[EM] Why the concept of "sincere" votes in Range is flawed.

[Abd ul-Rahman Lomax]

At 06:30 PM 12/1/2008, Jonathan Lundell wrote:

>I don't really see a need for equal-ranking in a single-winner
>election. As a voter, I'm answering the question "if you were
>dictator, of this set of candidates, who would you choose?". I don't
>really need the option of naming two candidates to the same office; if
>I really have no preference between them, I can flip a coin, or choose
>the tallest, or ugliest, or whatever.

Odd, in fact, this is the way a "strategic voter" thinks. I.e., "if 
this election turns out to be close, and my vote can decide it, how 
should I vote?

If you have no preference, why do you vote at all? By flipping a 
coin, you are simply adding noise to the system, with no expected 
value to yourself, but it might harm others.

My question is not whether or not Jonathan Lundell needs equal 
ranking, but whether or not we should *prohibit* voters from 
equal-ranking. We do it now, in the U.S., and the result is a lot of 
spoiled ballots, for starters. The result is spoiled elections, for 
another effect. None of this explains why it is prohibited. Why? If a 
voter decides not to make a choice between two candidates, but to 
support both of them, why should it be prohibited? What's the harm? 
The voter is adding voting power, yes, but at the same time the voter 
is losing voting power. The voter is voting in more pairwise 
elections (with one vote more), but is abstaining from a pairwise 
election, between the two candidates. These are really alternative 
votes, effective simultaneously. I.e.: If A isn't going to win, 
please count my vote for B. And if B isn't going to win, please count 
my vote for A. It's like preferential voting, but symmetrical. And, 
of course, this action effectively abstains from deciding between 
those two candidates, but does contribute toward a majority for 
either, as the winner, if that is needed.

Why should it be prohibited, why should we discard the expressed 
votes of someone who votes for more than one candidate in a 
single-winner election?


>>I guess what I'm trying to say is that the problem of discerning a
>>honest vote from a strategic (optimizing) one seems to be inherent
>>to all cardinal methods, because we can't read voters' minds. That
>>is, unless the external comparison can be made part of the ballot
>>itself.
>
>I suggest that the problem is worse than that: that the voters can't
>even read their own minds, in this sense. Suppose that I would have
>ranked Edwards > Obama > Clinton in the recent US primaries. Fine, I
>can make Edwards=100, but I really don't have the foggiest idea what
>it would mean to make Obama=75 as opposed to Obama=50. Do I like
>Edwards "twice as much" as Obama? What can that possibly mean? It
>seems to me that range voting (including approval) immediately reduces
>to a purely strategic exercise. And what I'd prefer to do is to
>eliminate (to the extent possible) the motivation to strategize at all.


We can tell that you have not really considered Range Voting much. 
You've left out a totally critical piece of information. Two, 
actually. You haven't described the candidate set, and you have not 
described which candidates you thought were in range of winning. You 
don't need that second piece of information to decide how to vote, 
and certainly it doesn't need to be very accurate, but it makes 
deciding how to vote much easier, and, at the same time, makes it 
more effective.

So I'll describe how to "sincerely rate" three candidates. When those 
are the only choices, or, we might suggest, the only realistic ones. 
Doesn't this simplify the problem? I.e., there are twenty candidates, 
how the BFH do you rate them all? Answer. You don't, except to 
classify the unimportant ones or the ones you don't know. I'd either 
classify them bottom, in most Range methods, or maybe at default 
(midrange) in some.

You only need to determine a vote for realistic candidates. You can 
add any others and how you vote exactly, will depend on the Range 
implementation.

I'll assume Range 100. But I won't use all that information.

First of all, I'd vote for my favorite at max. I'm going to assume 
that my Favorite isn't one of the three!

Favorite 100.

Now, I'll look at the "important" candidates. Do I want to 
participate in the choice between them? If so, that's exactly what I 
will do, with (almost) one full vote;

Okay, Edwards>Obama>Clinton.

Edwards, 99
Clinton, 0.

If I want to express that I like Clinton better than some on the 
ballot, I might rate Clinton at 1. These are votes, the word "rating" 
is misleading. In Plurality, remember, I'd vote for one -- which one? 
my favorite or Edwards. That is the same as max rating one and rating 
at 0 everyone else.

Range Voting is just Approval Voting with fractional votes allowed. 
Allowed, not required. Just as Approval is Plurality with 
simultaneous votes allowed. Again, Allowed, not required.

Where to rate Obama. At 100%, jerk! -- just kidding!

Which would I consider more important, that Edwards beat Obama or 
that Obama beat Clinton, if it was a tossup which of these elections 
was the real one, the one that counts, the one where my vote counts?

In other words, roughly, *how much better is Edwards than Obama, or 
Obama than Clinton*.

You only have one vote to spread out, you want to put most of it 
where it is most likely to do some good. That would be, 
zero-knowledge, in the election pair where you care the most.

But remember, this is only one vote. Vote approximately, that's all 
that is needed. But, of course, if you know which of these pairwise 
elections is the one that will really count, you can simply vote in 
that one. With Range 100, I would always preserve preference order, 
there isn't sufficient loss of voting power to outweigh the 
satisfaction and other values to indicated whom I prefer, if I have a 
preference. Even if my preferred candidate has zero chance of winning.

