[Election-Methods] [EM] Juho--Schudy's statement is correct.

[Abd ul-Rahman Lomax]

At 10:32 AM 7/26/2007, Steve Eppley wrote:
>I have time only for a few quick comments about Mr. Lomax' message (below).
>
>First, he appears to have misunderstood what I meant about altruistic
>voters.  I asked what would happen if they voted sincerely (and selfish
>voters extremize).  Somehow he misinterpreted that as if I'd asked what
>would happen if they misrepresented their preferences.

Sorry. The problem is in assuming a definite correlation between 
selfish and extremizing. Extremizing is misrepresenting to the system 
one's true preferences. It seems intuitively likely to me that the 
*ideal* system would respond to such a voter by giving them what they 
want, which has been distorted by their vote, so it can easily be 
less than their true preferences would indicate.

However, we are dealing with Range Voting, and a particular kind of 
Range Voting which we already know is less than ideal. Better than 
most of what is on the table, but less than ideal.

Many consider that Range may, in many scenarios, reward extreme votes 
to be a serious argument against it. I'd say that the arguments which 
have been so made are incomplete, but that is really a side issue here.

The issue here is what the optimal strategies are in Range Voting. 
There may be no general answer. I believe that I have found a case 
where the voter optimizes personal utility by voting sincerely. I am 
not *yet* claiming general application for this, but, contrary to 
some assertions, this is not a small election. It can be as large as desired.

My conclusion comes from a more accurate determination of utilities 
than has been happening with the simulations, it asks a different 
question (there is a *specific* utility pattern involved, rather than 
random distributions of patterns), and the simulations have been, it 
turns out, Range 999999. It has been assumed by many that Range with 
greater N is better. The proofs aren't in, as far as I know, very 
little work has been done with *low* resolution Range. And my case is 
maximally low resolution, almost Approval.

>Second, about optimal Range Voting strategy.   It looks to me from my
>own analysis and that of others that, from the individual voter's point
>of view, the vote most effective at maximizing that voter's expected
>utility is one that extremizes (except in some unimportant rare cases
>where another vote can be as good.)

The case I propose is actually a quite general one, not truly rare, 
the only thing rare about it is zero knowledge. We understand that if 
the voter knows the election environment, and in particular, if the 
voter faces, in spite of the number of candidates, a pairwise 
election with high certainty, the optimal strategy extremizes *those* 
votes. But what about the others? A sincere vote for a candidate who can't win

*cannot possibly lower utility,*

and there are other considerations besides winning. Votes have 
effects. If a candidate is lousy, but has some support, Approval may 
give that candidate very low votes. If the candidate gets twice as 
good, there really may be no more votes. The real status of the 
candidate is not revealed, as long as the candidate is not rising to 
first place for a significant number of voters. As to second place, 
we really need to know who is in true *third* place!

So the claim that intermediate votes are without value is clearly 
false. The assumption is that all value is in determining the winner, 
and that is false. People also value being honest and sincere, by the way.

What I am finding is that optimal strategy depends on the preference 
pattern for the voter. We already knew that, didn't we? The claim is 
being made that approval strategy is best (for the voter) *regardless 
of preference pattern*. Is it? I have a counterexample. And it is a bit

>   I haven't had time to hunt for Mr.
>Lomax' definition of optimality to check whether he defines it from the
>perspective of the (social utilitarian) voting system designer, rather
>than from the perspective of the voter who seeks to maximize his/her own
>utility.

The latter! We already knew that the optimal voting pattern from the 
point of view of maximizing overall social utility is the sincere 
vote. (Indeed, the optimal pattern is non-normalized sincere voting, 
there is a way to define that).

However, the claim is that the voter has different utilities.

I must also point out that classic game theory falls flat, often, at 
predicting human behavior, and often analysts assume that this means 
that people aren't rational. However, many of the failures disappear 
if we consider that people might be, within certain limits, 
optimizing social utility. And we are not suckers, or altruistic, for 
doing so, except with a very narrow definition of altruism. We are 
acting to preserve our genes! And we are defining "our" as social 
animals, who act for the welfare of the social group.

So even if it is true that optimal individual behavior is to vote the 
extremes, many may choose not to do so. They will do so, I suggest, 
when the loss in individual expected utility is small. We will rarely 
lie when the reward for lying is small, for there is a cost to lying 
entirely aside from game theory considerations.

