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

[Abd ul-Rahman Lomax]

At 02:47 PM 11/27/2008, Kristofer Munsterhjelm wrote:
>For ordinal systems, it's pretty easy to consider what a honest 
>ballot would be, assuming a transitive individual preference. "If A 
>is better than B, A should be higher ranked than B". It's not so 
>obvious for cardinal systems. What do the points in a cardinal 
>system mean? We can get some measure of a honest ballot by 
>transporting an ordinal ballot into a cardinal ballot: if you prefer 
>A to B, A should have a higher score than B. But other than that, 
>what can we do? This seems to be a problem of cardinal systems in 
>general, not just a particular implementation like Range (or 
>Approval, if you consider Approval Range-1).

Yes. Preference can be determined, generally, rather easily, by one 
of two methods. The first method is pairwise comparison. With a 
series of pairwise comparisons, we can construct a rank order. 
Usually. It's possible, because different issue spaces get involved 
in each choice, that this will result in a Condorcet cycle. But that is rare.

The second method, though, bypasses Condorcet cycles, because it is 
essentially a Range method! That is, we look at the entire set of 
candidates and pick our favorite, then set this aside, having 
determined the rank of that candidate. We then look again, etc. We 
can also run this from the bottom, which of these is worst -- as far 
as we know (same restriction on the top, by the way, maybe one of 
those middle candidates is actually quite good, but we just don't 
know it yet. This is one reason why runoff voting can be much better 
than fixed-preference voting theory would predict.)

That sense, looking a collection of alternatives, that one is 
"heavier" than the others, is a Range judgment, it is not the product 
of a series of pairwise comparisons. We are designed or programmed to 
make judgments like this, rapidly. That's what Warren is talking 
about when he refers to natural systems. Range Voting is *natural*.

Determining Range Votes as numbers, though, is not natural, 
particularly. Imagine, though, the ranking process I gave, the Range 
one. I look at the set of candidates, and I start picking out 
candidates. If I'd be pleased by the election of the candidate, I 
rate the candidate +1. If I'd be displeased, I'd rate the candidate 
-1. And if I don't know whether I'd be pleased or not, I'd rate the 
candidate 0. This is a very, very simple strategy for Range 2. We've 
seen polls using this rating system, last election season, and they 
were very informative telling me, in a glance, what was going on. 
Most approved Democrat: Obama. Clinton wasn't even in second place, 
though she was close. Her vote was net negative, slightly. If you 
looked at the votes, she had lots of supporters, but lots of negative 
votes as well. On the Republican side -- you could vote in these 
polls openly, and there was no way to indicate if you were a 
Republican or Democrat -- the leader was .... Ron Paul. By far. 
McCain was, as I recall, second, though I'd need to check. If the 
Republicans had nominated Ron Paul, just about a political 
impossibility, it would have been a horse race.

It was really amazing to watch. These were major polls, conducted by 
a major news organization. Yet Ron Paul was hardly ever mentioned in 
stories about the election. Ron Paul always shot up after debates 
between the Republican candidates where he participated. The few 
mention of these polls dismissed them as being biased by hordes of 
bots, though no evidence that this had actually happened was 
presented. (I think the poll design and security made this slightly 
difficult, and my sense was that the only bias here was that most 
voters were relatively young. Ron Paul really was very popular.)

The method I gave for determining Range 2 votes uses our instincts 
for affinity and aversion. We are attracted by some and repelled by 
others, and some are neutral for us. As described, those would be 
sincere Range votes, Range 2, easy to determine. Now, we do know, 
usually, who the frontrunners are. If we care about casting an 
effective vote, as distinct from a purely sincere vote, which may or 
may not be effective, we'll look at how they fared in our ratings? If 
they are all in the middle or bottom group, we need to decide whether 
or not to shift the middle! This is a decision, setting what is quite 
equivalent to an Approval cutoff, only a little more sophisticated.

It's not a sentiment. Range Votes, like Approval votes, are decisions 
as to where to add weight, they are votes, not "opinions." They have 
an effect from the weight, not from the "sincerity." A "sincere" vote 
can be quite foolish, or it can be very helpful. It depends on the context.

So if we have not voted +1 for a frontrunner, and -1 for a 
frontrunner, we may want to shift our favored frontrunner to +1, and 
the worst to -1, and we may then move to +1 any candidate we prefer 
to the frontrunner to the same level, might as well. Likewise we'd 
move to the -1 pile any candidate we dislike more than the disliked 
frontrunner. We'd leave the rest in the middle, which includes 
candidates we don't even recognize their name.

Now, this is range with a default vote of 0, equivalent to midrange 
in 0-N systems. This is an alternative to default 0 (sum of votes 
range) or default abstention from rating (average range, it's 
called). I don't know if it has been specifically studied. If the 
rules require that a majority of voters rate a winner above zero 
average (which in this method is identical to sum of votes 0), then 
it's quite safe to mid-rate unknowns. It neither pulls up nor pulls 
down their ratings, and the ratings have an obvious meaning.

Compared to my expectation, a plus rating is better, a minus rating 
is worse. It would be easy and instinctive, and strategic votes would 
not be much different from sincere ones, i.e., raw expression of 
affinity or aversion. All that has happened with the strategic votes 
is that the center has been shifted to reflect our understanding of 
election probabilities.

