[EM] Relative vs. Majority Condorcet
Chris Benham
cbenhamau at yahoo.com.au
Sun Apr 28 21:32:02 PDT 2024
(This is a resend with a typo corrected.)
CLC,
"ICT" stands for "Improved Condorcet//Top-ratings". "Symmetrical ICT" is
someone's eccentric idea that I never understood and/or saw the point of.
ICA typically uses 3-slot ratings ballots (I'm sure that was the
version first proposed). If counting tied at the top ballots such as
A=B counting as both A>B and B>A there are some candidates that pairwise
beat all the others (it is now possible that A and B will "pairwise
beat" each other), disqualify all the others then elect the candidate
that is rated above bottom on most ballots. If there are no such
pairwise "beats all" candidates then do the same thing.
ICT is the same except that where ICA elects the not-disqualified
candidate that is rated above bottom on the highest number of ballots,
ICT elects the candidate that's rated top on the highest number of ballots.
The classic multi-purpose scenario:
49 A (sincere might be A>B)
24 B (sincere might be B>C)
27 C>B (sincere)
Chicken Dilemma specifies that is this scenario the B voters must not be
able to get away with a Defection strategy against C and so B mustn't
win, while Sincere Defense specifies that the A voters must not be able
to get away with their "offensive truncation" against the presumed
"sincere CW" B and so A must not win, in large part to save the C>B
voters the regret of not having Compromised by voting B>C or B.
Sincere Defense (or the simplest version of it) says that if more than
half the voters vote X above Y and Y no higher than equal-bottom then Y
can't win. And Woodall's Plurality criterion says that C can't win
because A has more first-place votes than C has any sort of (above
bottom) votes.
https://electowiki.org/wiki/Chicken_dilemma
>
> Definition
>
> Each voter is either an A voter, a B voter, or a C voter. Each faction
> votes its candidate (strictly) over everybody else.
>
>
> Premise
>
> 1. There are 3 candidates: A, B, and C.
> 2. The A voters and the B voters, combined, add up to more than half
> of the voters in the election.
> 3. The A voters are more numerous than the B voters. The C voters are
> more numerous than the A voters, and more numerous than the B voters.
> 4. The A voters vote B over C. The B voters refuse to vote A over anyone.
> 5. None of the C voters vote A or B over the other.
>
>
> Requirement
>
> B doesn't win
>
I thought I recalled that CD says that C in the "premise" ( A in my
example) must win. In any case you can't have compliance with all three
of Sincere Defense, Chicken Dilemma and Plurality.
Chris B.
On 29/04/2024 10:08 am, Closed Limelike Curves wrote:
>
> The way you describe ICT I find a bit odd.
>
> Yes, I think I made a few mistakes, including confusing ICT with
> symmetrical ICT (I have no idea what ICT is, assuming they're
> different; electowiki doesn't have an article).
>
> Kevin's ICA method easily meets Minimal Defense. ICT instead
> meets Chicken Dilemma (incompatible with Minimal Defense) but I
> think I recall was motivated by some example where the MCA winner
> looked quite odd.
>
> Could you clarify how the chicken criterion is incompatible with
> Minimal Defense? Intuitively I thought median ratings would do well
> against both.
>
> On Sun, Apr 28, 2024 at 12:34 PM Chris Benham <cbenhamau at yahoo.com.au>
> wrote:
>
> CLC,
>
>>
>> Yes, that's the main question I'm looking to answer with this
>> poll: do tied-at-the-top, or other tied-rank mechanisms, have
>> substantial support on this email list? (ICT is a similar, but
>> not-quite-working, attempt at satisfying Minimal Defense as well.)
>
> I assume by "mechanisms" you mean * mechanisms to force the
> method to comply with Favorite Betrayal*. As far as I can tell, no.
>
> The way you describe ICT I find a bit odd. Kevin's ICA method
> easily meets Minimal Defense. ICT instead meets Chicken Dilemma
> (incompatible with Minimal Defense) but I think I recall was
> motivated by some example where the MCA winner looked quite odd.
> I don't recall it but can probably find it later.
>
> Chris B.
> On 28/04/2024 12:40 pm, Closed Limelike Curves wrote:
>> Hi Chris, thanks for your response!
>>
>> I came to the conclusion that any good more sophisticated
>> FBC methods need to use Kevin's "Tied at the Top Rule"
>> mechanism.
>>
>> Yes, that's the main question I'm looking to answer with this
>> poll: do tied-at-the-top, or other tied-rank mechanisms, have
>> substantial support on this email list? (ICT is a similar, but
>> not-quite-working, attempt at satisfying Minimal Defense as well.)
>>
>> There is some small movement and enthusiasm for Condorcet
>> compliance, but none that I discern for strict FBC
>> compliance. I would think most voters would satisfied with
>> the massive reduction in Compromise incentive compared to FPP
>> afforded by properly implemented IRV, let alone the still
>> greater reduction we get from Condorcet.
>>
>> There's a major IRV-repeal effort underway in Alaska at the
>> moment because they had one (!) election with a favorite-betrayal
>> incentive. I'm also not aware of any movements for strict
>> relative-majority Condorcet compliance. The organization that
>> comes closest is EVC (with their Copeland//Borda proposal), but
>> even they're not very purist about it.
>>
>> And I'm generally allergic to, and find very silly, methods
>> that fail Irrelevant Ballots Independence like Median Ratings
>> methods and this "Majority-Condorcet" idea.
