[EM] "Margins Sorted Approval" poll candidate

[Michael Ossipoff]

If a single example can’t be found in which wv Condorcet does better than
Approval-Sorted Margins, then of course I’ll admit that Approval-Sorted
Margins is better.

I have a few questions about Margins-Sorted-Approval:

If I want to propose it to (say) a city-council or an initiative-committee
or focus-group, someone will ask what it’s advantage is…in what way it’s
better. What valuable property does it offer that other methods don’t?

What’s the answer to that inevitable question?

…& there’s the matter of motivation. What is it about double sorting that
motivates it?

It makes sense to start with Approval-ordering & then adjust to fix the
most important pairwise contradictions by switching. But aren’t the *
biggest* margins more important than the smallest ones? Then why fix the
smallest-margin mis-orderings first? & what’s special about adjacency in
the Approval-ordering? Isn’t the biggest pairwise contradiction most
important even between candidates not adjacent in the Approval-ordering?

…& why margins instead of wv, losing-votes, or any of the various measures
of a pairwise-defeat? In my experience, wv has been the important
defeat-measure for strategic protection.


On Sat, Apr 20, 2024 at 11:03 Chris Benham <cbenhamau at yahoo.com.au> wrote:

> Mike O.,
>
> https://electowiki.org/wiki/Minimal_Defense_criterion
>
> Stephen Eppley <https://electowiki.org/wiki/Stephen_Eppley> gives this
> official definition:
>
> If more than half of the voters prefer alternative y over alternative x,
> then that majority must have some way of voting that ensures x will not be
> elected and does not require any of them to rank y equal to or over any
> alternatives preferred over y.
>
> This definition is most similar to that of SDSC
> <https://electowiki.org/wiki/SDSC>.
> https://electowiki.org/wiki/Strong_Defensive_Strategy_criterion
>
>
> The answer to your first question (based on the definition I copied above)
> is yes. That is obviously implied by its compliance with Double Defeat. All
> that "majority" has to do is approve Y and not X. Double Defeat says that a
> candidate that is pairwise beaten by a more approved candidate can't win.
>
> The answer to your second question is yes if the other faction doesn't
> approve the CW and no if it does.  Like in this old example:
>
> 49  A (sincere is A>B)
> 24  B (the "sincere CW" but the faction may be defecting against C)
> 27  C>B
>
> If the C>B voters approve B then the approval order is  B>A>C and since B
> pairwise beats A and A pairwise beats C that order is final and B wins.
> But if they don't then the approval order is A>C>B and that order is final
> and A wins.
>
>
> 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.
>
>
> I don't that is always a good idea. If the faction sizes are close
> together then surely the risk for the Buriers of their strategy back-firing
> would be a lot greater than if the "bus" faction is quite a bit smaller
> than theirs. Also of course two large parties and one small one more
> closely resembles the current political landscape.
>
> An example can be found where one particular method does better than
> another.
>
> Good. I look forward to seeing your example where Winning Votes does
> better than Approval Sorted Margins.
>
> I don't know the answer to your last question.
>
> Chris B.
>
> On 19/04/2024 6:56 am, Michael Ossipoff wrote:
>
> 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
>>>
>>>
>>>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20240420/6e4fa54c/attachment-0001.htm>