[EM] Comment on MJ discussion

[Jameson Quinn]

> Exactly. Your letter-grades encourage sub-optimal voting.
>

"Zero-info" optimal strategy is to vote on an absolute scale such that for
recent elections you would have given equal numbers of each grade A-D and
twice that number of Fs. (Or slightly more sophisticated: give the same
score distribution as the electorate as a whole in recent elections). This
is encouraged by the grade scale, in fact more so than the equivalent
zero-info optimal strategy for Range (which is scaled Von
Neumann-Morgenstern utilities, something that behavioral experiments show
people are pretty bad at giving in any self-consistent manner). So for the
zero-info case, letter grades encourage optimal voting.

Also, as you move away from the zero-info case, this "honest" strategy
remains optimal for longer than with Range or Approval (by a factor of
1.5-2, depending on whether the independent variable is knowledge or
ignorance). And even in the case where you have full knowledge of every
other vote, the expected incentive to abandon this strategy and vote
approval-style is less than it is with Range.

So the idea that letter grades are "encouraging suboptimal voting" is not
entirely false, but on the other hand, it's really only true for
unrealistically-tight definitions of both "sub-" (incentive) and "-optimal"
(information).


>
> Kristofer continued:
>
>
>  That is, if the voter is faced with the
> question of assigning each candidate a grade, and the grades are well
> defined (each person knows what a B means), then the voters will grade
> according to that common standard. This means that MJ passes IIA: since
> the grades are common, a candidate dropping out doesn't change the
> grades of the other candidates.
>
> In contrast, Balinski & Laraki has experimental evidence that suggests
> that when the ballot is a yes/no (Approval style), voters are much more
> likely to act in a comparative manner - which is to say that they
> compare the candidates to each other, rather than comparing every
> candidate to a common standard. When they do that, B&L says, Arrow's
> impossibility theorem creeps back into the picture and you lose IIA
> compliance.
>
> [endquote]
>
> So B&L have discovered that Approval fails IIAC? :-)
>
> Here's the brief, simple, precise and clear IIAC definition that i've
> heard:
>
> Removing a losing candidate from the ballots and from the election,
> and then re-counting the ballots, shouldn't change the winner.
>
> Approval and Score pass.
>
> [end of IIAC definition]
>
> It sounds as if you, and B&L, must be using a more complicated and
> wordier definition of IIAC.
>

No. It's fewer words:

 Removing a losing candidate from the election shouldn't have changed the
winner.

It's no longer mathematically precise, because it introduces a human
behavioral factor and a contrafactual. That doesn't make it meaningless or
impossible to empirically measure, though. For instance, you could (in
theory) randomly assign half of the voters to vote on ballots with or
without a given candidate, and see if the results differ.


> Would you like to post it here? Don't forget to post it complete and
> precise.
>
> > If a voter grades a candidate as 'B' rather than 'A', the voter has
> > detected some flaw in the candidate and is expressing it in the grade.
> > To treat that voter's vote as simply above or below the median is to
> > debase it. Why should the voter take the trouble to assign a grade if
> > it's only use is to place the vote in the higher or lower half of the
> > votes cast?
>
> Kristofer said:
>
> There are three reasons for this.
>
> The first, let's call it "flexibility of meaning". Taking the median
> means that the system doesn't impose any particular meaning of the
> grades. It doesn't matter to the method *how much better* an A is than a
> B, because it'll still work. Thus, the method doesn't require the voter
> to rate the candidate. He can simply choose from the grades.
>
> [endquote]
>
> If you rate a candidate non-extremely, then you won't know whether
> you're pulling hir up or down.
>
> You might very well not be having any effect on the relative final
> scores of a particular candidate-pair. Or you might be affecting their
> relative standing oppositely to your voted preferences.
> And, as I said, you might be helping someone you've rated lower
> against someone you've rated higher. A ballot that rates Favorite at
> top, and Compromise somewhat lower, could change the winner from
> Favorite to Compromise. That sort of thing won't happen with Approval
> and Score.
>

With MJ, as with Approval and Score, it may happen that after the election,
you wish that you had voted otherwise. Gibbard proved that this can happen
with any non-dictatorial electoral system, so that's no surprise. Yet your
expected regret is actually LOWER with an "honest" MJ vote than with any
given zero-information Approval or Score vote. So as far as I can see, the
complaints about the formal valence of your vote within the mechanics of
the election system, are just words.

Kristofer said;
>
> The second is strategy resistance. By taking the median, anybody voting
> higher than the median will accomplish exactly the same thing by voting
> highest possible, and anybody voting lower than the median will
> accomplish exactly the same thing by voting lowest possible.
>
> [endquote]
>
> Meaningless, because the voter doesn't know where the median is.
>

With experience and a modicum of polling, voters will be able to have high
confidence that the top two medians will fall in certain ranges.
Distinctions outside the intersection of these ranges will be safely
expressive. That is, you can safely draw a distinction between your
favorite at A and your favored frontrunner at B, or your nightmare at F and
your disfavored frontrunner at D, if you wish to.


