RE : Re: When and how can we speak of "individual utility" and "social utility"?

--- Abd ul-Rahman Lomax <abd <at> lomaxdesign.com> a écrit :
> While it is already true that Range and Approval *do* 
> satisfy that Criterion, in my opinion, on the argument that the 
> majority has consented to a different outcome,

"Majority criterion" has a specific meaning. It in effect says that a
majority can elect their first preference without concealing lower
preferences. You can hardly say that Range satisfies MF on the argument
that a majority could have concealed their lower preferences. That
would be like saying a product is free of charge to you because you can
choose not to buy it.

Kevin Venzke

	

	
		
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Re: When and how can we speak of "individual utility" and "social utility"?

Lomax says:

>But we should not let this distract us from the fact that utility
>analysis is really the *only* approach to judging how well election
>methods perform, it is not like we have other methods competing with it.
>
>Election criteria might be considered such methods, but they are
>clearly indirect. Even the most basic of them, such as the Majority
>Criterion as usually defined, is clearly flawed in that we can easily
>propose election scenarios, and not rare ones but common ones, where
>it requires results that by any reasonable definition of election
>success are defective.

I comment:

Those are incredibly ignorant statements.

The fact that two criteria are incompatible doesn't mean that one of them 
requires defective results. And the fact that majority rule is incompatible 
with maximizing summed utility when everyone (hypothetically) votes 
sincerely doesn't mean that criteria relating to majority rule require a 
defective result.

Of course, even with Cardinal Ratings (CR), the pizza majority can easily 
get its way. Likewise in political elections.

Lomax, for the little-caring majority to outvote the strongly-caring 
minority is not a defective result, except, typically, to people who are new 
to the subject.

Approaches to proposing Approval

I was saying before that the worst thing you can do is introduce people to 
Approval by telling them that they can vote for as many candidates as they 
want to. That’s perceived as illegal Plurality and as a violation of our 
right to 1-person-1-vote (1p1v).

But how about this:

Start by describing the -1,1 point rating method. Or, of course, if the 
person has already heard about Approval balloting and expressed opposition 
to it,  then propose -1,1 to that person.

Point out that a -1 rating is every bit as powerful as a +1 rating, because 
obviously  your -1 rating for a particular candidate will exactly cancel out 
one other voter’s +1 rating for that candidate.

So, if there are 10 candidates, and I give +1 to six candidates, and -1 to 
four candidates; and if you give +1 to one candidate, and -1 to nine 
candidates, you’re not having any less voting power than I do.

Then point out that, without changing the winner, the counting work could be 
halved by only counting the +1 ratings. And that the voting work could be 
halved by only voting the +1 ratings. So why not just ask voters to mark as 
many candidates as they want to,  with the meaning that the voter is giving 
+1 to each candidate s/he marks, and -1 to every candidate s/he doesn’t 
mark.

That should introduce someone to Approval without the “unequal voting power” 
misunderstanding, and should answer the person who opposed Approval by 
claiming unequal voting power.

Set-Voting

I’m not saying that you didn’t already know this:

Approval can be regarded as a generalization of 1-vote Plurality as follows: 
Plurality lets you vote a set of one candidate better than the candidates 
not in that set. Approval generalizes that by letting you vote any set 
better than the candidates not in that set.  For any two mutually exclusive 
sets, you can vote one over the other.

That may be the best description of what Approval is, but would it be a good 
way to introduce Approval to people?

Mike Ossipoff

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Plurality has 4 times the inequality of voting power

I’ve told why Approval doesn’t give more voting power to people who mark 
more candidates.

But what if we define a “voting power” that can vary between voters? What 
quantity would make sense as that voting power? How about the voter’s 
opportunity to increase his/her expectation in the election?

Say we don’t know which two candidates will be the frontrunners. If there’s 
a 2-way tie, we don’t know which two candidates the tie will be between.

And say, for simplicity, the candidates’ merit, or “utility” for the voters 
is only two-valued. The voters’ sincere personal ratings of the candidates 
have only two levels or values.

So the amount by which you can increase your expectation can be measured by 
the number of pairs of candidates of unequal merit that you’re voting 
between, by voting for the better one and not for the worse one.

By what factor can two voters’ expectation-increasing opportunity differ?

In Plurality:

The most fortunate voter  rates one candidate 1 and all the rest 0. S/he is 
voting between N-1 meaningful pairs when s/he votes for that one.