(Pure von Neumann-Morganstern utilities would show infinitesimal 
difference in rating with infinitesimal probability of winning. It 
would put all the voting eggs into real baskets.)

(Somebody tell us how to calculate von Neumann-Morganstern utilities 
from absolute ones, okay? I'm too lazy to figure it out at the moment.)

So: how could I estimate my preference strengths? I'd start by 
midrating Clinton. That's a Borda count vote, and Borda is quite a 
respectable method. To vote Borda, in Range, I'd suggest considering 
clones identical, they will be rated the same because you have no 
preference between them. By definition. This is one way that Range is 
superior to Borda; Borda with equal ranking allowed *is* Range (that 
is, as many ratings as there are candidates, so if one equal ranks, 
there is a rank emptied each time one equally ranks. Then distribute 
the candidate sets though the rating space. In this case, three 
candidates, we've already placed one at max (almost), the other at 
min, so Obama goes at 50%. You could leave it at that. How does it 
look? Is Obama better or worse than "in the middle? If so, nudge it 
until it seems better. Already, you are deciding less than one-half 
vote. One vote isn't a big deal, in public elections, how much is one 
half vote, or one-fourth vote?

Now, I made it simpler by considering that the three were the only 
viable candidates. If there are more, again, and you want to vote 
zero-knowledge, sincere, starting with a Borda vote is quite 
reasonable. Group together candidates that seem equally good or bad, 
you will get more reasonable ratings. And spread them across the 
space in preference order. And then nudge them if it doesn't seem 
reasonably expressive of how you feel or judge them.

Your vote is going to be averaged together with many other votes. 
It's like a guess. Large numbers of people making a guess that is 
averaged together can come up with surprisingly accurate results, 
under the right conditions.

You could get a little more sophisticated. How much would you be 
willing to contribute to the election campaign of each of these. I'd 
guess, for the primary, that you wouldn't send money to Clinton. 0. 
If she was the candidate for the party, that's a different thing. 
*Range ratings are relative, not absolute. Voting 0 for Clinton does 
not mean that you detest her. It just means that, in this election, 
you are not adding weight to her as a choice. You *certainly* are not 
enthusiastic about her. So how much would you be willing to 
contribute as a campaign donation to either Edwards or Obama, suppose 
you can't tell which it will be, but it will be one of them. Say the 
money goes to a Dump-Clinton PAC. Let's say, $100. Okay, you actually 
are going to contribute this, right? This is sincere, and the actual 
donation proves it. Except that, of course, you are going to divide 
up the money between them. Where do you send your $100? If it goes 
entirely to Edwards, you are an idiot. Sorry, got carried away.

But seriously, if you've decided to send it all to Edwards, that's 
where your vote should go, too, I'd suggest. They are the same thing, 
both help advance a candidate, and you prefer Obama to Clinton, so, 
really what's that worth to you. Sending all the money to Edwards 
means it isn't worth anything to you.

Already already. $80 to Edwards and $20 to Obama. (Imagine, you'd be 
able to tell your grandchildren that you did, in fact, send a 
contribution to the Obama campaign, before he was the Democratic 
candidate.) You'd want to assign your sincere vote to the same 
relative value. But Edwards is at (almost) 100 rating. So both votes 
would be increased proportionally from the relative dollar value 
Edwards 99, Obama, 25.

If that seems too low for Obama, maybe you should reassess your 
contribution ratio.

Look, there are many ways to do it, and they are all fine, except one 
thing should be understood. To the extent that you don't vote the 
full range for the set of reasonable winners, you are abstaining from 
the real election. Range is just a more sophisticated version of 
Plurality, after all. You want to exercise full voting power, vote a 
full vote. Want it to count, to actually have a chance of influencing 
the outcome, vote it for a candidate who can win. Think that this is 
circular. Fine. Vote with pure sincerity, don't worry about who will 
win. But, note, I had you vote 100% for your Favorite. You could not 
do more for that candidate, except that you might consider derating 
Edwards; the problem is that, by the conditions set up, your favorite 
winning is really impossible. Polls can be off, but not *that* far. 
So the vote would be merely symbolic.

Probably the simplest method, if one has any difficulty, is to use a 
Borda method, spread the candidates, in preference order, across the 
Range. Saari will think you are a genius, and I'm sure he won't mind 
that you, while you are at it, fix the little ICC problem that Borda 
has. (Borda is vulnerable to manipulation through clones. It's fixed 
with equal ranking. In fact, allowing equal ranking does nice things 
to just about every voting system. It would make IRV much better. 
Think about it: the voter could vote Approval style. Or IRV style. 
Voter concerned about Later No Harm? Fine. Guarantee it. Only three 
ranks on the ballot, but you'd like to show support for a fourth 
candidate? Fine, add another vote in third rank. Or shove two 
candidates into rank one or two.

Most voters won't do it and won't need it, but the few percent who do 
can sometimes improve election results greatly *and they will not harm them.*