[EM] What is the ideal election method for sincere voters?

Abd ul-Rahman Lomax abd at lomaxdesign.com
Sun Mar 4 20:41:40 PST 2007

At 08:51 AM 3/4/2007, Juho wrote:
>On Mar 3, 2007, at 9:06 , Abd ul-Rahman Lomax wrote:
>>If we cannot agree on the best method with sincere votes, we are
>>highly unlikely to agree on the best method in the presence of
>>strategic voting, though I suppose it is possible....
>Range is good with sincere votes. Its utility function (sum of
>individual utilities) is good. I think there are however also other
>good utility functions that can be used depending on the election and
>its targets. Therefore it is maybe not necessary to "agree on the
>best method with sincere votes".

Let's consider the method of deriving social utility from individual 
utilities to be a detail. There seems to be some general agreement 
that simple summing is not without value, but it is also clear that 
summation is a simplification and that some other function may be 
more ideal. However, political reality may intrude. Summation has a 
history, more complex functions don't, as far as I know.

As I've mentioned, there is already an adjustment made in individual 
values, typically, we may generally assume, some kind of 
normalization. The normalization may cover some of the inaccuracy in 
summation. For example, the distribution of wealth such that a single 
person gets all the wealth gives the same sum in economic value 
(let's neglect the other issues!), but when it is normalized and each 
person's utility has the same Range, summation favors spreading it 
out. That is, with N voters, more than two,

(N - 1) * 1 + 0 > (N - 1) * 0 + 1.

Even though the underlying absolute utilities were equal in sum. 
Indeed, this would seem to favor robbing the rich few and giving to 
the many poor, but that's only true if the rich have sufficient 
wealth to make a significant difference to the poor. I'd suggest that 
this is only likely to happen in a seriously unjust society. And 
that, of course, is a whole other question.

The fear that in a democracy the people will automatically seize the 
wealth of the rich and redistribute it is, I think, not valid in a 
mature democracy. It may be valid under conditions of mob rule, or 
the equivalent, rule by demagogues whose real goal is power and/or 
wealth for themselves.

>Let's say we are selecting pizzas (A,B). There are three voters whose
>preferences are (9,6), (9,5) and (0,6). Pizza A is the best selection
>according to Range.

Which is why, of course, small groups would be advised to use Range 
only as a polling device. And, indeed, with large groups, I've 
suggested that Range polls be ratified, because under conditions like 
this, the majority, which properly *does* have the power of decision, 
may wish to do something other than maximize the raw, undeliberated 
Range values.

>  I can however imagine that when selecting a pizza
>the intention could be to have nice time out with friends. The third
>voter obviously hates the A pizza. Maybe we should use some other
>utility function, maybe one that maximizes the worst utility to any
>individual voter. This kind of a method would select pizza B.

Absolutely, simple summation can fail. If somehow we could express 
absolute utilities, and include the mutual effects, since voter 
utilities are *not* independent variables, summation would be 
correct. But we have, usually, no way of doing that. If the choice is 
one where economic effects are the sole consideration, the summation 
may be ideal; and where a choice deprives an individual entirely, 
it's possible that this person would be compensated by the others. 
I.e., that loss would be covered by an indemnity. And this would be 
factored into the utilities.

(If an action benefits many and harms few, it may take only a small 
loss for the many to restore the few to a proper level of benefit. 
The proper goal is to maximize the sum, and the sum is not some fixed 
number. It is conceivable that a true consensus action can be found, 
one with high utility, or at minimum no harm, for *all*.)

>It is also questionable if it always makes sense to select the
>favourite alternatives of those votes that have strong feelings and
>not to respect the opinions of voters with milder feelings that much.

If we were deciding a series of choices, and the "strong" and "mild" 
feeling voters were always the same people, then, I'd suggest, as the 
strong got their way each time, the "mild" voters would begin to 
consider themselves unjustly deprived. They would become strong in 
their feelings and votes. Unless they agreed that that the "strong" 
getting what they want was just.

