[EM] "Margins Sorted Approval" poll candidate

[Chris Benham]

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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