[EM] Quick and Clean Burial Resistant Smith

[Forest Simmons]

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
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20220107/bade42ec/attachment.html>