At 08:36 PM 9/17/2005, Rob Lanphier wrote:
My understanding of the argument made to Condorcet
advocates is that Range has a much higher probability of picking the
Condorcet winner than other methods of equal simplicity (e.g. Cumulative
voting, Plurality, Borda). However, it's difficult to explain the moral
appeal of Range without explaining Condorcet.
The claim is a bit suspect. It would depend greatly on the conditions
of the election. Range methods in general would tend to select a
winner with broader support, Condorcet-compliant methods *will*
select the single most popular candidate, the winner of all pairwise
elections. The philosophy, actually, is quite different. However, in
many elections the approval winner will be the Condorcet winner. The
real question is who the best winner is for society, and to answer
that I think we need to look at the foundations of democracy itself.
Consider
45: A>B>>C
45: C>B>>A
10: C>A>>B
The pairwise elections:
A:B 55:45
A:C 45:55
B:C 45:55
C is the Condorcet winner. However, the Approval winner (assuming
that the voters vote approval as shown) is B by a landslide. The
Approval votes are:
A: 55
B: 90
C: 55
There seems to be some sort of idea that the Approval winner would be
some sort of "lowest common denominator," with the implication that
such an obvious wimp must be inferior. Yet to convince 90 percent of
the electorate that one is an acceptable candidate is hardly a small
achievement. I see no reason to believe that Approval will elect
inferior leaders; quite the contrary. One may become the Condorcet
winner by stirring up partisan fever.... and the value of this to
society is, shall we say, doubtful.
There are a lot of details in how Range would be implemented that
could be critical. I've preferred to stay with the simplest Range
system, basic Approval. I'd add to that the ability to specify a
preference, but if you *use* that information in the election, you
end up with something that could be less satisfactory. Whatever is
done, it should be made crystal clear to the voters. If that
additional option was added, my own preference would be to clearly
state that the preference information would not be used to determine
the winner unless there was a tie in the approval vote. Voters should
know that they may mark as many approved candidates as they like. And
they should also know how marking multiple "preferred" candidates
would be treated (again, as I'd have it, it would not affect the
election outcome, but it could affect public campaign funding, and it
would also provide information for future use, for the voters and for
analysts.)
Other downsides of Range are:
1. It only tends to pick the Condorcet winner. Since Condorcet systems
pick the Condorcet winner by design, that makes them naturally more
appealing by that logic. If you get people bought into the utility of
picking the Condorcet winner, you'll be over halfway to convincing
people to use a Condorcet system.
Of course. If you want to pick the single most popular candidate, you
want the Condorcet winner. The philosophy is different, quite
different. Sometimes the Condorcet winner is also the Approval
winner. Such a winner is pretty obviously the best possible winner!
It is when they differ that the questions arise.
My own opinion is that any organization is weakened when it is led by
a winner who enjoys only the support of a weak majority of the
members, not to mention the support of less than a majority. The
former situation qualifies as democracy, in my opinion, but barely.
The latter seriously stretches the definition. We do not have
government by consent of the majority if the majority did not consent to it!
2. Range voting is particularly vulnerable to criticism of violating
"one person, one vote". Granted, everyone has the same opportunity, so
personally, I don't put that much weight into the argument, but I have
to concede that some votes influence the vote total more than others.
In cases where the Range winner isn't the Condorcet winner (where a
Condorcet winner exists), it's really difficult to make the case that
one person, one vote hasn't been violated.
I've written on this very many times. The only voting method that is
not vulnerable to some kind of charge of violating the one-person,
one-vote "rule" is plurality. All other methods allow voters to cast
more than one vote in a single winner election. However, aside from
cumulative voting, which is not on the table (except in the
reassignment phase of Asset Voting), none of the methods allow more
than one vote to be active at one time.
In Condorcet, the candidates are considered pairwise. With respect to
each pair, only one vote is effective, unless the voter equated the
two, in which case the vote is moot, it has the same effect as if the
voter had abstained (except the totals are higher, which might have
non-elective effects, and quite rightly so). The same is true of
Approval. If Approval violates one-person, one vote, so do Condorcet
and IRV and all the other methods. IRV doesn't look like it violates
it by pretending that there are a series of elections, and only one
vote may be case in each. But the same kind of isolation takes place
in Condorcet and Approval. Only one vote has elective effect, in the
end (in single-winner). You can easily see this by considering an
Approval Election. Take the voters who cast more than one vote, and
eliminate all the votes they cast that were not for the winner. The
election result does not change. Only one vote actually affected the result.
