[Election-Methods] Improved Approval Runoff

[Abd ul-Rahman Lomax]

At 01:23 AM 8/21/2007, Paul Kislanko wrote:
>There is no such thing as "utility" to a voter. That is an abstraction used
>by analysts for which I have seen no definition that is useful to me, a
>voter, despite having pleaded for one on this list for at least three years
>now.

The term is widely used, and it has generally accepted meanings, 
though often lacking precision. There are certain assumptions 
underlying the concept.

And there are equivalent terms. Expected Satisfaction is one.

If Candidate A wins this election, how satisfied would you be?

0 Very Dissatisfied
1 Moderately Dissatisfied
2 Slightly Dissatisfied
3 Neither Satisfied nor Dissatisfied
4 Slightly Pleased
5 Moderately Pleased
6 Very Pleased.

This could be a Range 6 ballot.

It is usually a bad idea to claim that something that many find a 
useful concept does not exist. It does, at least in some way....

Utility is used in game theory to find optimum actions. Each possible 
choice is assigned a utility, some value. In some cases, this can be 
done accurately; if, for example, various outcomes have economic 
value, they might be valued in dollars. There are voting schemes 
where one essentially bids with taxes. (I find this idea interesting, 
and not necessarily plutocratic, if what is being decided with the 
"votes" is how taxes will be spent. But it is not my purpose here to 
examine this kind of proposal, it is merely an example where 
"utility" has a very specific meaning for a given voter. It would be, 
in this case, how much you were willing to bid to get the outcome you want.)

The utilities in Range Voting are really the same as utilities in game theory.

In simulations, it is assumed that people have some kind of internal 
process for assigning value to candidates. While, in fact, there may 
be no such valuation, rather people consider candidates pairwise and 
rank through a series of pairwise comparisons, people also have a 
sense of preference strength, and, through pairwise comparisons and 
preference strengths, one can estimate a scale. Can there be a 
Condorcet Cycle? Not in the simulations, but, in reality, it might be 
possible, for when we compare two candidates, we may compare them 
based on a particular set of characteristics that are salient for 
that pair; with another pair, another set may be used, and thus it 
becomes possible to have a cycle.

The simulations that I'm aware of use "issue space." If I am correct, 
it is presumed that there are a series of issues, with a linear scale 
associated with each. Voters and candidates are assigned positions on 
each of these scales, according to some distribution considered 
realistic (it would not realistically be a linear distribution; 
rather the opinions of people cluster). The distance between the 
voter's position and the candidate's position is "regret" if that 
candidate is elected, on that scale. I don't know, actually, if only 
one issue scale is used, or if there are a series in vector space. In 
any case, resulting from this is an assignment of numerical values to 
each candidate. In the simulations, this is the utility. That, then, 
is translated into a Range vote using various strategies.

Range votes are, however, just votes. They are not "utilities." But 
*if* there are commensurable utilities, and voters vote Range Votes 
proportional to them, Range optimizes utility summed over all voters. 
If the utilities are "relative expected satisfaction," somewhat like 
what I listed above, Range, then, optimizes overall voter 
satisfaction with the result, minimizing dissatisfaction.

Obviously, there is a series of assumptions being made. However, they 
are reasonable ones. We are quite capable of ranking candidates, and, 
in addition, of estimating preference strengths. This, then, means 
that we are capable of *rating* candidates. Rating is just ranking 
with varying spread between the ranks. Rating is utility is expected 
voter satisfaction; however, in the end, all of this is theory and 
perhaps rationalization, the reality is that the voter is casting 
votes which have effects on the outcome.

It just happens that Range apparently *does* optimize overall 
satisfaction, not perfectly, but better than other methods on the 
table. Even if voters vote "strategically," i.e., choose the votes 
which game theory would indicate are optimal. It's really rather 
silly, the objection about strategic voting in Range. We want people 
to express what they want, and how strongly they want it. If they 
think they gain advantage by voting strongly, *they have strong 
preferences,* at least if they are sane.

(There are hysterics who make everything a matter of strong 
preference. But Range Voting is not turning society over to 
hysterics. There are probably hysterics on all sides of the issues, 
and they average out. The presence of "hysterical voters" -- who 
would vote quite as people claim strategic voters would vote -- 
merely shifts the election toward Approval, which is really the same 
method, just more black-and-white, and, it seems, the presence of 
even a few voters who vote intermediate ratings improves the outcome. 
It may be like adding high-frequency noise to a signal to increase 
precision in measuring it, a trick that really works even though it 
sounds counter-intuitive)

>If you can't define "utility", don't use that in any argument. If you can,
>please do so.