To follow how this kind of thing has been expressed by others, the 
strategic Range votes show how a candidate compares to our expected 
election result. Better, worse, or no opinion, no preference that I 
could express with any clarity. The "sincere vote" is raw, 
instinctive, and doesn't consider probabilities, or at least not as much.

There are other means for using higher resolution Range, but ... 
folks, it's hard enough to get Range 1. As to higher resolution 
Range, the present efforts should be to push it for polling, where it 
clearly shines. Those poll numbers could be rather directly 
translated to votes in any other voting system.

>Thinking further, it would seem that cardinal systems can solve it 
>in two ways. Either the points are in reference to something 
>external ("how much would I like that X wins in comparison to that 
>nothing changes from status quo"), or it refers to a subjectively 
>defined unit ("how much do I 'like' X" for an individual definition 
>of "like"). I think ratings, as commonly (and intuitively) used, are 
>of the second part, but that leads to problems with the aggregation 
>of the points. If one voter likes many things and another likes only 
>a few, how do you compare the two preferences? Ranking gets around 
>that since it only asks about relative information (though one could 
>argue there's a very weak form of this problem with equal-ranking; 
>how different does your opinion have to be of two candidates before 
>you no longer equal-rank them?).

Range 2 can simply use affinity or aversion to provide a three-step 
classification. It can start out absolute, i.e., we don't need to 
consider the candidate set, that's how I described it, I think. Then 
it can be shifted -- or it could start out -- as preference over 
"status quo" or "expected election outcome."

All of these votes are sincere, in a way. Only the "raw" affinity or 
aversion method, though, is non-strategic. It need not know what the 
context is. But that's not how we make decisions!

For Range 4, we have 5 ratings. We could, again, set them as -2, -1, 
0, 1, 2. We classify the candidates as before, into positive and 
negative and middle. Since we are deciding how to vote, we might as 
well begin with a comparison to expected outcome: how pleased would 
we be by the result? That question takes into account what we expect 
will happen if we don't vote. We first categorize results into Good, 
Middle, Bad. *in comparison to what we expect.*

Then we'd look within the plus category, of it's going to be one of 
these, which would be the best? We could make the Borda assumption, 
and simply divide them in two, a better half and a worse half. Again, 
we would not violate preferences in doing this, and we might treat 
clones as if they were a single candidate.

And then we have our strategic consideration to make or not make. Do 
we shift the votes to improve the expected effectiveness of our vote?

When it comes to public Range elections, I'd expect that there would 
be some good guidance available on how to vote effectively or 
sincerely, and a discussion of the implications of each.

But, in the end, these are just votes. In Range 4, you can vote from 
0-5 for any candidate, so each step is 0.2 vote. The candidate with 
the most votes wins. Everyone should know that.

Please, please, drop average range and the quorum rule. If you want 
some chance for dark horses, use a positive/negative system with the 
default vote at zero.

Want a quorum rule, though, there is already one widely accepted: a 
majority of voters must approve the candidate. You simply need to 
define that. In Range 4, as described, it can't be 0, but it might be 
+1 or higher. (That's because 0 is used for the default, so +1 is 
"better than the default.")


>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.

We don't really have the problem. If voters intelligently optimize, 
they will still come up with good results, with a good method. That 
ought to be obvious, actually. Range, optimized, is either sincere or 
Approval, which, optimized, is simply Plurality (or, ideally, 
Majority, i.e., runoff needed if no majority). Because the problem of 
vote-splitting has been fixed, the results should be good.

I've elsewhere argued that there is a paradox in assuming that an 
particular Approval vote is strategic rather than insincere. What is 
a "strategic" Approval vote?

There are two possibilities:

A voter dislikes a candidate, but votes for the candidate because the 
candidate is a frontrunner and the sincerely "approved" candidates 
are not. I.e., the voter supposedly has a relationship of approval 
with a set of candidates, having nothing to do with context. In the 
classification above, this would be pure affinity.

However, this flies in the face of how we make actual "approval 
decisions." We compare a possible choice with our expectation. If the 
choice is better than our expectation, we accept it or approve it. If 
it is worse, we do not. *This is ordinary approval, the ordinary 
meaning.* It is a *relative term*, but because of certain linguistic 
habits, we ascribe it to the object instead of to our own comparisons.

My daughters are learning violin. When they play well, I "approve" 
it, I give them lots of praise. Is that intrinsic to the playing? No, 
it is a relationship with what I expect of them. A year from now, let 
one of them play exactly the same, and I might wince. (It's Suzuki 
method violin, so I might try not to literally wince, but, I'm sure, 
my effusive praise will be working a bit harder to find an excuse....)

The assumption that we have, unconnected with expectations -- i.e., 
of probabilities -- some "approval" state that we can simply realize 
and mark on a ballot, is sloppy thinking. So imagining that there is 
something off about explicitly considering probabilities is, again, 
even more sloppy.

Would I approve of Ron Paul for President? Depends on who else is 
running! Bush? In a flash! Obama ... at one point I thought that 
might be more difficult. However, that was before I saw the loaves and fishes.

(Folks, we need to watch Obama like hawks, precisely *because* he 
seems so good! That's when it's really dangerous.)