Richard,

I have a few questions and comments on your ballot with accompanying
remarks.

I have trouble understanding the motivation behind "RCIPE".   It seems
to me that it must
elect the Condorcet winner unless, initially or after one or more
eliminations, there is a bottom
cycle (and thus no Condorcet Loser) in which case it is possible that
the Condorcet winner will
have the fewest top-choice votes and be eliminated.

And that is why it fails Clone-Loser, because the candidates in the
bottom cycle cycle could be a
set of clones and if they were replaced with a single candidate then
there would be a Condorcet
loser who would be eliminated instead of possibly the Condorcet winner.

I find this all very odd, and I'm not sure what you are"buying" in
comparison with plain Hare (aka IRV).

Unlike RCIPE, it meets Clone Independence and Later-no-Help and
Later-no-Harm and already meets
Condorcet Loser.  So you are trashing quite a bit just to get a bit more
"Condorcet efficiency".

Why do you think that RP(wv) and Schulze are significantly different
from each other?  There needs
to be more than 3 candidates in the top cycle (aka Smith set) for them
to give different winners and
I gather that even in that very rare circumstance they usually give the
same winner.

And why do you think that MinMax(wv) is better than either? Doesn't it
fail Smith and Clone Independence?

Why do you think Woodall is better than Benham?

What is the (or your) definition of "Schwartz-Woodall" ?    And what do
you think is the positive point of it
compared with plain Woodall?

Chris B.

On 2024-04-18 08:58, Chris Benham wrote:

From my explanation post, with a few words added in brackets:

Woodall:
https://electowiki.org/wiki/Woodall%27s_method
This method takes ranked ballots. First make a note of the initial
Smith set. Then keep doing IRV until only one candidate of the initial
Smith set remains. Elect that candidate. Note: This is not Benham - the
initial Smith set never changes.

Schwartz-Woodall:
The same as Woodall, but with the Schwartz set [instead of the
Smith set]. The Schwartz set is slightly less prone to ties.

So what I read as its difference to ordinary Woodall is "fewer tie
problems but harder to explain". Richard's opinion might differ, of course.

-km

Chris B., thanks for your questions!  Here are my answers:

On 4/17/2024 11:58 PM, Chris Benham wrote:

RCIPE -- Ranked Choice Including Pairwise Elimination -- is a compromise
method.

It inherits lots of the cloneproofness of IRV because that's the backup
elimination process when an elimination round does not have a pairwise
losing candidate.

The elimination of pairwise losing candidates causes RCIPE to seldom
fail the Condorcet criterion and other "majority" criteria.  It took
some head scratching to discover a case in which RCIPE fails the
Condorcet criterion.  (As I recall Kristofer gets credit for finding
such a case.)

Chris B., all of your concerns seem to be about the "pass" or "fail"
categorization of methods.

I regard HOW OFTEN failures occur to be much more important than a
checkbox that says "yes" or "no" failures of this kind NEVER occur.

Visually this perspective is conveyed by measuring failure rates:

http://www.votefair.org/clone_iia_success_rates.png

About this graph: Under the simulation conditions of these measurements
the RCIPE method has zero clone failures.  In real elections there can
be a few clone failures compared to IRV.  Those few failures don't
concern me.

It's easy to overlook the many failures that do not fit within NAMED
failure types.  Those unnamed kinds of failures are being ignored!

For example, clone failures and Local IIA failures are just two
categories within the broad category of IIA failures.

This is why I presume the Schulze method fails the various unnamed IIA
criteria in order to have zero clone failures.

Just because those increased kinds of failures don't have names doesn't
mean they should be ignored!

comparison with plain Hare (aka IRV).

The payoff is that RCIPE would not have failed in Burlington and Alaska!
That's huge.

Avoiding any failures in REAL elections is what I'm "buying" by
advocating RCIPE instead of IRV.

Another difference from IRV is about what FairVote calls "overvotes."
RCIPE counts them correctly.  That could become a huge deal in the
upcoming Portland election for mayor -- where two or more marks in the
same "choice" column will be ignored as if those marks were not on the
ballot.  If the race is close, that counting error could cause the wrong
candidate to win.  (This counting error is less likely to affect STV
election results for Portland city council members because winning the
second seat instead of the first seat is not a big deal.)

Clarification: I regard IRV as a steppingstone to RCIPE, so I have
supported adopting IRV here in Oregon.  I dislike the misrepresentations
that come from the FairVote organization, but I'm not using that
organization's flaws as reasons to fully reject IRV.  (We have to crawl
and walk before we can run.)

from each other?

Schulze is much more difficult to understand.  That's important in this
poll which is supposed to be about what can be adopted for use in real,
governmental elections.

it fail Smith and Clone Independence?

See above about my lack of concern about the difference between "never"
and "almost never."

Woodall?

I don't recall what I was thinking during every detail of my ranking
process.

Broadly my thinking is:

• I'm a big fan of pairwise vote counting.

• I recognize that IRV's flaw is that the candidate with the fewest
  transferred votes is not always the least popular -- as demonstrated in
  Burlington and Alaska.

• I dislike Borda being any part of a method because it requires honest
  voting to yield fair results.  (Honestly, honesty doesn't happen in
  elections.)

• Approval voting requires tactical voting.  There's no way to avoid it.
  I know that Approval fans disagree.  Yet I assure them that when I
  have to make a decision between approval and disapproval I have to do
  the equivalent of mentally flipping a coin.

• I strongly dislike score/rating ballots for single-winner methods
  because they are vulnerable to tactical voting.  Specifically, it's
  impossible to know whether a ballot is from a person with strong
  religious beliefs or a person who is acting like a "drama queen" (or
  whatever the modern name is for this concept).  This tactical
  vulnerability is important in single-winner elections.