In my view, extreme votes are not lying; they are, rather, truer 
expressions of preference. If I want so much for a candidate to win, 
A over B, that I will downrate B, *I may have a higher preference 
than I was thinking.*

To my mind, a full vote preference does not have to be any particular 
preference strength, in absolute terms. It's up to the voter to 
decide! So I don't like to call extreme votes "insincere." For 
convenience, I call simple expression of utility, generally 
normalized, which is a distortion in itself, "sincere," with everyone 
else. But it really means something more precise, such as normalized 
accurate perception of utilities, or absolute perception of 
utilities. In short, what I've called "fully sincere." For short.

By using the word "sincere," unfortunately, we call up all kinds of 
moral judgements. We believe it is better for people to be sincere 
than to lie or not disclose. But what is ironic to me is that, to 
prevent some sort of reward for distortion, some of us want to 
prohibit telling the full truth! Since some won't.

>Are we all agreed that extremizing is the (game-theoretically) optimal
>Range Vote in the case where there are only two candidates?

Yes. Not necessarily the "best" vote, but best for maximizing the 
voter's personal utilities. Whether or not the voter wants to vote 
that way is another story.

Consider the pizza election. With two flavors only, pepperoni and 
mushroom. There are three voters (there can be *many* voters, but 
let's say its proportional, my two voters are standins for twice as 
many as the opposing faction.) Two prefer pepperoni, but only 
slightly. The other, quite simply, cannot eat pepperoni, so we can 
say that the preference strength is maximal. The lone voter obviously 
should vote Approval style.

But what about the voters whose utilities are, say, 100 and 99? They 
really do love mushroom, but pepperoni has only a slight edge?

What's the best pizza to choose? And does our voting method and 
recommended strategy choose it? If not, we really should be 
considering why not and what we might do about it.

That doesn't mean we can solve the problem. The problem is 
artificially constricted if we limit ourselves to "election methods." 
That's not how real groups would resolve this question.

Note that Range, with enough voters, won't always pick what I 
consider the ideal pizza, it depends on how many voters and the 
preference spreads. But Range+2 will.

Range+2 is top-two range, and it is known to outperform standard 
Range in utility. And I think the simulations actually understate its 
performance. Hold a Range+2 election with the two candidates (and 
perhaps some others, doesn't matter; I originally stated the pizza 
election as three to avoid the normalization problem, to allow 
normalization without harm. In the two candidate case, normalization 
can *drastically* distort the utilities.)

What will happen? Pepperoni and Mushroom will have a runoff. But the 
pepperoni voters now know that there are many voters who have a 
strong preference. They may elect to change their vote, to give up a 
tiny bit of utility in order to make a huge difference for a few. We 
do this all the time! We do it when we pay taxes that are used to 
support people in dire need.

But if they judge that the strong preference is fake or not serious 
or whimsical, on the part of the minority, they may stick to their 
guns. And they will, quite properly, prevail, as they should have the 
right to do. They are the majority.

All this, though, is dicta. The best personal utility optimizing 
strategy for the 2-candidate case is extreme voting. However, when 
the benefit is small, voters may well elect to simply vote sincerely, 
understanding that this means that they may be giving up a small 
benefit in favor of a larger benefit to a minority.

You could call that altruistic, but it is really social behavior. 
These trades ultimately benefit everyone, for many interactions take 
place, many choices, and if every one of them maximizes overall 
benefit, and positions shift, as they do (it is not always the same 
set of voters who are losing and who are benefiting), over time, if 
net social utility is being maximized, so is personal.

So the optimal strategy *in one election* may be extreme voting -- it 
certainly is for some cases, maybe even most -- but that is not 
necessarily the best strategy for Life. Including elections.

And, properly, the decision is the voter's. Nobody should be telling 
the voter what to do, the advice, unless it is purely informative, is 
insulting.

Telling someone what their optimal strategy is insulting, unless 
carefully specified. *If you want to accomplish A, then your optimal 
strategy is ..." but, in that case, to avoid introducing bias, one 
should also state the reasonable alternative goal, and maximizing 
overall SU is the clear other option, leading to a different and, 
indeed, possibly more pleasing strategy: vote sincerely and accurately.