On 05/15/2012 10:11 AM, Michael Ossipoff wrote:
Or dither if you want to, but don't blame it on the voting system.
I think you have misunderstood some key concepts I have been using. Let
me try to make them more clear.
When I talked about "dithering", I did not mean it in the sense of
"hesitating, worrying, being uncertain" (although there can be elements
of that in Approval strategy). I was instead making an analogy, which I
think was quite appropriate, to the "dithering" of the graphics world.
This is why I also referred to grayscale and black-and-white.
As applied to graphics, dithering is a process where you reduce the
number of shades (or colors) in a picture, and emulate the presence of
more shades (or colors) by placing dots of the colors you do have
available in the proportion required. This is a process that, like
deciding upon how to vote in Approval, makes use of global information
to make a local decision - in the graphics case, whether the pixel at
any particular coordinate should be white or black. See
https://en.wikipedia.org/wiki/Floyd-Steinberg_dithering for an example.
My point about the dithering analogy is that the method imposes a
constraint and then the software/voters have to calculate how to make a
good approximation within the constraint. When I say "I'd rather not
have to do that", I mean that I would like to just submit my full
information - the "whole picture" - rather than having to deal with how
to render or dither it into a format compatible with the constraints of
the method.
Furthermore, since the analogy shows that one's moving quite a bit from
the "front end" (the actual voting method) into the "back end" (which
may involve polls), it seems that if one's very concerned with strategy,
as you are, one should also consider strategy in the back-end. For
instance, if I'm a Bush voter in a three-way race, I might report that
I'm voting Nader alone. This will make it seem that Nader has sufficient
support to win, so the Nader-voters vote for Nader alone. But they've
been had, because now Gore lacks the Nader+Gore votes to get past Bush,
and Bush wins. Of course I would have to turn a significant fraction of
the Bush voters in this direction, but your Condorcet examples also
require the coordination of a significant fraction of the voters for a
strategic end. (And if you say that the Nader voters would be more
cautious when they see Bush's support, then Approval+back-end doesn't
really pass IIA, does it? Nor is the strategy as easy as frontrunner
plus anymore.)
The above could be formalized by making a DSV version of Approval. If
that DSV method is ranked, then one of two things will happen: Either it
fails criteria like FBC or monotonicity, which means that
Approval+back-end might not be as good as you think, or it doesn't,
which means DSV Approval would be a good ranked method on its own. If
Approval is good even when people play the strategic game, why not have
the method itself play the game for them?
Okay. The second concept I think you misunderstood was "half-empty" vs
"half-full" and "noise". I'll first explain the first distinction, and
then the second.
I'll use another analogy here for Condorcet vs Approval. Approval is
like an analog TV signal. If you add uncertainty, it degrades a little.
Add more noise, and it degrades more until, if the voters have
absolutely no idea what they're doing and vote randomly, you have snow.
On the other hand, Condorcet is like a digital signal. You keep adding
uncertainty (or strategy) and nothing happens until a break point, then
it starts to get weird, and a little more will get it past the point and
everything goes black.
Range is like Approval in this respect, and MJ is like Condorcet*. When
I refer to your "half-empty" view, I refer to that you seem to think
that voters (alone, i.e. not coordinated by party central) will add
strategy into Condorcet even when they're on the side of the break point
where nothing happens -- because they fear that if they don't, then when
it is driven to the other side and gets seriously weird, the weirdness
will favor the other side**. Similarly, in MJ, you think that it'll
reduce to Approval because the voters will think that, even though
voting strategically probably won't make a difference, the method might
be pushed over to the other side and then they need all the help they
can get.
Plurality is not all that good on the right side of the break point and
in any event breaks very easily, so people strategize there. But I think
that in sufficiently robust methods (like Condorcet or MJ), it's not
going to happen; or if it does because of voter irrationality, the
voters can be taught through feedback that they don't need to assume the
worst. The benefit, am I right, is that when the voters generally stay
on the right side of the break point, they can enjoy the expressivity of
Condorcet and not have to think about dithering (quantizing) their ballots.
So if strategy isn't what I concern myself about, then what is? It is
the idea that voters, through incomplete information, get a bad result
-- and that's "noise".
I'll give an example first of all. Say you have a three-way 1D election
with the Greens to the left, Democrats to the right, and Republicans a
little further to the right. The median voter is somewhat to the left of
the midpoint between the Greens and the Democrats. Then, for each voter
in an Approval election, there is some probability that he gets the
"Nader only or Nader+Gore" decision wrong. Say that he "gets it wrong"
if he votes differently than he would after n-> inf iterations of
complete information of others' votes in the last round (i.e. the
equilibrium which would probably consist of voting Nader alone).
Then if enough people get it wrong, the winner will be Gore instead of
Nader, and since each voter has some probability of getting it wrong,
then there is also some probability of enough people getting it wrong to
swing the election to Gore rather than Nader. If the election is
three-way and close, that probability could be significant***; and if it
swings the wrong way, then I think the voters who voted the wrong way
would get very annoyed. At least I would. I would go "so this method
burdens me with a quantization decision and if I happen to decide
wrongly, possibly through no fault of my own, it punishes me? Is this a
joke?". Enough voters feel like this, and there would be a backlash.
Approval would in that respect then be like IRV: appearing sensible when
you have two + minor parties, but in a three-way race, the problems surface.
In contrast, in Condorcet the voters just rank. Black's theorem handles
the rest, and I really doubt the voters would truncate in great enough
numbers when the only real contestants are Bush, Gore, and Nader.
Because of the robust nature of Condorcet (the "digital signal" analogy
way near the start), even when people make mistakes about whether they
prefer Gore to Nader or vice versa, the method generally arrives at the
reight outcome.
You could even be more rigorous by considering methods to be
maximum-likelihood estimators in the presence of noise. If the noise is
of the form that "people get X vs Y wrong with fixed probability", then
Kemeny is the MLE, for instance - the one most likely to get at what the
voters had intended if their expression wasn't noisy.
--
* The comparison is more apt than one would think at first glance,
because there is a relation between average and Borda on one hand and
median and Condorcet on the other. See
http://lists.electorama.com/pipermail/election-methods-electorama.com/2011-January/026999.html
for more information.
** You seem to be more inclined to look at ballots in a strategic manner
in general, I think. For instance, when you said that you would only use
a few ranks in (some Bucklin variant I don't remember), that struck me
as quite strange. Are not ranked ballots expressions of preferences? No
- not if they're primarily *strategic*. My initial puzzlement was at how
you directly jumped to the instrumental point of view. Of course, I
could be wrong in my inference because I don't know with absolute
certainty how you really think (as you don't with me). We only have what
we write to go on.
*** This could be tested through simulations.
----
Election-Methods mailing list - see http://electorama.com/em for list info
