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.)
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