But, of course, the voter does not know which of those votes is going
to be the effective one, if the voter votes for more than one. (If
any of them are effective.) This is the same with the ranked systems.
In IRV, the voter essentially votes for the favorite, then says, if
the favorite is not elected, I vote for B. In Approval, by voting for
two, the voter indicates, if A is not among the top two, then I vote
for B, and if B is not among the top two, then I vote for A. And if A
and B are the top two, never mind. I might wish that I hadn't voted
for both of them, but my consolation will be that the outcome will be
more satisfactory to me than any of the other alternatives!
3. If you try to explain why Range is superior to current plurality
systems without explaining Condorcet, you're going to have a hard time
explaining why it's superior to Cumulative voting.
The meaning of Cumulative voting in public elections is less than
clear, but I would assume that it would mean that all voters would be
given a certain number of votes to cast. They may cast all of them
for one candidate, or they may spread them out. I have not been
considering Cumulative voting for public elections, but there is
nothing intrinsically offensive about it, *providing* that all voters
get the same number of votes. And this is the *real* meaning of
one-person, one-vote. It means that all voters are equal. I would
also say that it *should* mean that all votes are equal, but our
election systems generally waste votes. Votes cast for losers are
wasted. To some degree this is inevitable in single-winner, but it is
not inevitable with proportional representation created through Asset Voting.
And Asset Voting would, as I mentioned above, be Cumulative in the
reassignment phase.
Cumulative voting is
much easier to justify in terms of "one person, one vote", and the
benefits of Range voting over Cumulative voting aren't obvious getting
very deep into the mathematics of voting (and getting you back to
criticism #1). The downside is that Cumulative voting is barely an
improvement over Plurality.
I have not seen a good analysis, so I don't know the basis on which
this claim is made. Cumulative Voting as a secret-ballot election
method is probably about the same as plurality, though, I would
guess, except when used multi-winner, in which case it should produce
better minority representation. But I have not studied Cumulative
voting in that context. In the Asset Voting context, the revoting
would be public and theoretically subject to negotiation and a whole
deliberative process.
Worse, I'm afraid that we could be 90% of
the way to getting Range implemented, and have some well-meaning but
sadly mistaken politician make a last minute "tweak" to the system
unwittingly turning it into Cumulative voting.
This problem would exist, if it exists, with any voting reform, it is
beyond me why this fear would exist with respect to Range alone.
I didn't just pull the Cumulative voting idea out of thin air. I was
trying to explain Range to my wife (whose only expertise on this is by
unwilling osmosis), and explain the one person, one vote problem. She
countered with "well, why don't you just limit the total number of
points each person gets to vote?". I think that in the face of heated
political opposition to Range, this will be a common reaction. So, I'm
countering your sample of one with my own sample of one. ;-)
Garbage in, garbage out. The wife, quite understandably since her
husband doesn't seem to understand the one-person, one-vote issue,
also did not. So the solution was a solution to a non-problem. Yes,
limiting the number of points would radically change the system,
defeating the whole rationale behind range. But it would not be worse
than plurality. But probably not much better, either, if at all.
My understanding is that FBC is mutually exclusive of the Condorcet
winner criteria. As I've stated above, when Condorcet winner is
violated, there's a good chance that one person, one vote has been
violated.
What happens in the example is that some people, able to cast a full
vote, cast only a fractional vote. Therefore they seem to have fewer votes.
Example: Range vote of 0-5 (integers only). 1000 voters, 2 candidate
(A and B)
800 votes:
A: 3
B: 2
200 votes:
A: 0
B: 5
Total:
A: 2400
B: 2600
B wins, despite the fact that A would win 800-200 in a head-to-head
matchup. This is because the B>A voters receive 5 net points per voter,
while the A>B voters are only getting 1 net point per voter.
Because the A>B voters wasted their votes, failing to understand that
the ratings in Range are relative, not absolute. Because some voters
would not understand that they are half-way staying home if they
don't vote the maximum range, I have suggested that Range Ballots be
normalized before being used for totalization. The raw ballots would
still be available for informational purpose, so if someone was
voting, for example, their "favorite" as, say, 2, and the rest as 0
or 1, their statement would not disappear. But the ballot would be
normalized, i.e., the votes would be counted in this way:
800 votes:
A: 5
B: 3.333
200 votes:
A: 0
B: 200.