>In some election it may make sense to give each voter same weight.
>One could either normalize the votes or accept the one man one vote
>principle (= weight of each opinion is 1.0). (Note that e.g. in the
>Condorcet methods weight of each expressed preference ("X is better
>than Y") is exactly 1. That does not take into account different
>preference strengths of different voters but gives all opinions the
>same weight.)

Yes. It is clear to me that, at least for sincere voters, an election 
method must consider preference strength if it is to be of general application.

>You also questioned the vulnerability of Range to strategic voting.
>Approval style voting may be either sincere or strategic.

That's correct. Many writers seem to assume that it is insincere. 
After all, George Bush isn't Adolf Hitler, so, the thinking seems to 
be, if a voter gives Bush a zero, it is not the true assessment. 
However, this is rooted in a misunderstanding of how Range works, a 
neglect of the general theory of choice. Choices are of different 
levels of importance, and what we are doing with election methods, 
ideally, is simply trying to make the best choice. We use, sometimes, 
the aggregation of opinions from many people in order to do this, 
and, I'd suggest, this is as successful as it is because such a 
process ideally takes advantage of distributed intelligence. 
Democracies are stronger than dictatorships because many are smarter than one.

The meaning of a vote in terms of utility depends on the choice being 
made. If a choice is only of minor importance, we still want to make 
the best choice, and we want to allow all voters the same level of 
influence over the result *unless they choose to exercise less 
influence.* That choice is what Range allows.

>  Let's say
>that X and Y go out for pizza. All the pizzas are quite ok to both
>but X is a bit selfish and wants to make the decision on which pizza
>to order. Voting strategically in bullet style makes perfect sense to
>him. The worst outcome is to toss a coin on which one's favourite
>pizza to take. If Y votes sincerely, X will decide.

Of course, selfish people end up with no friends to share pizzas 
with. Most sane people will want their companions to be pleased, 
sometimes more than they want themselves to be pleased. But if people 
pretend to want what they think their friend wants, the choice can be 
suboptimal. So for a group of people to choose a pizza, we would 
suggest, the best vote is simply a sincere judgement of the choices. 
If it turns out that there is no choice which reasonably satisfies 
everyone, then what is in order is generally not a rigid 
determination from the Range numbers, but deliberation which begins 
with the sincere Range numbers and considers outcomes and alternatives.

"I see that I can't have a pizza that I'd want to eat without 
depriving someone else of the same. I can eat later. Go ahead...."

But with large numbers of voters and no process for deliberation, 
indeed, Range may be the method of choice. However, the real problem 
here is the "no process for deliberation" part. And it is this which 
I'm generally trying to address with FA/DP.

I can forsee FA/DP organizations taking Range polls as a starting 
point for deliberation. The FA is not going to itself make the 
decision, ordinarily, it merely facilitates the decision-making 
process. Because it is an FA, it is maximally unbiased, and because 
it is DP, there is maximum access to the deliberative process. It's 
open and transparent. (I expect a lot of side-channel traffic in DP 
organizations, direct communications between proxies and clients, 
these are not necessarily public, but rather serve to ultimately feed 
ideas and judgements into the public structures, and likewise to 
transmit back to clients potential decisions and the reasons for them.

>Using Condorcet or other more majority oriented methods instead of
>Range may either be a result of favouring more strategy resistant
>methods (and corresponding utility functions) or sometimes also a
>direct result of electing the most applicable utility function.

I don't think that Condorcet methods were developed to maximize 
utility; rather I think that the idea of the pairwise winner was seen 
as intuitively correct. In fact, if all voters are fully informed and 
aware of the general status, that is, the opinions and strengths of 
preference of others, Condorcet methods should actually be ideal. 
Range, however, is what collects this information more directly, a 
ranked poll only, sometimes, approximates it.

>In addition to the viewpoints tat I discussed above there are at
>least the proportionality cosiderations, both with multiple winners
>and single winners distributed over time, but I understood that these
>already fall out of the scope of your mail.

I should be the last person to complain about divergence from the 
"scope of my mail." I don't even stay on my own subject, not to 
mention subjects established by others.

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