[Election-Methods] Challenge: Elect the compromise

[Abd ul-Rahman Lomax]

At 08:51 AM 8/23/2007, Jobst Heitzig wrote:
>Dear Steve!
>
> > However, assuming the intensity difference between the A faction's 100 and
> > 80 is much less than the intensity difference between the B faction's 80
> > and 0,
>
>That was not the assumption I wanted anyone to make.
>
>Those of you who believe in measurable utility: please assume that 
>the ratings reflect utilities in the *same* units.

Jobst, you misread Steve. He said what you intended. He assumed that, 
essentially, 20 was much less than 80.

He merely noted that it was, indeed, an assumption. I also noted that 
the assumption would be rarely true. The ratings are, clearly, 
normalized, and normalized ratings, in general, are not truly 
commensurable as utilities.

You can't have it both ways. If you have absolute utilities, i.e., 
they are in the same units, you would generally not have the same 
spread between the factions.

However, we *assume* equality in the Range units, for the purposes of 
election. What is really happening is that the units are percentages 
of a vote. They are *related* to utilities, but normalization makes 
it inaccurate, and, for this reason, Range, as an example, does *not* 
necessarily choose the SU winner. It merely does a better job than 
most other methods on the table.

There are, I believe, ways to improve the performance of Range, and, 
as it happens, the one I've been proposing also makes Range MC 
compliant in the overall method, including a possible runoff. 
Obviously, Range *cannot* be MC compliant directly, for it can pass 
over the favorite of a majority, when this is only by a relatively 
small preference strength, to elect a stronger preference of a 
minority. However, Range ballots would generally show that this was 
the case, and a runoff could be triggered.

Contrary to what some might think would automatically happen, the 
reverse is, I think, likely: the Range winner would prevail, this 
time with the explicit consent of a majority of those voting in the 
runoff. Why I think this should be interesting, but does anyone care?

>All others: please interpret the ratings
>    A 100, C 80, B 0
>as saying that the person would prefer C over each lottery that 
>elects A with a probability of p less than 80%, and B with a 
>probability of 1-p, and that the person would prefer over C each 
>lottery that elects A with a probability of p above 80%, and B with 
>a probability of 1-p.

Clever as a method of specifying utilities, though, as it happens, 
people do not necessarily compare utilities that way. We can suggest 
Range Votes that use this kind of analysis, but that's a deliberate 
intellectual strategy.

Note that this definition is not consistent with the assumption 
suggested above, to repeat:

>Those of you who believe in measurable utility: please assume that 
>the ratings reflect utilities in the *same* units.

The definition for "all others" refers to relative utilities, not 
commensurable ones, using the same "units."

Given that I don't "believe" in measurable utility, am I an "other"?

Absolute utilities are an inside-the-black-box concept. It is useful 
to consider that they exist, but measuring them? I don't have a clue 
how to do it.

Certainly the lottery comparison does not reach to them. An auction 
or Clarke tax might. A Clarke tax causes stated utilities to have an 
actual cost, you pay for the utility gain you get by having 
participated in the election. Hence, in theory, you will vote sincere 
utilities, assuming that a host of practical problems could be solved.

I can estimate my *relative* utilities, but it is would be 
problematic for me to generate even what I call the first-normalized 
utilities; these are the closest to absolute utilities that I'd 
routinely have. They are utilities in the range of absolute best to 
absolute worst, over the entire possible universe of candidates. Even 
this is not truly commensurable, but there is at least a common 
basis, the range of sensibilities of the voters.