Totals:
A: 4000
B: 2666
Looks better, doesn't it?
This would be a clear violation of one person, one vote in most people's
eyes (including my own). Granted, the A voters weren't voting with
optimal strategy, but that gets back to the strategy criticism I have
with Range.
I'd highly suggest spending a little more time with Range. This stuff
has been discussed at some length on the Range Voting list.
The ballot instructions might ask voters to place their favorite (and
any equals) in the maximum rating. That rating might even be called
"Favorite." Or it might be called "Maximum Rating Given." It would be
explicit that the other ratings were relative to that.
Or normalization might be used without the need for such an instruction.
This problem does not exist at all in Range 2, i.e., Approval, since
you can't split the votes, you either vote (1) or you don't (0).
I will be willing to bet that there's some element of this problem in
any FBC complying method.
Without commenting on FBC, in this case the problem has not been
understood. The problem was that the voters wasted their votes, not
that they had fewer votes than others. To exercise a full vote under
Range, you must rate at least one candidate at maximum. This is
obvious, actually, if you look at what happens after the smoke
clears. Range allows you to vote fractional votes, essentially. The
maximum effect your vote will have will be the largest fraction you
vote. If you choose to only cast a 60% vote, and for some strange
reason all other voters who supported your favorite voted like that,
you get the result shown.... But normalizing the votes fixes the
problem completely.
That's not how I'm thinking of the question. I'm thinking "do I want
insincerity in rare cases, or all of the time?" I'm convinced that the
cases where insincerity is smart in Condorcet are rare enough not to
merit serious consideration. On the other hand, it seems that some
degree of insincerity is required almost all of the time in Approval
elections.
This is commonly said. It's a stretched meaning of insincerity; it
depends on assigning a meaning to an Approval Vote that Approval
Votes don't have. Approval Votes are threshhold votes. By voting for
a candidate in Approval, you are saying that the candidate is as good
as your "Approval Threshhold." Or better. You are not comparing the
approved candidates, you are making no implication that you approve
of one over another. This is not insincere.
If you were saying that they were equal, it would indeed be
insincere, if you did not consider them equal. But by Approving them,
you are not saying that. You are merely saying that you prefer the
winner of the election to come from the set you have approved. That's all.
If you add the ability to state a preference, which could have
definite benefits even if the preference votes are not used (they are
counted the same as approval, under this suggestion), you make it
explicit that you *do* favor one over another. Or, possibly, a set
over another set. But most would simply check a single preferred candidate....
I suspect there will be a strong tendency to "bullet poll" if Approval
ever becomes the norm.
Look, give us approval, and within a few years we might have FAAV,
Fractional Approval Asset Voting. As simple to vote and to count as
Approval, but it minimizes wasted votes, by allowing them to be
recast intelligently.
That seems like the correct strategy in polling
versus the general election, and it'd only be a matter of time before
the political machine discovers that and tries to reinforce that
behavior (e.g. through education of their base, and possibly even covert
smear campaigns against insurgent "extremist" opponents)
Long term (and maybe short term), I have a plan that bypasses the
"machine." But that is another topic. One step at a time.
I find the problems of Approval and Range harder to swallow. You seem
to find the problems of Condorcet methods harder to swallow. I hope
both of us can concede that our proposed methods aren't perfect, and
accept that we're choosing different tradeoffs. That's why I'm willing
to accept agreeing to disagree, short of convincing you that you've made
the wrong tradeoff.
The Condorcet vs. Approval argument will rage indefinitely until and
unless the underlying purposes of elections are examined. They really
do implement two different philosophies.
Given the number of caveats and problems with Range and Approval, I feel
that an all-out push for either would be a distraction away from the use
of Condorcet. I would hate to see use of Condorcet be delayed by a
failed attempt to institute Range or Approval voting.
Since some of the alleged problems are illusions (1-person, 1-vote,
for example), or are equally applicable to Range or Condorcet
methods, it is hard to tell which would distract from which.
I think we can all agree that both Approval and Condorcet would be
improvements over plurality. So it would indeed be a shame if either
caused the failure to adopt the other, while not being adopted itself....
I'd suggest that the election methods community needs a method of
developing and measuring consensus. That's my project, actually.
Voting methods, per se, are inadequate for this, if that is all there
is, but good methods can help.
Again, one step at a time.
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