[EM] Kristofer: MJ & RV

[Kristofer Munsterhjelm]

On 02/07/2012 11:16 PM, MIKE OSSIPOFF wrote:
> Kristofer:
>
> You say that MJ and RV are the methods to propose because they're the
> ones that meet the two criteria you defined.
>
> Have you demonstrated that they're the only ones?

No, I didn't say that, and no, I haven't demonstrated they're the only 
ones. In fact, it's easy to invent another method that satisfies the 
properties.

Consider a method I'll call "maximum minimum rating", which simply 
elects the candidate whose minimum rating is the greatest. It breaks 
ties by looking at the next-to-minimum rating, and so on.

This method satisfies both of the properties. I would actually go 
further and say that every method that consists of electing the 
candidate who maximizes some f(x), where x for a candidate consists of 
the ratings for the given candidate alone, and where f(x) is monotone 
(i.e. increasing some rating in x can't decrease the value of f(x)), 
satisfies the properties. If I'm right, any such method also has 
Approval-style voting as its maximum strategic vote.

(The converse is not true, I think.)

As for what I meant, let me clarify.

I didn't say that MJ and RV are the only methods to propose because they 
are the only methods to meet the criteria I mentioned. I said that if 
you want those criteria, and it's reasonable that you do for a rated 
method, then you can't have a method that actually punishes 
Approval-style strategy. Thus, the best you can do is to not be affected 
by that strategy until enough people use it -- and that's what MJ does.

Now, if you prefer trading off these properties (which imply a quite 
strong rated variant of the FBC in aggregate) so you can make a stronger 
guarantee that other forms of strategy doesn't pay, then that's okay. 
You just can't both have your cake and eat it.

> What about Approval? It's simpler. Simpler to define, implement and
> vote. And supplementable by the conditionality options that I've
> described, to get rid of the co-operation/defection problem.

If I'm to use ratings, I would prefer something that doesn't require 
that I fit my ballot to the polls. To do the frontrunner plus strategy 
in Approval, you have to know who the frontrunners are, and that data 
itself might be inaccurate due to strategy.

In a sense, Approval solves the strategy problem by simply making 
strategy part of its usual working. It's a bit like (though not nearly 
as bad as) a method that satisfies LNH by simply not looking at the 
later ranks. By consistently acting like the worst came to pass, you get 
rid of any temptation to *go* to that worst case, because you're already 
there.

Aren't your conditional methods ranked methods rather than rated ones? 
The criteria I mentioned aren't applicable to ranked methods because 
ranked methods can't pass IIA - and ranked methods make much fewer 
assumptions about utility than rated ones do.

Don't get me wrong. I would greatly prefer Approval to Plurality. I 
would also prefer Approval to a certain much more complex non-summable 
ranked method. I would, however, prefer MJ to Approval. As for Approval 
vs Range... I'd have to think quite a bit. On the one hand, Range 
permits greater expression than Approval, but on the other, everybody 
can see the approval strategy in Range and so that may act to discredit it.

> Your reply regarding MJ seemed basically to be saying that maybe you
> won't regret voting sincerely in MJ. That's great if you like "maybe".
>
> When you say that some will rate sincerely, you're moving the topic to
> psychology. And I like the way you guys like to theorize about how people
> would vote, while declining to find out what voting is like in the
> various proposed methods, via a poll.

We have the Laraki & Balinski MJ poll. The voters didn't strategize 
there, though you could of course say that's because they didn't see the 
implications of the system yet. To take that into account, you'd have to 
poll the same people many times -- enough that they may sit down and 
think "you know what, if I do this, I can only benefit...". I'm not sure 
how you would do that. Perhaps Quinn can do it in his Turk polls.

> But maybe you're right. Maybe in MJ some would rate sincerely and some
> would, instead, voting in their best interest.
>
> Whether that is good or bad depends on whether the suckers are your
> co-factionalists or mine.

In MJ, defectors have no effect unless there are enough of them or 
they're lucky, since the median is a robust estimator and 
Approval-strategy basically involves adding outliers to influence the 
estimator.

Thus, it is "good or bad" depending on whether the "suckers" are in 
enough of a minority. If not, very little happens. The strategizers as a 
group only have an effect if they can add enough votes at either the top 
or bottom to move the median (after tiebreaks) by at least one rating.

And so we're back to where we started. If people strategize "just to be 
sure", even if they don't see the effects of that strategy, then 
strategy reinforces itself and you're right. If not, then strategy 
doesn't matter, because it can't grow popular enough. In the former 
case, you could go to Approval to even the field. In the latter, if you 
use MJ instead of Approval, you save the majority from having to do the 
sort of "who's the frontrunner" effort that you should do in Approval, 
and you also have better information from which to infer the winner.