[EM] More about Approval

[MIKE OSSIPOFF]

Though I prefer MDDA, Approval and RV are the simplest, most modest, most 
easily-implemented votng system reforms.

And Approval (along with strategic RV) has the most interesting voting. All 
sorts of strategies, all sorts of ways of describing the voting choices and 
results. That's one reason why Approval is so popular: It's fascinating, and 
there's a lot more to it, and more merit, than one might at first expect.

Easy implementation, interesting voting.

Yesterday I said that, when all the candidates are obviously desirable or 
undesirable, then obviusly a sincere ballot votes for the desirable ones. 
But, when there's a gradation, then the sincere Approval ballot is one that 
votes for (only) all the above-mean candidates.

Maybe I should say something about why that is.

A sincere Approval ballot is one that votes as much preference strength as 
possible. It maximizes the sum of the strength of the preferences that it 
votes. The algebraic sum, in case it votes contrary to a preference--but of 
course we couldn't very well call it sincere if it did.

Say you like i better than j, and you vote for i, and not for j. The 
preference strength of that pairwise vote is Ui-Uj. Now, say it's given that 
you vote for j, and you decide to also for i. Voting for both i and j, 
you're not voting a  preference between them, so the fact that you're voting 
for i keeps you from voting a preference strength of Uj-Ui, which is 
negative. So voting for i, as before, gives a postive addition to the sum of 
your preference strengths that you vote, by removing the Uj-Ui preference 
vote.

So, whether or not you vote for j, voting for i increases the sum of your 
preference votes by the positive amount Ui-Uj. As I said, that's if you 
prefer i to j.

Of course if you prefer j to i, then the opposite is true, and voting for i 
decreases the sum of your voted preferences by Ui-Uj.

I don't want to delay this posting till I find a proof of this, but I think 
we agree that the mean utility is also the "center of gravity", the 
centroid, of where the candidates are, on the utilitly scale. That is what 
you estimate when you estimate their mean. The most typical  position on the 
utility scale.

The sum of candidate distances above that point equals the sum of candidate 
distances below that point. So, if a candidate is above that point, then the 
sum of candidate distances above him/her is less than the sum of candidate 
distances below him/her.

If you vote for someone above that point, then you're adding more summed 
utility difference (preference strength) below him than above him.

So,  by what I was saying earlier, if you vote for someone above that point, 
you're increasing the sum of your voted preferences.

So, since you want to maximize the sum of your voted preferences, then vote 
for that candidate who is above that centroid point. Vote for all the 
candidates above it, and for none below it, because voting for someone below 
it would lower the sum of your voted preferences.

This has been written at the keyboard instead of pre-written on paper, and 
so I hope it doesn't contain an error, or less-than-best wording.

In Approval, voting for the above-mean candidates is also the zero-info 
strategy. So, with Approval, as with rank-methods, the sincere vote is also 
the zero-info strategic vote.

In RV, a sincere ballot is different from a zero-info strategic ballot, 
since an RV strategic ballot is voted like Approval, with only the most 
extreme ratings. That different sincere ballot lets the election more 
accurately maximize social utility. But of course in RV strategists can take 
advantage of sincere voters. In Approval that can't happen in a 0-info 
election, since a strategic ballot is identical to a sincere ballot.

So Approval would be better than RV when there might be some strategic 
voters.

So might BeatpathWinner (the Schulze version that I recommend for 
organizations and committees). And BeatpathWinner doesn't do badly by social 
utlity (SU), because often the CW maximizes SU. In spatial examples it 
always does so, with city-block distance, and, by the assumptions always 
made in simulations it always does so with Euclidean distance too.

But sometimes there's non-spatial disutility. Maybe a candidate has some 
kind of a scandal that puts off voters throughout the political spectrum. 
For that reason, utility isn't entirely spatial, and it can't be guaranteed 
that the CW always maximizes SU.

So, for completely sincere, non-strategizing electorates, where SU 
maxmization is desired, it's better to use RV. And if you want to maximize 
SU, but there might be some strategy, and it's fairly 0-info, Approval would 
be then be a better choice than RV, because, to the extent that the election 
is 0-info, there's no difference between sincere ballots and strategic 
ballots, so strategizers won't take advantage of sincere voters.

By the way, a few years ago there was discussion on EM in which it was 
argued that, in small committees, the publc-election strategies for Approval 
don't strictly apply. That, for example, the above-mean 0-info strategy 
doesn't strictly apply. But the reason for that was because your own ballot 
changes the probabilities, and because there can by ties with more than two 
candidates. But if it's zero-info, that means that you have no information 
about probabilities. Then it seems that none of that matters, and the 
probabilities can be ignored, because they're the same for all 
candidate-pairs. So, doesn't that mean that the above-mean strategy should 
be optimal in 0-info elections even in small committees?

Forest?

On another subject, fairly recently some of us agreed that Approval will 
quickly home in on the voter median point and stay there. It will stay there 
just as sure as MDDA or Condorcet would. So that suggests that Approval is 
only a little short of MDDA, since it's just that Approval takes one or two 
elections to get to the voter median point, while MDDA will get there 
immediately.

But that depends on the assumption that the progressives will stop voting 
for the Democrat as soon as Nader outpolls the Republican.

(It seems to me that it isn't possible to talk about the poitical 
consequences of these methods, and why their differences should matter to 
you, without talking about specific parties and candidates. And, 
unavoidably, saying it from the point of view of a particular faction. Is 
that off-topic? Or is the interest of a faction inseparable from the merit 
of these methods?)

Can we  count on the progressives to stop voting for the Democrat as soon as 
Nader outpolls the the Republican? Sorry, but if there's anything the 
progressives have taught me, it's "don't count on anything from the 
progressives".

So the ability of progressives to use Approval or RV in their best interest 
is iffy.

I often liken Approval to a solid, reliable handtool. The trouble with a 
handtool is that, compared to an automatic CW-finding machine like MDDA, you 
have to know how to use the handtool, because it's manual, and you have to 
do it yourself.

Judging by 2004 (and previous years), I have to say that I wouldn't want to 
count on the progressives being able to use Approval in their best interest.

The question of MDDA vs Approval (or RV) can be accurately likened to the 
question of driving your child to school vs giving the car-keys to the child 
and saying "Drive yourself to school. Let's find out how you'll do."

That being said, of course we have to settle for what we can get, and it's 
most likely that Approval and RV (especiallyi RV) is what we can get. At 
least they meet FBC. And maybe we can hope that they'll home in on the 
voter-median because the progressives will know how to vote with Approval.

I make the comparison with MDDA just to argue that we'd be much better off 
with MDDA, if we can get it. But I don't know if the chance of an MDDA 
initiative succeeding is great enough to justify trying for MDDA instead of 
RV or Approval.

Mike Ossipoff


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