[EM] Ultimate SPE Agenda Processing: Sink Swap Bubble

Forest Simmons forest.simmons21 at gmail.com
Mon Apr 3 00:14:33 PDT 2023


On Sat, Apr 1, 2023, 9:30 AM Kevin Venzke <stepjak at yahoo.fr> wrote:

> Hi Forest,
>
> Le samedi 1 avril 2023 à 10:31:08 UTC−5, Forest Simmons <
> forest.simmons21 at gmail.com> a écrit :
> > Here's an example of another standard test case for Sink Swap Bubble
> ("Bubba" for short).
> >
> > 48 C
> > 28 A>B
> > 24 B (sincere is B>A)
> >
> > The smallest faction has thrown the sincere CW under the bus ... knowing
> that most Condorcet
> > methods, including classical wv methods like Ranked Pairs, would break
> the resulting ABCA
> > beat cycle at the weakest defeat A>B, leaving B as the winner.
>
> > Bubble changes the order to B<A<C ... the finish order of the method ...
> thus disappointing
> > the defecting faction with a finish order polar opposite to their
> sincere preferences ...
> >
> > When will they learn that you cannot mess with Bubba?
>
> I've said this before, but I'm not a fan of this kind of method because,
> what if you're
> wrong about the sincere preferences? Then by electing C, you're actually
> punishing the A>B
> voters for not using compromise strategy. This muddies the water as to
> what behavior
> "chicken resistance" is actually incentivizing.
>

Until we can read minds, we cannot be sure, but some scenarios are more
likely than others.

>
> Can we really be so confident that an unstated preference hides a specific
> meaning?
>
> I also ask what you think of this modified scenario:
>
> 48 C
> 28 B (sincere is B>A)
> 24 A>B
>

I'm not committed to any particular definition of chicken or burial
resistance ... I'm more interested in prevention than cure.

If there is a ballot cycle, prevention has probably failed ... at least in
the three faction case ... it seems much much more likely in that case that
the cycle was created artificially than inadvertently.

Consider the beat cycle XYZX with with X at the top of the agenda and Z at
the bottom. It seems to me (all else being eaual) the two most likely
scenarios are that Z was the sincere CW ... but (1) successfully buried
under Y by the machinations of the A faction counting on a standard wv
method that would make A win. Or ...  that (2) the X faction truncation of
Z created the cycle that gives X the win under RP(winning agenda), SPE, or
DMC.

Our method disappoints the faction X responsible for creating the cycle by
electing Y, the candidate that the burial or truncation insincerely helped
(by raising or by truncating below) to create the cycle subverting the
sincere CW ... namely Z.

The sincerity check will actually elect Z ... but most electorates will
think the check is too costly... so they will have to be content to
disappoint the faction guilty of creating the insincere cycle ... cycle
prevention for future elections.

In that case the winner is from the middle of the Smith set Y ... the same
candidate you would get if it turned out that Z was not the sincere winner.

Better than random ballot Smith in any case ... including better prevention
than random ballot Smith.

Here's the model that convinces me that in the 3 faction case cycles are
almost surely artificial: The 3 village model. Each village runs one
candidate and everybody in the village copies their candidate's preference
ballot ... based on distances between "villages" whetherby geography or
issue space.

Suppose without loss in generality that A and B are teo closest candidates
so that B is A's second choice and A is B's second choice.

If no village has 50%+ of the voters, then C is the sincere Condorcet Loser
... so the larger of the A or B faction is the sincere CW regardless of W's
second choice ... or truncation ... or symmetric completion.

The only unilateral way of creating a cycle is for the second place faction
(the smaller of A or B) to truncate or bury its second choice.  Let's say
...

a A>B
b B
c C

This truncation creates an ABCA cycle.that B would win under most Condorcet
methods.

If the B faction nuries A, then C becomes the ballot CW ... no way they are
going to gry that. For that reason it seems obvious to me that insincere
CW's are the last thing we need to worry about.

Of course, there are all kinds of reasons for ending up with four or more
factions with only 3 candidates ... and a few of these witll even  have
sincere cycles  ... but once you have constructed such  a cycle you realize
it is much much more likely that a cycle in insincere than natural.

So let's make sure our methods do the right thing for the most likely
scenarios before we start worrying too much about "sincere cycles."

It has taken me a long time to come to this way of thinking, and I'm not
set in stone ... but I believe that any positive reinforcement for
insincere cycle creation is very bad ... and adopting wv Condorcet is a
step in that bad direction.

This BUBBA proposal discourages formation of these cycles while being
simple, seamless, monotone, clone free, and ISDA.

Have you seen any other Universal Domain method that can compete on these
counts?


> I guess you'll say that B is allowed to win because B is both the sincere
> and voted CW. But
> that's a different question from what a "chicken-resistant" method
> *should* do, if we
> really believe in this approach.
>
> Kevin
> votingmethods.net
>
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