[EM] Strategy-free criterion

[Kevin Venzke]

Hi Chris,

I start this reply by introducing MDDA 2. Yes, after 19 years! We just add a rule
at the start:
1. Disqualify all candidates with sub-majority approval if possible.
2. Disqualify all candidates with a majority pairwise defeat if possible.
3. Elect the most approved remaining candidate.

This now matches MAMPO's four properties: FBC, MD, SFC, and Plurality.
Experimentally, my challenge in proving this is that I'm having a hard time
randomly generating any scenarios at all where the two MDDAs differ. But we know
MDDA v1 violates Plurality (even if random scenarios won't produce it for me), and
MDDA v2 pretty clearly doesn't.

(Why not do this before? I guess I thought MAMPO was more elegant, and I could not
foresee that I would have simulations where MDDA outperforms MAMPO.)

On to the reply...

>>  "Does that mean that you find  failure of Mono-add-Plump acceptable?"
>> Compared to Plurality criterion failures, sure.
> 
> No, that is very very weird and wrong.  A failure of Mono-add-Plump is
> completely absurd and outrageous and a failure destroys the credibility
> of the winner, whereas a failure of the Plurality criterion is merely
> very embarrassing and hard to sell.

I'm not sure I follow, that a winner barred by Plurality has more credibility than
a winner who won under the rules but is challenged by a second candidate who
regrets how his supporters filled out their ballots. Candidates who win despite
being barred by Plurality usually seem to have won not due to their own merit.

> Also giving away Plurality can "buy" something sort-of worth having. For
> example MinMax Margins is not an absurd method and has a "maximal set"
> of Woodall properties.  It fails Plurality but meets Condorcet and I
> think Mono-add-Top and Later-no-Harm.

I would've gone with MMPO as the example, but OK. As a Condorcet method,
MinMax(margins) doesn't satisfy LNHarm.

> But I refuse to believe that we need to give up Mono-add-Plump (or
> Mono-append) compliance to get anything remotely worth having.

I don't know whether you're right about that or not. Just because I've gotten
interesting results from MDDA doesn't mean they could only come from MDDA. I have
also seen some impressive performance from DAC in some situations, and I don't know
right now what accounts for that. I usually just say "DAC is like Bucklin" but this
is seemingly not quite right.

> (And if I'm wrong about that I wouldn't accept the bargain.)

That's fine, if many people feel that way then that will be decisive. I feel there
are a number of criteria like this that are "absurd to fail" according to the
intuition of some number of people. To me it's not very interesting because it
doesn't lead to a clear metric that could be tested. I wouldn't want to say a
method is "good" just because no one can call it absurd.

>> Something I will have to post about at some point is what a
>> game-changer it is if we
>> take it as an assumption that elections will have two frontrunners and
>> all voters
>> use frontrunner truncation strategy. Arbitrary-looking majority rules
>> prove very
>> useful in maximizing performance.
>>
>> In such a setting I find that MAMPO is usually not as good as MDDA or
>> RMPA, but all
>> of them outperform all Condorcet methods at sincere Condorcet efficiency.
> 
> A near-universal assumption among Condorcetists is that if (assuming the
> voters are free to rank enough candidates) there is a voted CW then that
> must be the sincere CW and everything is perfect.

Sure, if that's all you have, that's all you can do. The only way you can arrive at
a suspicion that other methods could outperform Condorcet at sincere Condorcet is
with a model that started with sincere preferences (somehow generated) and
translated them (somehow) into voted preferences.

> You imply that your aim is to elect the "sincere CW" (if there is one). 
> I think we should be trying to elect a candidate with no lower Social
> Utility than the highest SU voted Smith set member.

Sincere CW and SU as goals are tricky to disentangle I think. You can mess around
with the voter distribution and force methods to behave differently wrt SU, but I
don't have an intuition yet about the nature of the change in some methods'
performance. In 2D spatial simulations I find that there is usually a sincere CW,
incidentally.

My thought on your goal is that if we say that we know the SU (due to some model of
behavior that we're using to test scenarios), why wouldn't we just prioritize that?
The makeup of the voted Smith set would just be an artifact of strategy. But maybe
you would say that electing outside Smith would look unacceptable. Fair enough.

> The person who coined SFC (and supports MD) also coined the Chicken
> Dilemma criterion, which is directly incompatible with MD.
> 
> https://electowiki.org/wiki/Chicken_dilemma
> 
> I am in sympathy with both criteria so one of my standards is that a
> rankings-only method must meet one or the other.

I don't like the CD criterion because of the three incentives it creates, only one
of them is positive. And even if that were not true, it seems rash to resolve
elections according to the speculation that any pairwise majority over the first
preference winner "ought" to have been accompanied by a mutual majority.

Kevin
votingmethods.net