[EM] Re: Condorcet's strategy problem

[Abd ulRahman Lomax]

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.