> Kristofer continued:
>
> So in that
> sense, there's no reason to vote bottom or top
>
> [endquote]
>
> Nonsense. The only way to reliably help a candidate is to vote hir at
> top. The only reliable way to help your preferred candidates against
> less preferred candidates is to rate the preferred at top, and the
> less preferred at bottom.


> Kristofer said:
>
>
> ; and if honesty is the
> default position, it will take very many voters indeed to make strategy
> actually have an effect, compared to rated-ballot systems.
>
> [endquote]
>
> Kristofer wants to make a virtue of unresponsiveness.
>
> If people are rating X above where X's median previously would have
> been, then it doesn't matter how high they rate hir. That's  what
> Kristofer is touting.
>
> He's forgetting that the voter doesn't know where X's median is.
>
> The MJ-advocates' main belief and argument is that MJ discourages
> optimal voting, because sub-optimal voting might or might not achieve
> the same result.
>
> ...might or might not have any effect at all, regarding a
> pair-comparison that's important to you.
>
>
> Kristofer continued:
>
> A
> strategizing voter might still get some probability of a better outcome
> by voting top on some candidates and bottom on others
>
> [endquote]
>
> That's called optimal voting.
>
> Kristofer continued:
>
> , or by voting a
> particular way if he knows what the median is, but these qualifying
> "ifs" would keep most ordinary voters from doing that.
>
> [endquote]
>
> Excuse me, but there was no "if" in your earlier statement, about
> optimal extreme voting.
>
> Kristofer is getting it backwards. If you rate X at top and Y at
> bottom, you're reliably fully helping X against Y. There' s no "if" or
> "maybe".
>

The set of optimal votes always includes an extreme vote, so in this sense
you're right here.


> If you do otherwise, that's where you get "maybe".


The set of optimal votes always includes a large number of votes which are
not extreme. If you consider that votes have an expressive as well as an
instrumental purpose, then in fact the extreme vote is essentially never
the truly "optimal" one.

You will argue that since before the election is over you never know which
votes will be optimal, aside from the extreme ones, that only the extreme
ones are truly optimal. This is wrong in two ways. First off, before the
election is over you never know for certain which of the extreme votes will
be optimal. Secondly, the median is a very statistically-robust measure, so
if the bulk of voters behave in any minimally-predictable fashion, you can
set confident outer bounds on the winning and second-place medians, and
still "optimally" draw expressive distinctions outside those bounds.


>
> We live in a technological society. Among some people, there's a
> tendency to worship science. Anything that;s more complex is felt to
> likely be better. That's MJ's mystique.
>

Bullshit. And not a productive line of argument, even if it were true. Stop
it.


> It's just complicated enough that it's easy to obfuscate (for oneself)
> what's going on, and whether it's an improvement. Given the need to
> worship technology, and the consequent love for complexity, it's easy
> to be tempted to deceive oneself that MJ must be doing something
> good--even if one can't say what it is.
>
> So I suggest: If you can't clearly articulate how MJ brings
> improvement, and if you can't answer my criticisms of it, then maybe
> you could reconsider your beliefs about it.
>

If you can't move outside your own framework enough to give a better
account than the above of why my arguments appeal to me, then your
counterarguments have little chance of being convincing. I certainly try to
understand the internal validity of your arguments, and I think I often
succeed. If you read even just this one email, you'll see several cases
above where I grant the logic of what you're saying, and then say why I
don't think it means what you think it does.

Third, the median satisfies majority by grade. If a majority says X has
> grade B, and B is the highest grade used, then X wins. This is a
> protection against "crankiness", as someone (I don't remember his name)
> proposing median voting for budget calculation problems said. If you use
> the mean, then someone who is very loud will get his say
> disproportionate to his number. Range voting advocates say this is an
> advantage, but in a political system, if a majority gets overruled, it
> could easily try to regain its "right" by less peaceful means.
>
> Thus, if
> point #2 is about resistance to deliberate strategy, this is about
> resistance to outliers otherwise.
>
> [endquote]
>
> This time, then, Kristofer is assuming sincere voting. But why should
> anyone rate "sincerely" (utility-proportional)? Why, when it isn't in
> their best interest.
>
> MJ advocates seem to have a _moral_ belief about sincerity. They
> believe that it's somehow wrong, or dishonest, to vote optimally, in
> one's best interest.
>

You keep repeating that we believe this, even though I've clearly stated
before that I don't. There's nothing individually immoral about voting
strategically. The reason that you want a voting system which doesn't
excessively encourage strategy is that a greater proportion of "honest"
(non-extreme) votes enables a socially-better outcome on average.


>
> Hence the MJ-ist's desire to discourage optimal voting. Of course you
> won't discourage it, even if you try.


Unsubstantiated assumption.


> As I suggested above, the fact
> that sub-optimal voting might or might not give the same result hardly
> discourages optimal voting.
>
> And MJ-ists haven't justified their moral stand about "sincere
> voting". Why (in their mind) is it important to discourage optimal
> voting, and try to make people vote utility-proportional?
>

It's not about discouraging strategy, it's about not encouraging it
excessively. As for why, see the simple statement above.

Jameson
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