[EM] "Margins Sorted Approval" poll candidate

[Michael Ossipoff]

1) Does Margins-Sorted Approval meet Minimal-Defense?

2) Can offense-truncation by one faction take the win from a CW ranked in
2nd place by the other faction?

Answers for wv:  1) Yes. 2) No.

On Thu, Apr 18, 2024 at 14:17 Michael Ossipoff <email9648742 at gmail.com>
wrote:

> An example can be found where one particular method does better than
> another.
>
> 3 candidates;
>
> CW, BF, & Bus
>
> (BF is buriers’ favorite. Bus 🚌 is the candidate under whom they bury CW.)
>
> To test wv Condorcet for burial deterrence, I checked 24 cases:
>
> All 6 faction-size orderings for the 3 candidates.
>
> and
>
> 4 ways for the middle CW’s voters to rank the other 2, with regard to
> which they rank in 2nd place:
>
> Neither
> BF
> Bus
> Half one & half the other
>
> The faction-sizes are kept as close together as possible, because equal
> sizes is the middle about which the variation happens, & is probably the
> most likely single configuration.
>
> Divide the number of burial’s backfires by the number of its successes,
> for the backfire/success ratio…abbreviated
> b/s.
>
> For wv Condorcet, b/s = 10.
>
> What is it for Margins-Sorted Approval?
>
>
>
> On Thu, Apr 18, 2024 at 10:14 Chris Benham <cbenhamau at yahoo.com.au> wrote:
>
>>
>> One of my nominations and my top choice in the current poll:
>>
>> Margins Sorted Approval (specified cutoff):
>>
>> *Voters rank from the top however many candidates they wish and can also
>> specify an approval
>> cutoff/threshold. Default approval is only for candidates ranked below no
>> others (i.e. ranked top
>> or equal-top).
>>
>> A Forrest Simmons invention. Candidates are listed in approval score
>> order and if any adjacent pairs
>> are pairwise out of order then this is corrected by flipping the
>> out-of-order pair with the smallest
>> margin. If there is a tie for this we flip the less approved pair. Repeat
>> until there are no adjacent pairs
>> of candidates that are pairwise out of order, then elect the
>> highest-ordered candidate.*
>>
>> I'm going to compare it with another of my nominations, another Condorcet
>> method that collects the
>> same information from the voters:
>>
>> Smith//Approval (specified cutoff):
>>
>> *Voters rank from the top however many candidates they wish and can also
>> specify an approval
>> cutoff/threshold. Default approval is only for candidates ranked below no
>> others (i.e. ranked top
>> or equal-top).
>> The most approved member of the Smith set wins.*
>>
>> Although it asks voters for a bit more information than other Condorcet
>> methods like Ranked Pairs,
>> Schulze, MinMax etcetera, I think it is a lot easier than them to explain
>> and sell than them.
>>
>> Condorcet//Approval (explicit) was discussed here in April  2002 by Adam
>> Tarr. I find voluntarily (in a
>> Condorcet method) electing a candidate outside the Smith set to be weird
>> and unacceptable, but all the
>> examples he gave that I saw apply just as well to
>> Smith//Approval(explicit).
>>
>> Now why do I prefer Margins Sorted Approval?
>>
>> The main reason is that it is quite a lot less vulnerable to Burial
>> strategy.  Say there are three candidates
>> and most of the voters normally truncate.  Say A is the predicted FPP and
>> Condorcet winner, B is the
>> predicted FPP runner-up and C  is coming last by quite a big margin.
>>
>> In that case the voters most likely to be tempted to try a Burial
>> strategy will be the B supporters against
>> A, using no-threat C as the "bus".
>>
>> 43 A|
>> 03 A>B| ("strategically naive" voters)
>> 44 B|>C  (sincere is B or B>A)
>> 10 C|
>>
>> The B>C Buriers have given A a pairwise defeat, so now there is an
>> A>B>C>A cycle.
>>
>> The approval scores:  B 47,  A 46,   C 10.
>>
>> Now if this was Smith//Approval  the 3 A>B| voters would have blown the
>> election for A by approving B.
>>
>> But ASM notices that both approval-score adjacent pairs (B-A and A-C) are
>> pairwise out of order and by far
>> the smallest of the two approval-score margins is that between B and A
>> and so flips that order to give
>> A>B>C.   Now neither pair is pairwise "out of order" so that order is
>> final and A comfortably wins.
>>
>> Now to borrow an old example with none of the voters truncating:
>>
>> 49  A|> C  (sincere is A or A>B)
>> 06  B>A|
>> 06  B|>A
>> 06  B|>C
>> 06  B>C|
>> 27  C>B|
>>
>> Now there is a cycle A>C>B>A and the approval scores are A 55, B 51,  C
>> 33.
>>
>> Again Smith//Approval has a problem, the Burying strategists have
>> succeeded.
>>
>> But again Approval Sorted Margins fixes it. Both adjacent approval-score
>> adjacent pairs (A-B and B-C)
>> are out pairwise order and the A-B margin (4) is smaller than the B-C
>> margin (18) so we flip the A-B pair
>> to give the order B>A>C.   Now neither adjacent pair is pairwise out of
>> order so that order is final and
>> B (the sincere Condorcet winner) wins.
>>
>> The other reason I prefer Margins Sorted Approval  to  Smith//Approval
>> (explicit) is mostly aesthetic.
>>
>> I find it much more elegant (even beautiful). It would meet as many
>> monotonicity criteria as it is possible
>> for a Condorcet method to meet. Without even trying, it meets Reverse
>> Symmetry.
>>
>> By comparison I find Smith//Approval(explicit) a bit clunky.
>>
