[EM] Ultimate SPE Agenda Processing: Sink Swap Bubble

[Forest Simmons]

On Thu, Apr 6, 2023, 10:00 AM Forest Simmons <forest.simmons21 at gmail.com>
wrote:

> For public proposal ...
>
> 1. Initialize the agenda order according to Implicit Approval ... ties
> resolved by top rank counts.
> 2. Let A be the most favorable candidate after Sink Sorting the sgenda.
> 3. Let C be the Most Favorable Enemy of A.
> 4. Let B be the Most Favorable Enemy of C.
> 5. If B's top count is greater than C's Implicit Approval, resolve the
> doubt beteeen B and C by Candidate Proxy.
> 6. Otherwise elect C.
>
> For the Candidate Proxy Plurality doubt resolution the weight of each
> candidate's vote is the number of ballots on which it was ranked top
> (counted fractionally for equal top).
>
> This candidate proxy device obviates a second trip to the polls by the
> voters.
>

Example:

27 C>A
24 A (Sincere A>C)
49 B

The agenda order from least to most favorable is C<B<A

There is a beat cycle in cyclic order ABCA

The agenda has no pairs in need of pairwise rectification  ... so sink sort
does nothing.

The Most Favorable Enemy of A is indeed C ... (as in the archetypical
story).

The Most Favorable Enemy of C is B.

B's top rank share is 49, which is indeed greater than 27, which is C's
Implicit Approval ... so without some kind of special dispensation
exempting C from the Plurality Criterion, we cannot elect C,  even though
it is secretly known to be the sincere CW ... (by the State of California).

A sincere proxy vote between B and C resolves this issue ... showing that C
is actually preferred over B by a 51 to 49 majority.

In fact, A is one of the candidate proxies, and in this role she is eager
to vote her sincere preference of C over B ... nothing to lose ... much to
gain ... and partial redemption from her initial chicken defection perfidy!

-Forest



So C is elected ... despite the misleading appearance of a Plurality
Criterion violation. The A faction is lucky we went to the trouble of
undoing its truncation defection mischief ... instead of just standing back
to watch C get disqualified in favor of B ... the negative feedback it
deserved!

Perhaps this is the most gentle and expeditious way to warn would be
manipulators ... like little Johnny's mother told his teacher on the first
day of school ..."Johnny is a sensitive child ... if he ever does anything
bad, just hit the little kid next to him ..."

