[EM] Re: Utilities?

[James Green-Armytage]

>
>Why do you try to give the impression that I want to introduce something
>strange? 

	Let me return this to layman's terms.
	One person says: "I like Nader more than Gore. I like Gore more than
Bush. I like Bush more than Nader."
	Many eight-year-olds should be able to point out the logical flaw in this
set of sentences.
	And yet you consider it to be some sort of affront to freedom and
democracy to not have a ballot that accommodates such preferences. You use
the word "force" to suggest that there is some sort of violent aspect in
excluding cyclic ballots.
	I think that this is silly, and that there are far more important voting
methods problems to worry about than this. I believe that I am getting
towards the point where I have said all I can think to say about cyclic
preferences per se, at least for the time being. On some level I still
wonder if you've been putting me on. You talk about fulfilling liberty by
allowing cyclic voting patterns, but you haven't talked of the practical
benefit of such, and therefore I remain uninterested. If you haven't found
my comments helpful, I apologize.

>But if you want to make a serious public proposal, you have to
>argue that the assumptions you made theoretically are indeed fulfilled
>by *all* of your voters (we still want to have equality of voters, right?)

	No ballot can perfectly express how voters feel about the different
candidates. The purpose of the exercise is to get something that is a
decent approximation, while being manageable and effectively functional.
>
>> Why should we assume that voters have acyclic preferences? I don't
>> know how hardcore my assumption of this is, but it does make sense to
>> me, and I don't see a need to take its negation into account when
>> doing election methods design for public use. It's not that I'm sure
>> that acyclic preferences are impossible; I just don't think that
>> they're especially important or worth worrying about. 
>
>Sorry, but this is completely wrong. I don't assume anything. You do.
>How can we assume that some voters' preferences are not important???

	In the first sentence of the paragraph, I was restating your question
before answering, rather than posing it to you. Sorry about the confusion.
>
>As to how ratings could be defined, you wrote:
>> "Rate the candidates on a scale from 0 to 100. 100 is a candidate you
>>  like the most, 0 is a candidate you like the least. 50 is a
>> candidate such that you prefer this candidate over a 0 candidate
>> about as strongly as you prefer a 100 candidate over a 50 candidate."
>> etc.
>
>So, what would my ratings be when I prefer K to B much more than I
>prefer D to K? Would they be D 100 > K 90 > B 0, or perhaps D 100 > K 95
> > B 0 or D 100 > K 80 > B 0? WHO CAN TELL?

	Again, it's an approximation. Most voters understand the concept of
rating stuff on a scale from 0 to 100, and pretty much an rough indication
of their relative preference strength (a gut reaction) will serve our
purposes quite well. Over a large group of voters, these individual
roughnesses will even out into a meaningful statistical pattern.
	If you must have a more strict definition, though, I suppose you can
continue my definition above via a thought experiment. Basically, you can
define any rating in the scale through the use of halfway points.
Candidate A at 100 is my favorite candidate. Candidate B at 0 is my least
favorite. I can define 50 by making up an imaginary candidate C such that
my preference strength of A>C is equal to my preference strength of C>B. I
can define 75 by making an imaginary candidate D such that A>D is roughly
equal in strength to D>C. And so on, with 62.5, 68.75, 84.375, and so on.
I assume that any point can be reached this way, eventually. But really,
none of this is necessary, as voters' intuition will do just fine. And
even if some voters do something else, like exaggerate their largest
preference gap so that all above it are at 100, and all below it are at 0,
that will be fine as well, as long as it doesn't tend towards
disequilibrium.
	By the way, if you like to make an issue of liberty in voter expression,
I tend to think of cardinal methods as being more liberally expressive
than ordinal, second-order ordinal, or explicit pairwise methods. Surely,
there is a much wider range of possible expressions with a cardinal ballot
than there would be with any of the above alone.

my best,
James