The least fortunate voter rates  one candidate 0 and all the rest 1. S/he 
can vote between only 1 meaningful pair.

So, with Plurality, the maximum ratio between voters’ voting power is N-1

typo

I said:

The least fortunate voter either rates 1 candidate 1 and N-1 candidates 0, 
or rates N candidates 1 and rates N-1 candidatres 0.

I meant to say:

The least fortunate voter either rates 1 candidate 1 and N-1 candidates 0, 
or rates N-1 candidates 1 and rates 1 candidate 0.

Mike Ossipoff

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Ehiquette

There is value to discussing conflicting ideas while avoiding 
personally negative rhetoric.  Doing so improves the quality of the
discussion for everyone.

I only mention this on the chance it might make a difference.  I'm
not particularly wanting formal procedures for filtering by the
group.  I'm able to do my own filtering well enough.  But it's better
if more of the filtering were done by and at the source.

-- David Cary

 
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Re: UncAAO

Dear Forest,

you proposed UncAAO:
> UncAAO stands for Uncovered, Approval, Approval Opposition.  Here's
> how it works:
>
> For each candidate X,
>
> if X is uncovered,
>
> then let f(X)=X,
>
> else let f(X) be the candidate against which X has the least approval
> opposition, among those candidates that cover X.
>
> Start with the approval winner A and apply the function f repeatedly
> until the output equals the input.  This "fixed point" of f is the
> method winner.
>
> ["Approval opposition" of X against Y is the number of ballots on
> which X but not Y is approved.]

It would be interesting to compare this to other monotonic and 
clone-free methods that always pick the winner from the uncovered 
options.

For example "total approval chain climbing" (TACC), a method I proposed 
a long time ago: Construct a chain of options by starting with an empty 
chain, then processing the options in order of ascending approval 
score, and adding the option at hand to the chain iff that option 

Re: When and how can we speak of "individual utility" and "social utility"?

At 05:28 PM 2/28/2007, Michael Poole wrote:

>I suggest you re-read what I wrote.  This rambling has nothing to do
>with what I wrote.

I'm glad. Which is not at all an incentive to reread what Mr. Poole 
wrote.... I did not intend what I wrote to be a commentary on his 
writing, but simply to be what occurred to me in a context which was 
developed out of what he wrote.... and enough on this irrelevancy. 
One matter to confront:
[...]

{I had written:)
> > Now, if a process includes a top-two runoff, and the top two are the
> > Range winner and the Condorcet winner, where they differ, does the
> > method satisfy the Majority Criterion? I'd claim that it does, quite
> > clearly. While it is already true that Range and Approval *do* satisfy
> > that Criterion [....]
>
>They do not satisfy that criterion.
>
>   1 person votes A=99, B=0
>   2 people vote A=50, B=60
>
>The Majority Criterion demands the election of B.  Range elects A.

There is a top-two runoff, after this Range election. The top-two 
runoff is a simple election, the ballot says "vote for one," and the 
candidates are A and B. Who will be the victor in this election?

Re: RE : Re: When and how can we speak of "individual utility" and "social utility"?

At 07:11 PM 2/28/2007, Kevin Venzke wrote:
>--- Abd ul-Rahman Lomax <abd <at> lomaxdesign.com> a écrit :
> > While it is already true that Range and Approval *do*
> > satisfy that Criterion, in my opinion, on the argument that the
> > majority has consented to a different outcome,
>
>"Majority criterion" has a specific meaning. It in effect says that a
>majority can elect their first preference without concealing lower
>preferences. You can hardly say that Range satisfies MF on the argument
>that a majority could have concealed their lower preferences. That
>would be like saying a product is free of charge to you because you can
>choose not to buy it.

Yes. It has a clear meaning. I'm suggesting, 
however, that the Majority Criterion is based on 
an deeper criterion, which is Majority Rule.

This phrase has been ripped from context, which 
actually weakened the apparent claim by 
acknowledging precisely what Mr. Venzke points 
out, that there is a degree of constraint imposed 
on the "consent" involved. And this phrase came 
only as an aside to the central point, which was 
that the Majority Criterion is fully satisfied by 
a Range election in which a top-two runoff is 
held between the Range winner and the Condorcet winner, if they differ.

(I have not at all examined the question of how 
to handle Condorcet cycles, but the essence of 
the idea, with relation to the Majority