-Forest



> On Wed, Apr 5, 2023, 11:37 PM Forest Simmons <forest.simmons21 at gmail.com>
> wrote:
>
>> Here's a compromise:
>>
>> Let A be the Agenda Uncovering winner.
>>
>> If voters are sincere, A is my best estimate of who should be elected.
>>
>> If A is defeated pairwise, then the votes are probably not sincere.
>>
>> So if A is undefeated, elect A ... Else elect C, the Most Favorable Enemy
>> of A ... the candidate most likely to have been thrown under the bus by the
>> A voters to create an artificial cycle to their advantage.
>>
>> If a sufficient number challenges the outcome, have a manual runoff
>> between A and C.
>>
>> This won't punish A, but it will make the burial futile ... a big waste
>> of time ... putting some friction into the dynamics.
>>
>> -Forest
>>
>> On Wed, Apr 5, 2023, 2:28 AM Kristofer Munsterhjelm <km_elmet at t-online.de>
>> wrote:
>>
>>> On 4/4/23 07:23, Forest Simmons wrote:
>>> >
>>> >
>>> > On Mon, Apr 3, 2023, 2:20 AM Kristofer Munsterhjelm
>>> > <km_elmet at t-online.de <mailto:km_elmet at t-online.de>> wrote:
>>>
>>> >> This is about chicken resistance in general, no? I suspect there's
>>> >> a more general impossibility result hiding here: that methods that
>>> >> are burial resistant and Condorcet (in the way the Smith-IRV
>>> >> hybrids or Friendly is) have to make uncharitable interpretations
>>> >> of ballots that, if they were honest, would imply a very different
>>> >> candidate should be elected. (I have no proof of this, but it seems
>>> >> a reasonable hunch.)
>>> > This is exactly what I have found. Classical Condorcet assumes honest,
>>> > sincere voters with imperfect estimation of the truth ... wv
>>> majorities
>>> > have the best chance of discerning that truth. But, as examples show
>>> ...
>>> > these methods are easily subverted by unscrupulous opportunistic
>>> > sophisticated voyers.... and as you and Kevin have noted, methods that
>>> > punish burial and defection must sacrifice VSE ... until the
>>> > unscrupulous learn it will almost always back fire.  When everybody
>>> > learns that lesson, the sincere CW will be a ballot CW much more
>>> frequently.
>>>
>>> Perhaps there is some kind of pigeonhole argument that could prove it,
>>> but yes, it makes sense. Intuitively there's a Pareto front where, every
>>> type of strategy resistance level, there's an optimal VSE method, and
>>> that this optimum value shrinks the more strategy-resistant the method
>>> is... because a constrained optimum is never *better* than an
>>> unconstrained one. Of course, this informal argument does not show how
>>> "expensive" strategy resistance is, only that we shouldn't be surprised
>>> if there's some cost.
>>>
>>> (Although the general argument could also be used to shown that
>>> cloneproof methods, say, can't be any better VSE-wise than the best VSE
>>> method without a constraint of cloneproofness, in that case it seems
>>> that the price is much lower. Anyway.)
>>>
>>> >> And then the ultimate deluxe method (in one sense) would be
>>> >> something along the lines of:
>>> >>
>>> >> - Conduct an election with "honest" method X and "suspicious method" Y
>>> >> (or putting it differently, "compromise resistant" X and "burial
>>> >> resistant" Y).
>>> >> - If the winners are equal, we're done.
>>> >> - Otherwise do a manual runoff, where the voters' behavior will be
>>> >> honest (majority rule with two candidates is incentive compatible).
>>> >> Elect the winner.
>>> >
>>> >
>>> > That's easier said than done ... definitely needs more explorstion.
>>>
>>> > But hears the subtle difficulty of a combo method:
>>> >
>>> > Suppose C is the sincere CW and A creates a cycle by burial of C under
>>> > the bus B. The honest methods, including wv, SPE, Agenda Uncovering,
>>> > etc. ... all choose A. The burial resistant methods all choose the bus
>>> B.
>>> >
>>> > A sincere runoff between A and B will choose A.
>>> >
>>> > On the other hand, the sincerity checks of Bubba and Agenda Chain
>>> > Climbing will restore C.
>>> >
>>> > But restoring C makes burial less risky for the buriers!
>>>
>>> That's a good point. But we should be careful not to take this too far.
>>> Suppose that we have a set of elections, e_1...e_n, and a subset of
>>> these, call it ebA, where burial is advantageous in method A. Then
>>> suppose ebB is a strict subset of ebA and denotes the elections where
>>> burial is advantageous in method B.
>>>
>>> Then all else equal, we would consider B to be a better method than A,
>>> even though B seems to make burial less risky for buriers.
>>>
>>> What we need to consider is under what elections are there nearby
>>> elections where burying X doesn't make Y win, but makes Z win instead.
>>> That's where burial backfires. Now if these are reduced, then you could
>>> say that it's ambiguous whether the new method is better, because the
>>> rate of burial would increase. But we don't know that this is the case
>>> for the (A vs C) runoff overlay.
>>>
>>> Or putting it differently: random ballot has no risk whatsoever for
>>> burial... but no reward either, so it's okay.
>>>
>>> I agree, it doees make the method much harder to analyze, though.
>>> Perhaps I'll try to find an optimal runoff-based method using my optimal
>>> strategy susceptibility analysis at some point and see what the rate is
>>> :-)
>>>
>>> James Green-Armytage considered a different way to break UD: by having
>>> allies of the honest CW be able to withdraw from the election.
>>> https://jamesgreenarmytage.com/dodgson.pdf I haven't read the paper,
>>> but
>>> from the abstract it seems he's saying that in 1D space, the resulting
>>> method is strategy-proof (!)
>>>
>>> -km
>>>
>>
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