Let me put it this way: utility is as well or better defined than 
many concepts which are routinely used on this list.

The term has a range of meanings, from informal, where it is simply a 
synonym for "value," without insisting upon some numerical 
assignment, to more technical usages.

I've written quite a bit on the Range list about how utilities are 
converted to votes. It is assumed that we have some internal scale 
which weighs candidates, giving them some value from maximally 
negative to maximally positive. These maximums are actually the 
strongest possible opinions we could hold, far stronger than we would 
normally hold, they are the limits of human experience. Different 
people, I assume, are capable of different ranges of experience, so 
these utilities are not strictly commensurable. However, if we equate 
the distance between minimum and maximum for all people, we come up 
with what I've called the "first normalization." Smith and others, I 
think, have used underlying utilities that are of this kind, often 
expressed as a real number in the range of 0 to 1. It would probably 
correspond better to human experience to use -1 to +1, being an 
expression of maximum aversion to maximum attraction, but for our 
purposes here, the absolute range does not matter. We are going to 
normalize it all to a single scale for everyone.

*Then* comes the "second normalization," where the candidate set may 
come into play. The utilities described above are often termed 
absolute utilities, though they are not truly absolute. Nevertheless, 
they are presumed to be independent of the candidate set. But when we 
vote in a Range election, normally we do not have anywhere near the 
full range of possible utilities represented, we don't have, as I've 
termed them, the Messiah and Antichrist both on the ballot, we don't 
usually have either of them. If we did, I missed it.

I'm going to assume that Mr. Kislanko has a sincere question about 
what utilities mean, practically, as a voter. I've written about this 
on the Range list, but here is an attempt to describe how to create a 
set of normalized utilities. I'm going to describe an algorithm that 
is strategically optimal or at least close to it. Yet it is also 
"sincere," though not necessarily "fully sincere," which is problematic.

Take the set of candidates on the ballot or reasonably as write-ins 
and select the frontrunners, those considered to be possible winners.

Examine this set and identify your favorite. Also identify the 
opposite, the least-preferred. Assign the rating of 100% to your 
favorite. Assign the rating of 0% to your least preferred. Remember, 
these are the frontrunners, your favorite might not be among them.

For every candidate preferred to the frontrunners, also rate the 
candidate at 100%, and for every candidate to which you would prefer 
any frontrunner, rate that candidate at 0%.

Now, take any remaining candidates andIdentify clones among these and 
consider them as one candidate, N is the number of candidates after 
clones have been merged. Rank them and then assign them a preliminary 
rating, in steps of 100/(N+1), which will evenly space them across 
the range of 0-100.

Then consider if the preference strengths so assigned are reasonable. 
For example, if N was 1, the spread given above would place that 
single candidate midway between max and min. If the candidate seems 
better than that, nudge the vote up, if lower, nudge it down, until 
the ratings gap seems to correspond to a sense of preference strength.

Instead of doing the spread above, evenly distributing the candidates 
to start, it might be simpler to tack in one candidate at a time, 
starting with the most important.

Remember, if a candidate is not as good as the best frontrunner, but 
still quite good, this candidate should properly be rated close to 
100%, and similar applies to the bottom end.

It is not an exact thing. But people make judgements like this all 
the time,and Range has been used for polls for as long as I can 
remember. People know how to rate! In the end, what one is doing, 
though, is adjusting fractions of a vote. It does not have to be 
terribly accurate. It will average out over many voters....

That it will average out also means that you can simply set an 
Approval cutoff and rate candidates better than that at 100% and 
candidates less than that at 0%. There is nothing offensive or 
insincere about this, though it provides less detail about your 
preferences, and, for various reasons, it somewhat increases your 
risk of regret.... but it's simpler, for sure.

It is entirely unclear that we will see high-resolution Range soon in 
public elections. But seeing Approval (I call Range 1) or the next 
step up, I call Range 2 (Cardinal Ratings 3), is much more possible. 
MSNBC has a number of polls up that are Range 2. (The ratings are -, 
0, +, and they report the percentage of voters who voted each, which 
provides more information than simply reporting the sums. It's quite 
interesting!)