[EM] Strategy-free criterion

[Kevin Venzke]

Hi CLC,

Closed Limelike Curves <closed.limelike.curves at gmail.com> a écrit :
>>> This is why I previously suggested that, ideally, a system should satisfy both
>>> zero-info honesty and LNHe+FBC. This seems like the maximally-honest combination
>>> of properties, because it handles low-information elections honestly, and
>>> high-information elections "as sincerely as possible" (i.e. no order-reversal,
>>> which is enough to guarantee the Condorcet winner is visible from the ballots).
> 
>> I am curious what your definition of "visible from the ballots" is. It's possible
>> to generate scenarios where the sincere CW is one of two frontrunners and yet still
>> loses under practically all methods, because they lose necessary support (from
>> truncation) from supporters of the other frontrunner while most of the CW's
>> supporters actually prefer a different candidate to the CW.
> 
> Am I missing something about the CW under approval? I was under the impression that,
> if everyone is following the polls and knows everyone else's voting intentions, the
> majority-preferred candidate will win because people will adjust their approval
> threshold until the CW is the only candidate with >50% approval.

If the polls are accurate I think that theory could work. What I'm saying is that if
two frontrunners are chosen arbitrarily, but one of them is the CW, that isn't a
sufficient condition for the CW to win.

Here's a contrived example, starting with the sincere preferences:
38: Yellow>Blue>Red
37: Red>Blue>Yellow
15: Blue>Red>Yellow
7: Yellow>Red>Blue
2: Red>Yellow>Blue
1: Blue>Yellow>Red

Blue is sincere CW, and Yellow is the best opposition to Blue (barely). With Blue
and Yellow as perceived frontrunners, these ballots are possible (truncating midway
between frontrunners):
45: Yellow
37: Red>Blue
15: Blue>Red
2: Red>Yellow
1: Blue

This returns Red as the voted CW and implicit approval winner.

Since Blue and Red both end up with majority approval, it's possible you will say
that the polls shouldn't have ended up with a Blue/Yellow match-up, but a Blue/Red
one. By my math (here omitted) that would give Blue majority approval and uniquely
so. (Interestingly Blue would not be the voted CW; Yellow would always have
sub-majority wins over the other two.) An odd thing about this outcome is that
Blue/Red look like they are from the same party and the 45% who favor Yellow don't
bullet vote at all. That makes me skeptical that a Blue/Red match-up would actually
happen in such a clean way.

>>> I think the best hope for a system that formally satisfies both criteria is
>>> probably somewhere in the generalized median family of voting methods.
>>
>> That would surprise me, but who knows.
>
> Huh, why would it surprise you?

I assumed you were talking about median rating or something like that.

The outcomes of our election methods can (almost as a rule) be dictated by a
coordinated majority (or a group of more numerous voters) so I expect a "zero-info
honesty" method to have some kind of inherent tether to this reality, as though the
coordination is done for the voters already, behind the scenes.

Kevin
votingmethods.net