[EM] Are proposed methods asymptotically aproaching some limit of utility?

[Abd ul-Rahman Lomax]

At 01:38 PM 3/11/2007, Juho wrote:
>On Mar 11, 2007, at 18:44 , Matthew Welland wrote:
>My current choice
> > would be
> > range voting. It is simple (only slightly harder to expain than
> > approval)
> > and it seems to do a good job at leaving voters satisfied.
>
>It offers some really nice properties with sincere votes. It however
>has the potential to lead to disasters if used in a mixed way so that
>some voter groups mark their sincere preferences while some others
>mark strategically only largest and smallest values.

This charge regarding range is a bit misleading. Range is a voting 
method which allows voters to vote all the way from bullet style, to 
approval style, to full Range. And every large Range election in the 
real world, I'm quite sure, will be "mixed." So the "potential to 
lead to disasters" charge is a serious one, if true.

I see no evidence that it is more true of Range than of any other 
election method generally discussed here. Warren Smith has done 
extensive simulations of Range under "sincere" and "strategic" voting 
mixtures of voters, and indications are that Range performs well. 
Warren's work is in progress, he does not pretend that it is fully 
conclusive. But it's better, basically, than anything else we have.

My own observation on the alleged dichotomy between "sincere 
preferences" and "strategically only largest and smallest values" is 
that all of these can be sincere, and, assuming that the voters have 
some basic understanding of the system, all are likely to be sincere.

Range never encourages a "fully insincere" rating of a candidate; 
such a rating is one which has the effect of reversing expressed 
preference order over sincere preference order. (But it is possible 
that some voters might do this, for one reason or another. It is not 
strategically mandated by the system, but suppose that a voter likes 
a candidate but does not wish to express approval of the candidate's 
party. So this voter might downrate the candidate, while not 
downrating other candidates who would otherwise get lesser ratings. 
This, however, only means that a voter can treat a candidate *for 
whatever reason* as less worthy.)

So if the voter maintains preference order, within what is expressed 
(that is, preference information may be unexpressed in Range if the 
voter votes equal ratings), then we can call the voting sincere.

I used to think that I understood what "strategic" voting in Range 
was, i.e., say I prefer A>B>C. And, say, I would rate them 1, 0.5, 
and 0 respectively. Ah, but I really want A to win. So I rate B, not 
at 0.5, but at 0.

Seemed simple, I was "exaggerating."

But wait! If I vote this way, it must be that I prefer A to B with 
more strength than I prefer B to C. So the conditions of the problem 
are contradictory. I assumed that the preference strength was equal, 
and thus the ratings would be equally spaced. But then I essentially 
assumed that they were *not* equal, because by downrating B to zero I 
was equating B and C, risking victory by C, my least favorite.

Essentially, my conclusion has been that Range voters will vote 
sincerely and the only problem has been that we assume that voting 
extremes is insincere. We do understand, readily, that voting zero 
for a candidate is not equating that candidate with Genghis Khan. It 
means, instead, that of this field of candidates, this candidate is 
rated among the lowest grouping of candidates, these are all 
candidates to whom I do not want to contribute any votes.

But we need to understand that, in addition to normalization, which 
moves the votes to the extremes, for at least one candidate, there is 
what I've called magnification, where the preference range expressed 
is decreased. It's like turning up the gain on a DC amplifier, with 
sufficient gain the output will peg the meter at max or min. Useful 
information is still provided.

I began to realize this with arguments over the relationship between 
Range and the Majority Criterion. Range allows a majority to elect 
its preference, *if* the majority cares sufficiently. If a majority 
bullet votes, the majority preference will be elected. When it is 
alleged that Range does not satisfy the Majority Criterion, what is 
meant that if a majority votes for its preference (we assume at max 
rating), but some of that majority also elevates above min rating 
some other candidate, there is a "risk" that this other candidate will win.

This is alleged as a problem with Range. It is not, because the 
majority has *permitted* this outcome.

In any case, if a majority in a Range election prefers a candidate, 
and considers the election of this candidate over all others to be of 
sufficient importance, it cannot fail to prevail. It is only if the 
majority -- at least some of it -- is willing to permit another 
outcome by elevating candidates other than first preference, that the 
winner may not be the first preference of a majority.

And we have shown by many examples that the assumption that the first 
preference of a majority should win an election would clearly lead, 
in some fairly common scenarios, to a less than satisfactory winner. 
The shorthand name we are using for this is Pizza.

A group of friends go out for Pizza. For some reason, they can only 
buy one kind of pizza. All but one favor Pepperoni; the one, perhaps 
for religious reasons or allergy, can't eat Pepperoni. What should 
the group choose. Well, it depends, I'd suggest on *how strong* the 
preference is for Pepperoni. If there is another choice which is 
reasonably satisfactory, that all could eat, most would agree that 
the best choice isn't Pepperoni, where the percentage of voters who 
can't eat it is significant. If a billion people prefer Pepperoni, 
and only one can't eat it, sorry, a small preference of a very large 
number of people amounts to a large preference when compared with one person.

But groups, in fact, will often go out of their way to satisfy all 
members *if possible*, for that is considered to have a high value, 
often. More important than getting Pepperoni.

As I've written, the best election methods aren't even called 
election methods here, because they are deliberative. In 
deliberation, facts like the importance of the choice to that single 
voter can come out, and the group can make a conscious and deliberate 
choice of whether or not to satisfy the single voter. My opinion is 
that majority consent is required.

But if we only have a single ballot, a single election, then Range, 
being a method which could be used by a group to judge preference 
strengths, would be optimum, and not only for choosing Pizzas, but 
also for choosing Presidents.

It's been proposed that Range elections, where analysis indicates 
that the Range winner is not the Condorcet winner (by some Condorcet 
method which allows equal ranking), a runoff be held between the 
Range and Condorcet winners. Real runoff elections move an election 
method which includes them toward deliberative methods, and the 
two-election combination would both satisfy Range analysis (social 
utility by the basic method of summing equalized expressed utilities) 
and the Condorcet Criterion (because if there is a run-off, the 
Condorcet winner must win it if no voters change their preferences. 
But may voters, generally, will, and if enough do so, the original 
Range winner becomes the new Condorcet winner, by beating the real 
Condorcet winner in a real pairwise contest, instead of a simulated one.)

It should also be noted that the proposed Range rules regarding how 
to count partial abstentions could lead to some anomalies, and I've 
yet to be satisfied by the suggested fixes. My assumption about Range 
is that it is sum of votes which is used. But the Center for Range 
Voting web site still shows the the use of average vote.

The argument for that is to make it more possible for a Dark Horse to 
win, but this very possibility is dangerous.