>> Unfortunately Benham and Woodall and Gross Loser Elimination and "almost
>> Condorcet" RCIPE  and
>> Hare (aka IRV) all fail Mono-raise (aka Monotonicity).
>>
>> In both my examples above, the three Winning Votes methods in the poll
>> (Ranked Pairs and Schulze and
>> MinMax and maybe "Max Strength Transitive Beatpath") all elect the
>> Burier's favourite.
>>
>> In the second example that is also true of Benham and Woodall and Gross
>> Loser Elimination.
>>
>> Chris Benham
>>
>>
>>
>>
>> http://lists.electorama.com/pipermail/election-methods-electorama.com//2002-April/073341.html
>>
>> I think that if you give people a ballot that looks like grades, they will
>> tend to assign candidates grades that reflect their cardinal rankings for
>> those candidates, provided they don't have strategic incentive to do
>> otherwise.  If lack of slots becomes a problem, we could switch to 1-10
>> rankings.  If a tendency to spread the candidates out tends to skew the
>> results, we could go with the "none of the below" candidate in ranked
>> ballots.  But for the time being, I think the 6-slot ballot would do fine,
>> and if I were to advocate this method I'd go with the 6-slot ballot.
>>
>> At any rate, I was just looking at how well this technique responds to
>> certain strategic voting scenarios.  In an earlier message (March 20) I
>> suggested that Approval Completed Condorcet ("ACC" from here on out) passes
>> SFC and SDSC from Mike's criterion.  It doesn't pass the "Generalized"
>> versions unless one slips in a Smith set requirement explicitly, which I
>> argued against in that message.
>>
>> I'm now going to compare ACC to margins and winning votes Condorcet
>> methods, using the example that has become my signature example on this
>> list.  The following are the sincere preferences of my example electorate:
>>
>> 49: Bush>Gore>Nader
>> 12: Gore>Bush>Nader
>> 12: Gore>Nader>Bush
>> 27: Nader>Gore>Bush
>>
>> If everyone votes sincerely, then Gore is the Condorcet winner.  The
>> problem arises when the Bush voters swap Nader and Gore on their ballots
>> (in margins they can achieve the same effect by truncating, but I'll ignore
>> that for this analysis).  So the new "preferences" are
>>
>> 49: Bush>Nader>Gore
>> 12: Gore>Bush>Nader
>> 12: Gore>Nader>Bush
>> 27: Nader>Gore>Bush
>>
>> In margins-based methods, the only way for Gore to still win the election
>> is for the Nader voters to bury Nader behind Gore.  The stable equilibrium
>> ballots become:
>>
>> 49: Bush>Nader>Gore
>> 12: Gore>Bush>Nader
>> 39: Gore>Nader>Bush
>>
>> And this allows Gore to still carry the election.  This sort of equilibrium
>> is what Mike is talking about when he says that margins methods are
>> "falsifying".
>>
>> In winning votes methods, the Nader camp can vote equal first-place
>> rankings rather than swap Gore and Nader entirely.  The stable result is
>> therefore:
>>
>> 49: Bush>Nader>Gore
>> 12: Gore>Bush>Nader
>> 12: Gore>Nader>Bush
>> 27: Nader=Gore>Bush
>>
>> In ACC... we first have to define where the approval cutoffs on the ballots
>> are.  Since the approval tally is only used to break cyclic ties, clearly
>> the Bush camp has no incentive to Approve of anyone except Bush.  I'm going
>> to make the assumption that since Gore and Bush are the apparent front
>> runners in this race (the only two with a decent shot at election), every
>> voter will approve one and not the other.  This is the logical approval
>> cutoff to use, based on the approval strategy threads that have been
>> circulating on the list of late.  So the ballots could look something like
>> this:  (>> denotes approval cutoff)
>>
>> 49: Bush>>Nader>Gore
>> 12: Gore>>Bush>Nader
>> 6: Gore>>Nader>Bush
>> 6: Gore>Nader>>Bush
>> 27: Nader>Gore>>Bush
>>
>> In this case, Gore wins the approval runoff 51-49-33.  So not only did ACC
>> avoid the need for defensive order-reversal like margins methods, but it
>> avoided the need for defensive equal-ranking like winning votes
>> methods.  This is a super result: totally strategy-free voting for the
>> majority side.
>>
>> There is a dark side to this result, though.  Say that some of the
>> Gore>Bush>Nader voters were extremely non-strategic and decided to approve
>> both Bush and Gore.  So the votes now look like:
>>
>> 49: Bush>>Nader>Gore
>> 6: Gore>Bush>>Nader
>> 6: Gore>>Bush>Nader
>> 6: Gore>>Nader>Bush
>> 6: Gore>Nader>>Bush
>> 27: Nader>Gore>>Bush
>>
>> Now, Bush wins the approval runoff 55-51-33.  This is where ACC's favorite
>> betrayal scenario comes in.  Since Bush wins the approval vote, the only
>> way the majority can guarantee a Gore win is to make Gore the initial
>> Condorcet winner, which requires that the Nader camp vote Gore in first place:
>>
>> 49: Bush>>Nader>Gore
>> 6: Gore>Bush>>Nader
>> 6: Gore>>Bush>Nader
>> 6: Gore>>Nader>Bush
>> 33: Gore>Nader>>Bush
>>
>> So this is more or less the same as the margins method equilibrium.
>>
>> In summary, if the voters are fairly logical in the placement of their
>> approval cutoff, then ACC seems almost uniquely free of strategy
>> considerations.  If the underlying approval votes do not back up the
>> sincere Condorcet winner, however, then ACC becomes just as vulnerable to
>> strategic manipulation as the margins methods are, if not more so.
>>
>> Comments?
>>
>> -Adam
>>
>>
>>
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