[EM] Quick and Clean Burial Resistant Smith

[Ted Stern]

Forest, here is an example of how restricting to the Smith Set actually
leads to a failure of Q&CBRS.

This is a false-cycle strategy example from Colin Champion.

Sincere:

2: A > B > C > E > D
1: A > D > B > E > C
1: B > A > C > E > D
1: B > A > E > D > C
1: B > C > A > E > D
2: C > A > B > E > D
3: C > B > A > E > D

B is pairwise winner.

C voters create a cycle by insincerely elevating last place candidate D
over B.  Last two blocks change to

2: C > D > A > B > E
3: C > D > B > A > E

With Ranked Approval, Approval (basic score) can be accumulated on the
diagonal, giving the pairwise array

[11.  5.  5.  6. 11.]
[ 6. 11.  6.  5. 11.]
[ 6.  5.  9.  9.  9.]
[ 5.  6.  2.  7.  6.]
[ 0.  0.  2.  5.  6.]

Smith set is {A,B,C,D}.  D is least approved of Smith Set, but now defeats
B, leaving A and C. A has higher approval and is the winner.

If you eliminate E and recount to get a corrected basic score, you get a
pairwise array (basic score on diagonal) of

[8. 5. 5. 6.]
[6. 9. 6. 5.]
[6. 5. 9. 9.]
[5. 6. 2. 7.]

Same Smith set as before, of course, and D still has lowest approval, and
by defeating B, eliminates it. Remaining Smith candidates are A and C, as
before, but now C has higher basic score and wins.

So C's strategy of strategic burial to induce a cycle is now victorious.

On Fri, Jan 7, 2022 at 2:17 PM Ted Stern <dodecatheon at gmail.com> wrote:

