[Election-Methods] RE : Is "sincere" voting in Range suboptimal?

[Abd ul-Rahman Lomax]

At 10:12 AM 7/26/2007, Kevin Venzke wrote:
>Ok. So if I were to modify my simulation to ignore trials where no pair
>of preexisting vote totals are at least as close as the maximum score
>from one vote, would you be interested in these results?

Sure, if I understand the criterion correctly. However, unspecified 
is the Range resolutoin, and there is no some suspicion that Range 
999 (is that your method?) has different optimal voter strategy from 
Range 2. In the former, it appears from your simulations that optimal 
strategy, large vote counts, is Mean-Based Approval. In the latter, I 
have a counterexample.

(If the bottom score is 0, by my notation, and the increments are 1, 
the max possible score is the N in Range N.)

>That seems true, however the mere fact that your vote isn't moot in
>some situation isn't something you can take to the bank. For instance just
>because it turns out to be possible for you to break an A-B tie by voting A
>10 and B 0, doesn't mean you are actually free to do it; you cast your
>vote without this knowledge.

That's correct. However, it is one of the possibilities, and the 
effect of it must then be considered in outcome expected utility.

>I don't think I understand your concern about precision. Yes, there are
>extremely few scenarios where one voter can make any difference. One
>simply runs enough trials to allow the final averages to settle somewhere.
>I write my simulations so that I can see the average move as trials are
>run, like a ball spun down a funnel.

There are two explanations for the divergence of results. First of 
all, my method is *exact*. It's not a simulation. And it focuses only 
on the cases where the vote is not moot, it does not even calculate 
the absolute utilities. The second is that you are using high-res 
Range. Warren's page based on your work does not state the precision, 
but I'd guess that you used three-place.

Further, my example focuses on a very specific utility distribution: 
2, 1, 0. It is quite possible that sincere ratings are worse than 
Approval with other distributions; thus this particular example and 
its effect gets lost in the noise. Given that my results so far are 
counterintuitive, I hesitate to make many predictions.

My work is either correct or it is not. The assumptions are simple. 
In a way, this is a test of the simulator!

Unless I made a mistake. Easily possible, I'm depending on the rest 
of you to discover it, if it is not there.

> > Further, Venske is not testing Range 2, but higher-resolution Range.
> > Approval *is* a Range method. What is the optimum Range *method* in
> > terms of maximizing voter expected utility with the best strategy? Is
> > it Approval -- this is what is being claimed by some, but without
> > comparing Approval to Range N, other than a high value of N. To my
> > knowledge, my study is the first to look at Range 2 in this way. And
> > it appears that Range 2 beats Approval.
>
>I'm not sure what you mean by Range 2.

Two increments in preference. If min vote is 0, and increment is 1, 
Range N has a max rating of N.

the percentage rating for a vote is then V/N, not V/(N-1).

And the basic range method is Range 1. Approval.

Etc.

Really, if the term goes into common usage, it will be much less 
confusing. Given that there is no standard for what N means in Range 
N, I decided to create one. Others will decide whether or not to use it.

How about we vote on it? (I'm a firm believer in deliberative process 
and don't trust polls that are simply created by an individual and 
then answered by some. The answer often depends on the exact 
question, and, further, polls without specific debate are ... 
knee-jerk responses, useful in emergencies, not for long-term questions.)

>  Yes, I assumed the voter could
>use as much resolution as he wanted. But if voting approval style is
>optimal in large elections, I don't see how it matters how much resolution
>was actually allowed.

This is another non sequitur which I used to believe. My study 
indicates that, at least in the one case studied (large election, 
Range 2, three candidates, voter has no knowledge and utilities are 
2, 1, 0), the utility is not only higher for the sincere vote, but if 
the method is changed to Approval, so that only approval votes are 
possible (simple to do, just select the vote patterns that are even 
numbers only), the expected utility for our voter declines *further.*

In other words, even if the optimal strategy for the voter is 
Approval -- which it is not in this case -- it is possible that the 
voter will do worse in expected outcome if the election is an 
Approval election.

Tragedy of the commons! If everyone goes for personal maximization, 
everyone loses! (on average, and this includes the personal maximizer).

>My simulation used several orders of magnitude more than 999 slots if
>that is what you mean.

So if the votes are six-place decimals, it is Range 999999. Or Range 
1000000, if 1.0 is a possible vote.

>Why do you say that apparently 999 is not the value of N which "maximizes
>the power of the voter to maximize personal utility"?

Look at the study!

Or do it yourself. Consider all 27 possible presenting vote 
combinations, equally likely, where the voter can affect the outcome 
(there are other combinations where three candidates are involved, 
but they are vanishingly rare, I have not studied the effect of them, 
but it should be truly insignificant *if there are many voters*. 
These are the combinations that make a certain Approval Vote optimal 
in the 2 voter case. They also are the combinations that make the 
vote of 200 more valuable than 220, even though the middle vote is 
exactly midrange.

Range 1: Best strategy: Plurality, a kind of Approval.
Range 2: Best strategy: Sincere
Range 9999999: from simulations, Best Strategy: Approval.

I think that the discussion will get a lot more valuable if people 
actually look at the case I studied. It's a counterexample to what 
people, including quite knowledgeable ones, have been repeating. If 
I've made a mistake, I'd love to know it.

It's extremely simple, which is what makes it possible to study the 
strategies exactly.

Many voters. Range 2 election (CR-3). Voter has utilities of 2, 1, 0. 
Zero knowledge, all vote combinations are equally likely.

That's it. Look at the expected utilities for each strategy. There 
are 27 cases, I believe, 27 presenting vote patterns where the voter 
can make a difference, and all of the 27 have the same frequency (no 
matter how many voters, but three-way near-ties have been excluded).

And then look at the effect of only allowing votes of 0 and 2. 
Expected utility declines, period.