• I do agree that score/rating ballots could be useful in multi-winner
  elections where strength of preference is worthy of being considered
  when there are interactions between who wins each seat.  But this poll
  isn't about multi-winner elections.  And governmental elections need to
  adopt single-winner methods first.  Only later will voters and
  legislators be ready to begin learning subtle concepts such as
  interactions between seat winners.

• STAR ballots are a dead-end ballot type.  (Always six columns, even
  when there are three or four candidates.  And always with the star icon,
  no thanks!)

Again, thank you Chris for your questions.

Richard Fobes
The VoteFair guy

On 4/17/2024 11:58 PM, Chris Benham wrote:

On 2024-04-18 20:43, Richard, the VoteFair guy wrote:

There doesn't need to be a fixed proportion of failures, does there?

Suppose I take Schulze and break ties by Plurality so that it's no
longer cloneproof. I don't think that the rate of non-clone IIA failures
would decrease just because it now fails clone independence.

So Schulze's rate of IIA failures don't need to be a consequence of
having zero clone failures. It's possible that other methods have clone
failures and just as many other IIA failures.

-km

I'm interested in your positive case for MinMax over Ranked Pairs (or River). To me it just seems essentially like a less sophisticated version of them.
Toby
On Thursday, 18 April 2024 at 19:43:33 BST, Richard, the VoteFair guy electionmethods@votefair.org wrote:

it fail Smith and Clone Independence?

See above about my lack of concern about the difference between "never"
and "almost never."

On 4/18/2024 1:17 PM, Kristofer Munsterhjelm wrote:

You are correct.

What I'm taking into account are two factors:

• How deeply down into the pairwise counts does the method look?

• How convoluted is the counting process?

The Schulze method looks very deeply into the pairwise counts.  However,
its counting process is so convoluted that it's very difficult to
comprehend.

I suspect that that convolution causes lots of IIA failures.

Research is needed to measure failure rates.

I really don't know what those measurements will reveal.

Interestingly, Yee diagrams serve as a simple way to measure some IIA
failure rates.  They clearly reveal the IIA failures of IRV.

We need something even better to identify and measure the failure rates
of better counting methods.

The graph I generated and referred to is just a beginning.  We need lots
more research that measures failure RATES.  Just looking at
pass-versus-fail checkboxes is not looking deep enough.

Then we will know more about the failures for which we do not have names.

Richard Fobes
The VoteFair guy

On 4/18/2024 1:17 PM, Kristofer Munsterhjelm wrote:

On 2024-04-19 01:44, Richard, the VoteFair guy wrote:

I'm not sure, since the elegance of an object doesn't need to relate to
the simplicity of the algorithm that finds them. E.g. it's very easy to
say what a prime number is, but a polynomial time deterministic
algorithm to determine if a number is prime can be quite complex.

Here's a simple result for IIA.

Define an election under a method M as failing IIA if:
- The original winner according to M is X, and
- It is possible to remove one or more candidates who aren't X, so that
the winner instead becomes some other candidate Y.

Then, for a Condorcet method, an election fails IIA iff it has no
Condorcet winner. Remove every candidate in the cycle, except for the
one who beats X pairwise, and then that candidate is the Y who wins.

For a non-Condorcet method, if it works like majority rule when there
are only two candidates, the election fails IIA either if there's no CW,
or if there is a Condorcet winner that the method doesn't elect.

In either case, you just remove everybody except the current winner and
a candidate who beats him pairwise.

So here for Condorcet methods, the IIA rate is simply the rate of non-CW
elections under the election distribution in question (impartial
culture, spatial, etc). It is not affected by other properties like
monotonicity, reversal symmetry, clone dependence, or even LIIA.

And the rate for non-Condorcet methods depends directly on how often
they fail Condorcet, and not on other properties either.

-km

On 4/18/2024 2:21 PM, Toby Pereira wrote:

Three decades ago, when I first became aware of vote splitting,
information about vote-counting methods was not available online.  (It
was only available in academic journals.)  So I used my math/physics
background to imagine a better method.

First I considered what I later discovered to be IRV.  I recognized that
it didn't look deep enough into the voter preferences.  Next I
considered what I now recognize to be Ranked Pairs.  That too didn't
look deep enough because it looks for a "biggest" or "smallest" number
(one at a time).  Next I considered doing the equivalent of fitting a
straight line to a set of data points.  That revealed what is
mathematically equivalent to the Kemeny method.  My version counts
support and finds the maximum sequence score.  (It's described in my
1993 book titled "The Creative Problem Solver's Toolbox.")  John
Kemeny's version counts opposition and finds the minimum sequence score.
Wikipedia describes the version I imagined.  Markus Schulze said the
two are mathematically equivalent and I have trusted that claim.

It was later that I learned about MinMax.  That seems to look deeper
into the pairwise counts compared to Ranked Pairs.

That's basically the source of my preference.

I'm still waiting for academic measurements that reveal how often each
method fails the various criteria.  When those measurements become
available I'll be able to better compare the methods.

Richard Fobes
The VoteFair guy

On 2024-04-18 23:21, Toby Pereira wrote:

Seems like he's saying "they're close enough and/or Condorcet cycles are
rare enough that the simpler method is better".

-km

Yep. So, @Richard, the VoteFair guy electionmethods@votefair.org, we can
decompose IIA failures for (almost) all methods into IIA failures =
Condorcet cycles + Condorcet inefficiency.

I think a better metric for measuring how badly a system fails IIA, rather
than the raw count, is a metric based on changes in winner quality
when some other candidate drops out. (Probably the worst-case fall in
utility?)

On Fri, Apr 19, 2024 at 3:51 AM Kristofer Munsterhjelm km_elmet@t-online.de
wrote: