[EM] Quick and Clean Burial Resistant Smith

[Ted Stern]

[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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