[EM] Condorcet-Kemeny clarifications

[Richard, the VoteFair guy]

On ..., Forest Simmons wrote:
 > You have shown by your EM postings that you are not content
 > to just regurgitate the opinions and pronouncements of the
 > "experts". You want fundamental understanding so that you
 > have the tools to form and defend your own opinions with
 > alacrity.. which you have done with admirable valor based
 > on above average curiosity and willingness to think
 > carefully while searching for truth.

Yes, I'm trying to look beneath the surface to see what lies deeper.

This is why I'm frustrated that many people are content to judge 
election methods based on the simplistic pass-versus-fail "grading" system.

 > We have seen that no method based solely on ranked choice ballots can 
satisfy the IIAC except by failing the Majority Criterion....

 > You invoked Arrow, but Arrow never said that Clone Winner and IIAC 
were incompatible.

I referred to Arrow's theorem as an example of a broader concept. That 
concept is that if a method has a zero failure rate for specific 
fairness criteria, then there are specific other criteria that cannot 
have a zero failure rate.

As you point out, there are proofs that support this concept for 
specific combinations of characteristics.

In my opinion we don't need to wait for more theorems to extend this 
concept to the broader concept: There are going to be other combinations 
of fairness criteria for which getting a zero failure rate for one of 
them means that we cannot get a zero failure rate for another one.

 > ... I am curious how you came up with the idea that K-Y trades in 
Clone Winner compliance for better IIAC compliance.

Hopefully I've just answered this question.

Expressed non-mathematically: "You can't have it all."

I'm attempting to use measurements to quantify the answer to the 
question: "How close can we get to identifying a method that has a nice 
balance of low failure rates across the most important fairness criteria?"

 > Clone winner failure is not about electing the wrong clone ... it's
 > about none of the clones of the erstwhile winner being elected.
 > ...
 > That is the spoiler problem.

As I understand it, the word "spoiler" overlaps with the clone 
independence (CI) criterion and the IIA (independence of irrelevant 
alternatives) criterion. Specifically:

* CI refers to the effect of adding candidates.

* IIA refers to the effect of removing candidates.

I think the word spoiler can refer to either an added candidate or a 
removed candidate changing the results, right?

This relates to a comment from Kristofer:

"One could even argue that IIA should benefit from clone independence, 
because clone independence is a form of IIA: Removing a clone who 
doesn't win changes who actually wins. So a clone failure *is* an IIA 
failure."

The Wikipedia definition of clone independence says:

"... the winner must not change due to the addition of a non-winning 
candidate who is similar to a candidate already present."

After an expert on Reddit pointed out that a different clone winning 
(instead of the originally winning clone) is not really a failure, I 
changed the software to handle it as you say, where a different clone 
winning is not a clone independence failure.

I admit I'm trying to look deeper. Especially into the criteria related 
to "strategic nomination." That's because money can be used to 
"nominate" and basically un-nominate candidates. My goal is to find 
election systems that reduce the currently excessive influence of money 
on politics.

 > If you want a method that is both clone winner compliant and IIAC
 > compliant, Approval Sorted Margins (ASM), or Majority Judgment Sorted
 > Margins (MJSM) is what you need.

To repeat, I'm *not* looking for zero failure rates. I'm looking for a 
nice combination of low failure rates.

Also, very importantly, I'm not interested in methods that use 
rating/cardinal ballots.

That's because ranked choice ballots are already appearing on ballots in 
various states in the United States.

A method that uses a rating/cardinal ballot would eventually lead to 
overlap. Specifically a voter would be asked to do both ranking and 
rating on the same ballot. That would be unacceptable.

In other words, in the U.S., ranked-choice ballots have already won the 
battle against rating/score ballots.

I do agree that in the distant future there will be situations where 
rating/score ballots are used, and useful. But voters would be way too 
confused to be introduced to both kinds at the beginning, which is where 
we are now.

 > Perhaps in your simulations you threw out cycles like these ...

The simulations ignore tied results. They do *not* ignore Condorcet 
(rock-paper-scissors) cycles -- unless that produces a tie for the winner.

Again, thank you Forest for your feedback. It helps to keep my thinking 
clear.

Richard Fobes


On 11/3/2021 2:44 PM, Forest Simmons wrote:
> Richard,
>
> You have shown by your EM postings that you are not content to just
> regurgitate the opinions and pronouncements of the "experts". You want
> fundamental understanding so that you have the tools to form and defend
> your own opinions with alacrity.. which you have done with admirable
> valor based on above average curiosity and willingness to think
> carefully while searching for truth.
>
> ...