination</a>
<br>
<br>
It says:
<br>
<br>
"If an elimination round has no pairwise-losing candidate,
then the
<br>
method eliminates the candidate with the largest pairwise
opposition
<br>
count, which is determined by counting on each ballot the
number of
<br>
not-yet-eliminated candidates who are ranked above that
candidate, and
<br>
adding those numbers across all the ballots. If there is a tie
for the
<br>
largest pairwise opposition count, the method eliminates the
candidate
<br>
with the smallest pairwise support count, which similarly
counts
<br>
support rather than opposition. ..."
<br>
<br>
Of course the second-level tie-breaker would be to use
pairwise
<br>
opposition counts. (The pairwise support counts and pairwise
<br>
opposition counts are not always symmetrical.)
<br>
<br>
Notice that the numbers in the pairwise matrix do not need to
be
<br>
mentioned.
<br>
<br>
Yes, the software will calculate the pairwise support counts
from the
<br>
numbers in the pairwise matrix. But that fact doesn't need to
be
<br>
mentioned -- to the voters, or in the legal description.
<br>
<br>
The resulting improved Ranked Robin method can be described as
follows:
<br>
<br>
"The [improved] Ranked Robin method elects the candidate who
has the
<br>
most number of one-on-one wins against every other candidate
plus half
<br>
the number of one-on-one ties. [*] If more than one candidate
has the
<br>
same largest number, the method elects from those tied
candidates the
<br>
candidate with the highest pairwise support count. The
pairwise
<br>
support count for each of the tied candidates is the sum,
across all
<br>
the ballots, of the number of tied [**] candidates who are
ranked
<br>
lower than the candidate whose pairwise support count is being
counted."
<br>
<br>
[*] The wording can be adjusted depending on which Copeland
variation
<br>
is desired. Adding the words "minus the number of one-on-one
losses"
<br>
would specify the other variation.
<br>
<br>
[**] Importantly, the ballot marks for the non-tied candidates
must be
<br>
ignored when resolving the tie.
<br>
<br>
When the election results are displayed, they might look
something
<br>
like this, where the names are from the Ranked Robin article,
and the
<br>
numbers don't apply to any particular case:
<br>
<br>
<br>
Matchup win and loss counts:
<br>
<br>
Ava: 4 wins (against ...) and 2 losses (to ...)
<br>
<br>
Bianca: 4 wins (against ...) and 2 losses (to ...)
<br>
<br>
Cedric: 3 wins (against ...) and 3 losses (to ...)
<br>
<br>
Deegan: 3 wins (against ...) and 3 losses (to ...)
<br>
<br>
Eli: 2 wins (against ...) and 4 losses (to ...)
<br>
<br>
Fabio: 0 wins and 6 losses
<br>
<br>
<br>
The result is a tie between Ava and Bianca because they
each have
<br>
4 wins, and that's more than any other candidate. Considering
just
<br>
these tied candidates, their pairwise support counts are:
<br>
<br>
Ava: 213
<br>
<br>
Bianca: 123
<br>
<br>
So Ava wins!
<br>
<br>
<br>
Notice there's no need to show a pairwise matrix!
<br>
<br>
To prevent a potential source of confusion, the Wikipedia
article
<br>
about the Borda count begins with the words "The Borda count
is a
<br>
family of positional voting rules which gives each candidate,
for each
<br>
ballot, a number of points corresponding to the number of
candidates
<br>
ranked lower." The last portion of this sentence describes
pairwise
<br>
support counts, but it has nothing to do with the Borda
count. The
<br>
Wikipedia article for "positional voting" correctly says:
"Positional
<br>
voting is a ranked voting electoral system in which the
options or
<br>
candidates receive points based on their rank position on each
ballot
<br>
and the one with the most points overall wins." The remainder
of
<br>
Wikipedia's Borda count article correctly specifies positional
voting
<br>
in the descriptions and examples. The Borda count article at
<br>
Electowiki does not include this first-sentence mistake. I'm
going to
<br>
let someone else figure out how the first sentence in
Wikipedia should
<br>
be worded. (I'd rather fight other battles.)
<br>
<br>
I'm calling attention to this difference between pairwise
support
<br>
counts and the Borda count because this issue has previously
caused
<br>
confusion in this forum.
<br>
<br>
Getting back to the Ranked Robin method, this improved version
is not
<br>
likely to significantly increase the failure rates of the most
<br>
important failure criteria, and it's likely to reduce some
failure rates.
<br>
<br>
Currently the Ranked Robin article claims that the method
passes some
<br>
fairness criteria that it actually doesn't pass. When the
Ranked
<br>
Robin article is improved to include a concise description of
the
<br>
method (which should be near the beginning), some experts here
can
<br>
identify which of the listed "pass" criteria need to be moved
to the
<br>
listed "fail" criteria.
<br>
<br>
Interestingly, the Ranked Robin method and its name were
created by
<br>
people who have previously promoted only STAR voting. I'm
pleased
<br>
that they are finally recognizing that STAR ballots are not
going to
<br>
replace ranked choice ballots throughout the US. And that
they
<br>
recognize the need to promote a method that takes advantage of
the
<br>
Forward Party's recommendation of "ranked choice voting."
<br>
<br>
Looking at the broader perspective ...
<br>
<br>
The current version of Ranked Robin already has these
advantages:
<br>
<br>
* Uses pairwise vote counting, which looks deeper into the
ballot
<br>
preferences compared to instant-runoff voting.
<br>
<br>
* Is precinct summable.
<br>
<br>
* Allows voters to mark more than one candidate at the same
ranking
<br>
level.
<br>
<br>
I suggest making it even easier to understand by using
pairwise
<br>
support counts. This improvement will eliminate the need to
educate
<br>
voters about the pairwise matrix. And I believe this change
will
<br>
still provide a similar level of fairness.
<br>
<br>
Certainly, in multiple ways, it's much better than
instant-runoff voting.
<br>
<br>
Richard Fobes
<br>
The VoteFair guy
<br>
----
<br>
Election-Methods mailing list - see <a class="moz-txt-link-freetext" href="https://electorama.com/em">https://electorama.com/em</a>
for list
<br>
info
<br>
</blockquote>
<br>
</blockquote>
</blockquote>
<br>
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