[EM] Range strategy pathological example (was Re: IRV vs Plurality)

[Abd ul-Rahman Lomax]

At 10:57 AM 1/27/2010, Jonathan Lundell wrote:
>On Jan 26, 2010, at 10:30 PM, Jameson Quinn wrote:
>>
>>One is, as you suggest, the strategy problem. Range, and it's limit 
>>in one direction, approval, require the voter to make cast a 
>>strategic vote; there really isn't any such thing as a 
>>non-strategic range or approval ballot. But voters are privy to 
>>different amounts of variably useful information about other 
>>voters' preferences, and other voters' strategic choices in view of 
>>those (perceived) preferences, and so on ad infinitum.
>>
>>Yes. There are two ways to fix this. One is to do something to 
>>"idiot-proof" the ballots - allow only near-top or near-bottom 
>>votes, or encourage middle votes only for lesser-known candidates. 
>>This essentially make Range into almost Approval, without losing 
>>too much expressivity (and thus no one is forced to vote 
>>unstrategically simply to gain expressivity). As you say, there's 
>>still strategy, but I think voters could handle it.

There isn't a problem needing fixing, not in the voting system, but 
there could be a problem in voter education. The idea that a range 
vote would change by the addition of an irrelevant, no-hope candidate 
shows a misunderstanding of range voting strategy, the kind that 
voters should, indeed, practice if the method is Range Voting. The 
only reason that so many Bore voters in the example Mr. Quinn created 
voted 8 for Cush compared to 10 for Bore is that, obviously, they 
detested Ader. But Ader was an irrelevant candidate, not going to 
win, so what they were doing was wasting 8/10 of their vote in a 
disapproval of an irrelevant candidate.

All statements I've seen about non-zero-knowledge voter strategy 
recommends rating max or close to max (and min) the frontrunners. 
That's the real race. What would I recommend for zero knowledge?

0 for anyone you'd hate to see win. 10 for anyone you'd be pleased to 
see win. But you could preserve preference by adjusting those. On 
average, for most voters, how you feel will be matched by the 
majority! On the other hand, perhaps from experience you know that 
your opinions are outliers, so you might adjust accordingly. This 
would suggest raising the rating of what you'd think likely to be the 
most liked candidate who is *not* your preference.

In a majority-required election, bullet voting is just fine. I'd add 
the same 100% vote for any candidates where I didn't have a 
significant preference against them for my favorite. If I only know 
one candidate, I'd only rate that candidate, at 100%. If there is a 
runoff, I'll have an opportunity to decide if I have a preference 
between the runoff candidates. If not, I probably won't bother to vote!

(But there is another reason I might vote in a runoff without having 
a strong preference: I could vote for both to indicate that I approve 
of both, or against both to indicate that I disapprove of both. The 
latter option should always be possible, in my opinion, even if 
irrelevant for determining a winner. It is accomplished by allowing 
write-in votes in the runoff. That can cause majority failure, yes, 
and that's valuable information for the society. It is not fixed by 
disallowing write-in votes, it is merely covered up and made 
invisible. That's one reason why the San Francisco decision about 
write-ins in runoffs was so stupid. A purely formal goal of finding a 
majority, by making it mathematically necessary, was substituted for 
the substance of attempting to find a real majority.)

>>If Range becomes Approval like then you might add also the 
>>weaknesses of Approval in your list.
>
>My objection to Range as requiring a strategic vote applies to 
>Approval as well. The strategy is (potentially) simpler to describe, 
>but it still can be executed well or poorly or naively, and for 
>success it depends on how well the voter can predict both the 
>preferences and the strategies and counter-strategies of the other voters.

This is vastly overstated. Quite simply, voters aren't going to wrack 
their brains to find the perfect, optimal strategy, because it's only 
one damn vote! Don't, I suggest, vote naively based on defective 
normalization. (I detest Ader, I love Bore, and Ader is so bad that 
even if I'd hate to see Cush elected, Ader is much, much worse, and 
I'll express that in my vote. Bad way to express it. The 10 for Bore 
is one full vote for the election of Bore, but by casting 0.8 vote 
for Cush, the vote is saying that "Bore is my favorite, but Cush is 
almost as good." If this were truly zero knowledge and the voter were 
worried about Ader being elected, this would be a reasonable vote, if 
the relative utilities are as stated. But the idea that half the Bore 
voters would have no knowledge of who the frontrunners are, while all 
the Cush voters do know this and vote accordingly, is crazy.

