[EM] Ultimate SPE Agenda Processing: Sink Swap Bubble

[Kristofer Munsterhjelm]

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