[Election-Methods] Two replies

[Abd ul-Rahman Lomax]

At 12:09 PM 8/12/2007, Juho wrote:
>On Aug 12, 2007, at 18:07 , Abd ul-Rahman Lomax wrote:
>
> > Yet he thinks he can judge whether or not a particular vote is
> > "strategic" by looking only at the vote.
>
>No intention to do that. I gave the voter opinions as well as actual
>votes cast as part of the example definition.

Juho *explicitly* said that he didn't need to know the actual 
utilities, he just needed to look at the votes. He *defines* 
"strategic voting" as "using extreme ratings only."

He is far short of precise in this, however. What if a voter uses 
only extreme ratings for the frontrunners and intermediate ratings 
for all other candidates, those considered by the voter to have no 
chance of winning.

*That voters can do this is one of the features of Range, it provides 
for what Warren calls the "incubator effect," where third parties can 
start to show their true strength -- or lack of it -- in real elections.

We *expect* the large majority of voters to use "Approval-style" 
voting for the major candidates; how they deal with other candidates 
depends on how they value them.

Juho is ignoring my basic objection to what he did: he used the 
supposed "voter opinions" to judge who was the "best" winner, but 
then the votes of a subset of voters were votes that would not, in an 
ordinary election, be how such voters would express their opinion, in 
a context where most voters were expressing so-called "sincere 
ratings" that are truly weak votes (every other voter in this 
election voted 30% of a vote, something that would *never* happen 
unless it was friends choosing a pizza. And if this was friends 
choosing a pizza, the winner is *obviously* the best. It only looks 
otherwise because of the allegation that the R2 voter ratings were 
"sincere." But R2 voted as if R2 had a strong preference. Quite 
strong, maximal.

And R2 voted in a way which in most elections would *probably* cause 
a loss for R2. In other words, the R2 vote only makes sense under the 
following conditions:

(1) R2 knows how the others will vote, sufficiently to know that 
voting full strength for R2 over D and R1 will cause R2 to win, not D.

(2) The others are going to vote, essentially, that they don't care.

Now, suppose you are out with your friends, and you are choosing a 
pizza. They all say what they prefer, but they add, "any of these are 
actually find with me, I'll enjoy them." You are the last to speak. 
You prefer R2. What do you say?

There really is no way to predict from the "sincere utilities" given. 
It may also depend on history. Suppose that in the past, R2 had 
always gotten the short end of the stick, never got his favorite. The 
others have just said that it's okay for him to ask for his favorite. 
So he does.

What is the problem with this?

Juho would learn a great deal if he would analyze with care his own 
opinions, try to express them *rigorously*, instead of just using 
vague phrases that are not clearly defined.

Range provides greater weight for greater preference strength. What 
*exactly* is wrong with this, allegedly. Any method which takes into 
account preference strength is going to fail the Majority Criterion, 
unless you arrange for the majority to explicitly consent.

I think that the majority *would* explicitly consent, most likely, in 
the subject election, so what is wrong with the outcome. If I'm 
wrong, then the preference strengths that the D and R1 voters voted 
were distorted.

>(I just spent some time in another mail stream on this list trying to
>promote the idea that one needs to clearly state the voter opinions
>and actual votes and avoid leaving that unclear.)

That's right. But to determine the SU winner, you need to know 
something more precise than "opinions," and you also need to connect 
the opinions with how they voted. If a voter had a set of opinions, 
and tossed a coin to determine how to vote, what is the connection 
between the opinions and the votes? Does it make sense if we posit, 
for example, strong opinions and a coin-toss vote?

Or the reverse, opinions weak enough that the voter might just decide 
to stay home, yet when the voter actually votes, it is a full-on 
vote-for-one, I very much care kind of vote.

Votes that only make sense with full knowledge of how the others will 
vote, and -- this is important -- the votes of the others essentially 
show "We don't care, be our guest."

The latter is actually possible, though not in public elections in 
the forseeable future. And if this *were* the actual situation, then 
there is absolutely nothing wrong with R2 winning.

Juho shows us the election situation and essentially *assumes* that 
what is wrong is obvious. But it is not obvious, at all; quite the contrary.

When asked what was wrong, he wrote "that the R2 voters got what they 
wanted by voting extremes." What is wrong with that? It *appears* 
wrong because he has postulated utilities that were otherwise. He set 
up a contradiction and voter behavior that only makes sense under 
very narrow conditions, but he ignores the conditions and presents 
the example as if it were some kind of general case. If the 
conditions were such that the voters would actually vote that way, 
they were such that R2 was fine as a winner. Better than I've ever 
seen in any election!

And the way I'd set up Range, this kind of election would trigger a 
runoff. So the consent of the majority would be explicit. (Or, 
alternatively, a ratification vote would be held, which is better 
from the point of pure democracy, but not from the point of view of 
efficiency. If the runoff is Yes/No Approval, with two candidates, 
then it can be fully democratic, because the electorate can vote No 
for both....)

In any case, there are two major issues when comparing election methods:

(1) How does it compare from the point of view of maximizing SU *on 
the average* (i.e., over many elections). Any single ballot method 
(short of methods which fall down as to the other issue, or without 
some means of assuring that utilities are accurate) is going to fail 
to choose the SU maximizer under some conditions. Range can do it 
when the expressed utilities are not commensurable, but generally 
utilities averaged over many voters *are* commensurable, in reality. 
Not always, so you can construct scenarios where Range fails to maximize SU.)

(2) What is the variability of the outcome? How risky is the method? 
This rules out Random Voter. Besides risk, Random Voter has two 
problems: first of all, it is basically a ranked method, Plurality. 
but without the strategic compulsion that appears in Plurality. And 
secondly, while it certainly encourages sincere voting, it cannot 
take into account preference strength. You get the choice of the 
chosen voter, no matter what the preference strength of that voter. 
Random Voters, however, with a larger number of chosen voters, I 
suspect would be able to deal with preference strength issues if 
Range ballots are used. And this would likewise encourage more 
accurate voting. But I haven't analyzed it in detail. It's a little 
like Warren's DDJ method of legislating. Random Voter does quite well 
at SU maxization *average* over many elections, because preference 
strengths average out....