[EM] "Margins Sorted Approval" poll candidate

[Ted Stern]

On Sat, Apr 20, 2024 at 12:07 PM Michael Ossipoff <email9648742 at gmail.com>
wrote:

> 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?
>

It is more resistant to burial and defection.


>
> What’s the answer to that inevitable question?
>
> …& there’s the matter of motivation. What is it about double sorting that
> motivates it?
>

First of all, I think the name is something of a misnomer.

If all ranked candidates are approved in some way, the initial ordering is
not based on approval but rather on *strong preference*.

So you start with a ranking of candidates based on which candidates are
most strongly preferred. But we want to end up with list of candidates such
that each pair of candidates is in order based on their *pairwise* preferences.
Therefore we will have to rearrange the initial *strong preference* ordering
in some way, based on adjacent pairwise orderings. See below.


> 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.
>

Remember that here margins are *not* based on votes in pairwise contests
but rather in comparing the strong preferences for two consecutive
candidates in the ordered ranking.

Sorting the candidate list, based on pairwise contests, can be done by
several means. Upward bubble sort gives you DMC. Downward bubble sort gives
you something different. But either of those could move candidates far from
their original strong preference ranking.

Margin sort (that is, the margin of adjacent strong preference metrics for
pairwise-out-of-order consecutive candidates) is a variation on bubble sort
that locally minimizes the change from the original strong preference
rating.

>
>
> 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
>>>>
>>>>
>>>> ----
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