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

[Abd ul-Rahman Lomax]

At 10:00 AM 7/25/2007, Kevin Venzke wrote:
>Just to be clear, by "moot vote" you mean the case where the observed
>voter fails to have an effect on the result, correct?

Actually, no, but close. They are all the cases where the voter's 
vote doesn't matter, no matter how the voter votes. The voter's vote 
may still fail to have an effect on the outcome if the voter votes in 
certain ways, but these are all the cases where the voter's decision 
has consequences for the utility of the election, as seen by the voter.

>The trouble with excluding these trials is that it is important to
>consider how often votes are moot given various ways of voting. If it
>didn't matter then it would probably be adequate to consider only single-
>voter elections.

That may be of interest. But that is a separate measure, one which I 
have not studied, and I'm not clear that it is at all relevant to the 
comparison before us. Proportionally, offhand, it looks to me as if 
the voter's vote is not moot in the same percentage of cases for 
Range or Approval.

With Range 2, 3 candidates, there are 27 cases in which the voter's 
vote is not moot, the voter *could* affect the outcome by breaking or 
creating a tie. With Approval, there are 12 cases. Somebody else do 
the math to confirm, but it looks to me that this only reflects the 
reduced number of possible opposing votes, not the power of the voter.


> > The simulations with results on the cited page, inspired by Mr.
> > Venske's work, use a primitive random distribution, quite like the
> > "zero knowledge" distribution in my present work. The utility
> > distributions are even, random for each voter. This is *not* the case
> > with the general purpose simulator Warren has built, rather IEVS has
> > utility input options that can use various distributions.
> >
> > So what is on these pages, rather primitively in some ways, studies
> > effecdt of various Range Voting strategies, a question of major
> > interest. They do not show how "sincere votes" stack up against
> > "approval votes" on the part of the rest of the electorate.
>
>However, in my simulations no assumptions were made about the other
>voters. Only preexisting total scores were generated, which could have
>arisen from any strategy.

But in another post, I point out that by looking at overall utility, 
rather than the utility of only those votes where the voter's vote 
can make a difference, a great deal of precision is lost. Given 
sufficient precision, the two methods should coincide, but it is much 
more difficult to maintain the high precision necessary with the 
method used by Venzke.

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.

So the new question for those interested, with the time, is, For 
Range N, what value of N maximizes the power of the voter to maximize 
personal utility? From my results, N is not 1. Nor is it, apparently, 
999, if that is what was used in the simulations. It is probably 
somewhere in between, and I predict that it will be a relatively low 
number, it is not impossible that Range utility starts to decline 
above 2. But that is only speculation at this time.

Wouldn't it be a happy result if the optimum value was small? No need 
to push for more complex ballots!

My own political strategy is to promote Approval as being a great 
improvement at very small cost. Then, I predict, there will be 
pressure to add a little more flexibility, and we now see here that 
Range 2 does, in fact, involve some improvement. And has the happy 
result that Sincere is a very good strategy, better than any Approval 
strategy. And since Range 2 only allows Range strategy or something 
very close to sincere if not fully sincere -- the exact threshold has 
not been tested --, we do know that sincere strategy is the best, in 
the case studied (zero knowledge, 3 candidates, middle utility for 
middle preference candidate.)

There is still lots that we don't know. It's obvious that as election 
probabilities become known, strategy shifts toward Approval. However, 
there remains, for candidates unlikely to be elected, value in the 
intermediate ratings. For example, they provide better information 
about voter opinion, quite useful for political parties in the 
future, helping them to come up with better nominees.