If those utilities are as stated, I'd have to expect that the Bore 
voters who were worried about Ader's election would surely be 
relieved that it didn't happen. But they would, indeed, possibly have 
some remorse at Bore losing, when preference analysis shows that 
voting more wisely ("strategically") would have caused Bore to win, 
and they'd see that Ader had no chance of winning, their fear was a 
false fear. So what will they do? Blame the voting system or blame 
their own ignorance?

I know that some would blame the voting system, but, really, that's 
not where the problem would have been.

First rule: start out by voting a Range or Approval system as if it 
were Plurality! It's a basic default vote, very sensible. And then 
don't vote for a frontrunner different from your favorite, unless you 
really have no preference. This is what the Bore voters who caused 
Cush to win did. They voted against their interest, in the name of 
"honesty." But communications only have meaning within definitions. 
What was the definition of the 80% vote, such that any other number 
would be "dishonest," and then, if it has a good effect (as seen by 
this voter!), such that by allowing that good effect, we are 
"encouraging dishonesty"?

I realized that the whole concept of "sincere vote" had not been 
carefully examined by voting systems experts when I saw what lengths 
James Armytage-Green went to in order to define "sincere vote" in 
Approval such that Approval would fail the Majority Criterion. It 
became obvious to me that the cart was dragging the horse: my friend 
had decided that Approval failed the MC and was creating the 
definition -- realizing that prior definitions were inadequate -- so 
that Approval would fail. But if we craft criteria to cause passage 
or failure of particular voting systems, we are not creating 
objective criteria at all, even though they may be, once adequately 
defined, applied.

More properly, every vote in Approval is sincere unless it reverses 
preference, i.e., unless it is "insincere," which is easily defined 
by preference reversal. Approval votes, however, conceal preference; 
but they only do so voluntarily (i.e, the expression of preference on 
which the Majority Criterion depends is allowed, but the voter has 
been given the option of suppressing it, presumably because it is 
below some threshold). There is, however, no specific preference 
strength below which equal ranking is "fully sincere," nor above 
which equal ranking is "insincere." Rank lumps together massive 
preference strength with barely detectable preference.

In Approval voting, the voter "sincerely" divides the candidates into 
two classes, with every member of one class being preferred over 
every member of the other class, or the voter votes insincerely. And 
Approval never rewards that insincerity with improved expectation of 
outcome, and that is why Approval Voting was originally called 
"strategy-free" by Brams.

The situation gets more complicated with Range, for sure.

>I don't really agree, though perhaps we can focus on the strategy 
>problem for not. The substance of my disagreement is again twofold, 
>one being that as a voter, I don't have any idea of what the scale 
>is. Translating a list of 30 policy statements, of more 
>or--probably--less credibility into a numeric value is something I 
>don't know how to do. The second is the comparability of my scale to 
>other voters.

Sure. Has it been said that voting should be easy when there are 
complex issues? What do you do when there are 30 candidates? There 
are 23 in some San Francisco supervisorial elections. Tell you a very 
simple answer: pray for Asset Voting.

Let an expert, one you trust, make the decision for you. Vote for 
your favorite candidate, basically, then let your candidate 
participate in deciding, if not already elected. Why not?

>This problem is independent of strategy. If, by some miracle, we 
>could come up with some sincere and objective utility rating of each 
>voter for each candidate, then it'd be trivial to maximize some 
>utility aggregation function (though we'd no doubt have an argument 
>about how best to aggregate). But those ratings, for all practical 
>purposes, don't exist. So I'm content to focus on the strategy problem.

We can impute and simulate ratings, but we cannot assume that they 
will be expressed in elections. What's been done with Range is to 
assume an equivalent to one-person, one-vote, that satisfying each 
voter is of equal importance to satisfying every other voters. But 
there is another consideration: I'll call it real motivation. Some 
voters are actually apathetic. They may know that they prefer A over 
B, but they won't contribute, for example, to the election of A. They 
don't care enough to do it, or to otherwise work for it, it doesn't 
have to be money. They won't show up in a special runoff election. 
This betrays an absolute preference strength, or lack of same.

In generally, assigning a cost to voting will cause an expression of 
real preference strength, and this is commensurable, though accurate 
measurement could certainly be difficult.

In the end, what people do with voting systems is to vote.