>>
>> I fully agree with you that this is a big problem for median
>> ratings. A voter who shows up and says they think all the
>> candidates are bad isn't provide any new information about the
>> relative quality of the candidates.
>> However, I don't think an all-equal ballot is providing no
>> information in every situation. As an example, say we had a
>> system like approval, but with a 50% threshold for election (and
>> elections with <50% support for the winner resulting in reopening
>> nominations). Then, a fully-blank ballot is a way for voters to
>> meaningfully express their preference for somebody else,//other
>> than the current crop of candidates.
>>
>> Something similar applies to the tied-at-the-top rule: a voter
>> who ties two candidates is saying they want these two candidates
>> to be compared using the tiebreaking mechanism, /rather than/ the
>> relative-Condorcet mechanism.
>>
>> On Sat, Apr 27, 2024 at 5:00 AM Chris Benham
>> <cbenhamau at yahoo.com.au> wrote:
>>
>>> There was some advantage of ICA & ICT that I really liked,
>>> but public proposals have to be as simple as possible.
>>
>> In that case I say forget about FBC methods other than
>> Approval. I came to the conclusion that any good more
>> sophisticated FBC methods need to use Kevin's "Tied at the
>> Top Rule" mechanism.
>>
>> There is some small movement and enthusiasm for Condorcet
>> compliance, but none that I discern for strict FBC
>> compliance. I would think most voters would satisfied with
>> the massive reduction in Compromise incentive compared to FPP
>> afforded by properly implemented IRV, let alone the still
>> greater reduction we get from Condorcet.
>>
>> In general FBC is much more slippery and "expensive" (in
>> terms of being compatible with other criteria) than
>> Condorcet. I went off my own "Irrelevant-Ballot Independent
>> Fall-back Approval" idea (which isn't "very simple") when
>> Kevin showed that it fails Woodall's Plurality criterion.
>>
>> And I'm generally allergic to, and find very silly, methods
>> that fail Irrelevant Ballots Independence like Median Ratings
>> methods and this "Majority-Condorcet" idea.
>>
>> You have an apparent "majority Condorcet" winner, and then a
>> few extra ballots that vote for nobody are found and then the
>> winner changes because the "majority" threshold goes up.
>> Absurd and potentially embarrassing.
>>
>> Chris B.
>>
>> On 27/04/2024 3:40 pm, Michael Ossipoff wrote:
>>> There was some advantage of ICA & ICT that I really liked,
>>> but public proposals have to be as simple as possible. Few
>>> methods proposed here are simple enough for public proposal.
>>>
>>> On Fri, Apr 26, 2024 at 22:50 Michael Ossipoff
>>> <email9648742 at gmail.com> wrote:
>>>
>>>
>>>
>>> On Wed, Apr 24, 2024 at 10:02 Closed Limelike Curves
>>> <closed.limelike.curves at gmail.com> wrote:
>>>
>>> /Does "Majority-Condorcet" mean the CW needs to have
>>> a majority over every other
>>> candidate?/
>>>
>>> Yes: a CW needs more than 50% of the vote, including
>>> tied ranks, to defeat every other candidate. This
>>> version of Condorcet is compatible with FBC.
>>>
>>>
>>> I guess a lot of CWs wouldn’t be getting elected.
>>>
>>> The best Condorcet methods don’t importantly fail FBC. A
>>> sincere CW can only lose by offensive strategy, & the
>>> better Condorcet methods well-deter offensive strategy.
>>> No need for any defensive strategy.
>>>
>>> Was it you who once said that people would try offensive
>>> strategy? The whole point of strategy is action based on
>>> an analysis of what the result will be. It’s a
>>> strategist’s business to find that out first.
>>>
>>> Anyway when it’s noticed to usually backfire…
>>>
>>>
>>> On Wed, Apr 24, 2024 at 3:43 AM Kristofer
>>> Munsterhjelm <km_elmet at t-online.de> wrote:
>>>
>>> On 2024-04-24 12:32, Kevin Venzke wrote:
>>>
>>> > The second option doesn't offer Smith, but if
>>> it did, I would note that Smith is a
>>> > poor guarantee of quality. Here's a 1025-voter
>>> election where a 2-vote candidate is
>>> > in the Smith set (along with all other
>>> candidates):
>>> >
>>> > 2: A>B>C>D>E>F>G>H>I>J>K
>>> > 1: B>C>D>E>F>G>H>I>J>K
>>> > 2: C>D>E>F>G>H>I>J>K
>>> > 4: D>E>F>G>H>I>J>K
>>> > 8: E>F>G>H>I>J>K
>>> > 16: F>G>H>I>J>K
>>> > 32: G>H>I>J>K
>>> > 64: H>I>J>K
>>> > 128: I>J>K
>>> > 256: J>K
>>> > 512: K
>>> >
>>> > While this is not realistic, I do think it is
>>> realistic that a candidate of limited
>>> > interest to most voters would sometimes manage
>>> to pairwise defeat a more viable
>>> > candidate. And we should be ready to interpret
>>> this as noise.
>>>
>>> That was phrased a bit oddly in the context of
>>> the rest of your post,
>>> but I understand you to be saying "the worst
>>> method that passes Smith
>>> may still be pretty bad", not necessarily that
>>> proposed methods passing
>>> Smith are actually bad. Is that right?
>>>
>>> -km
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>>
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