> [ISDA = Independence of Smith-dominated alternatives]
>
> ISDA worthy criterion to satisfy. Unfortunately, you lose summability by
> requiring a recount. Is there any way around having to eliminate non-Smith
> candidates and recount?
>
> I was going to suggest calling your method "Practical Ranked Approval", to
> avoid having to include terms like Smith, Game-resistant, Burial, etc. But
> requiring a recount might not be considered Practical. So the best you
> could say would be Strategy-resistant Ranked Approval.
>
> Thinking along the lines of practicality, I have been mulling how best to
> keep pairwise arrays to a reasonable size for practical summability. If
> pre-election polling is available, one could accumulate pairwise counts
> explicitly for any candidate with more than, say, 2% approval, and lump
> pairwise counts for other candidates under "Other". Compute the Smith Set.
> If Other is in the Smith Set, then reduce the threshold and recount.
>
> On Fri, Jan 7, 2022 at 1:57 PM Forest Simmons <forest.simmons21 at gmail.com>
> wrote:
>
>> Very true, and I would have said err on the side of VSE until Robert B-J
>> convinced me that sincere cycles are practically non-existent with an
>> occurrence of less than 0.5 percent.
>>
>> He got that statistic from Fair Vote's analysis of over 400 elections,
>> and they have no particular reason to exaggerate that statistic. So suppose
>> they're right, then do we conclude that any old Condorcet method is as good
>> as another?
>>
>> You know the answer to that, Kristofer, but I elaborate for the benefit
>> of the typical EM List reader:
>>
>> No, because, as Kristofer pointed out, it depends on the "neighborhood."
>>
>> Back in the fifties when I was a kid in rural/small town eastern
>> Washington state nobody locked their doors. In fact, they usually left
>> their keys in the ignition for convenience. But was that the
>> prudent/sustainable thing to do?
>>
>> Nowadays sixty years later, in those same neighborhoods people have
>> learned by experience to adopt city slicker habits of door locking.
>>
>> When 99.5 percent of election polls reveal the existence of sincere
>> Condorcet candidates, the election method with the greatest Condorcet
>> efficiency will come the closest to electing a CW 99.5 percent of the time.
>>
>> But don't all Condorcet methods have equal Condorcet efficiency? Isn't
>> the very definition of "Condorcet method" a method that always elects the
>> Condorcet candidate when one exists?
>>
>> That would be nice if there were such a method, but Gibbard-Satterwaithe
>> shows the impossibility of that ideal in any tough neiborhood.
>>
>> Then what is the real definition of "Condorcet Method"?
>>
>> It is a method that elects a ballot  Condorcet candidate. In tough
>> neighborhoods there will often be sincere Condorcet candidates that are not
>> ballot Condorcet Candidates ... because they are ranked insincerely on the
>> ballots.
>>
>> So how to ensure that sincere Condorcet candidates retain their Condorcet
>> status on the ballots?
>>
>> Only methods that take this question seriously can have sustainable
>> Condorcet efficiency.
>>
>> Let's do a thought experiment to compare the Condorcet efficiency of
>> Ranked Pairs, Benham, Schulze, and other Condorcet methods:
>>
>> Suppose that sincere preferences are given...
>>
>> 40 A>C
>> 35 B>C
>> 25 C>A
>>
>> Like 99.5 percent of electorates this one has a sincere Condorcet
>> candidate, namely C, which is preferred over A by a 60 percent majority,
>> and preferred over B by a 65 percent majority.
>>
>> The question of Condorcet efficiency in this example is "Which Condorcet
>> methods are most likely to elect C ?"
>>
>> But that depends on the neighborhood. In Grant County, Washington of the
>> fifties, any Condorcet method would elect C.
>>
>> But which Condorcet method would robustly elect C even in Brooklyn, New
>> York?
>>
>> That depends on which methods take the possibility of subversion
>> seriously... subversion of the sincere CW by intentional cycle creation.
>>
>> Under Schulze, RP, River, MinMax, etc. candidate A would likely win
>> because the A faction could confidently bury A under B, creating an
>> insincere defeat cycle with weakest defeat being the 60 percent C over A
>> compared with the 75 percent B over C, and the 65 percent A over B.
>>
>> All of these standard Condorcet methods are built on the assumption that
>> the smallest majority (60% C over A) is the one most likely to be "wrong".
>>
>> So they elect A, unwittingly rewarding the A faction for subverting the
>> sincere CW.
>>
>> But how about Q&D/C?
>>
>> It would elect C because it is a ballot Condorcet method intolerant of
>> the kind of subversion that rewarded the A faction under Schulze, etc.
>> Since the subversion would just backfire, no faction would be dumb enough
>> to try it.
>>
>> Let's look at how it would backfire were the A faction stupid enough to
>> attempt the burial of C under B:
>>
>> The candidate with the lowest basic score would then be C, so B would win
>> as the only candidate pairwise undefeated by C.
>>
>> So A's gambit would just change the winner from its second choice C to
>> its last choice B.
>>
>> Do you think any major faction in Brooklyn would gamble on a sure loss
>> like that?
>>
>> To be clear, what this example shows is that our Quick and Dirty/Clean
>> method has Condorcet efficiency superior to that of Schulze, etc.
>>
>> And why is it more Condorcet efficient? Because it was designed on a
>> realistic game theoretic principle, rather than a statistical error
>> correcting technique designed mainly for filtering out inadvertent
>> "mistakes" in judgment (or minority opinion).
>>
>> This example could be (and has been) multiplied indefinitely with the
>> same pattern of results:
>>
>> Q&D/C is much more Condorcet efficient than Schulze et al in rough
>> neighborhoods, as well as 100 percent efficient in easy neighborhoods (like
>> any and every Condorcet method is).
>>
>> So here's the best advice for Condorcet method design: focus on
>> frustrating cycle creators. Make sure that all attempts at cycle creation
>> backfire automatically. Beyond that accommodate any (possible but
>> vanishingly rare) sincere cycles by making sure the method always elects
>> simply, monotonically, and clone indepently from the ballot Smith set, as
>> does Q&D/C, a method that Pareto dominates all of the old Condorcet methods
>> on these criteria.
>>
>> To put it bluntly, all of those older methods are pretty much passe ...
>> uniformly dominated by Q&D/C when it comes to single winner elections for
>> public office.
>>
>> I'm sorry to talk so bluntly, but subtle words don't seem to register in
>> this context, especially among the self-styled movers and shakers [who
>> probably won't even read them anyway🤔]
>>
>> On a technical note ... to make sure that Q&D/C is ISDA, use a version
>> that immediately restricts to Smith, or at least counts the "basic scores"
>> relative to the Smith Set candidates.
>>
>> Forest
>>
>>
>> El vie., 7 de ene. de 2022 4:38 a. m., Kristofer Munsterhjelm <
>> km_elmet at t-online.de> escribió:
>>
>>> On 07.01.2022 07:05, Forest Simmons wrote:
>>> > Most designers of Condorcet methods asume that the gentlemanly thing to
>>> > do is to give the votes a benefit of a doubt and assume that they must
>>> > have voted sincerely but cycles are a result of errores of judgement.
>>> >
>>> > Because of these assumptions they attempt to filter out the erroneous
>>> > preferences statistically
>>> > .. the main heuristic is that larger majorities are less apt to hold
>>> > erroneous opinions than smaller ones ... hence cycles are broken by
>>> > annulling the defeats with the smallest majorities.
>>>
>>> There is probably a tradeoff between strategic resistance and honest
>>> VSE. The more you want one, the less you get the other, and at the
>>> extremes you completely disregard one or the other.
>>>
>>> So if we could construct methods to spec, the best approach would be to
>>> somehow infer just how much strategy the method needs to resist, and
>>> then maximize VSE in a suitable model (probably spatial) subject to this
>>> constraint.
>>>
>>> But we don't really know how strong the barrier has to be against
>>> strategy. As I've mentioned before, I think it differs based on culture:
>>> IIRC Ireland saw much less vote management under STV than did New York.
>>>
>>> If we only have one shot, it's reasonable to err on the side of strategy
>>> resistance. That's not to say that the honesty-favoring methods don't
>>> have their place, though: Debian seems to do pretty well with Schulze,
>>> for instance.
>>>
>>> As for methods like Plurality and (probably) IRV -- well, they're just
>>> Pareto-dominated. You can find methods with better VSE and the same
>>> level of strategic resistance, or methods that handle strategy better
>>> while providing the same VSE.
>>>
>>> -km
>>>
>>
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