[EM] "Margins Sorted Approval" poll candidate
Chris Benham
cbenhamau at yahoo.com.au
Sat Apr 20 11:02:50 PDT 2024
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 ofSDSC
> <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/20240421/5d18b575/attachment-0001.htm>
More information about the Election-Methods
mailing list