[EM] "Margins Sorted Approval" poll candidate

[Michael Ossipoff]

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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