[EM] Re: Condorcet's strategy problem

[Rob Lanphier]

Hi Mike,

I should be really clear here if I haven't stated this already.  If I'm
only considering the final outcome (not looking at it with my electoral
reform strategist hat on), my range ballot for voting systems looks
something like this (scale of 0-5):

Condorcet methods*: 5
Range Voting, Approval Voting: 4
...
Plurality: 0

* I'll refer to Schulze(wv), Tideman(wv) et al as "Condorcet" for the
rest of this email for the sake of simplicity.

I think Range and Approval are both acceptable, even good, systems.  I
just don't think they're the best.  I also think that Range and Approval
have enough political liabilities that they are no more viable than
Condorcet methods.

One way to think of it as this: if someone gave me the ability to
dictatorally declare Range or Approval as the new system over the status
quo, I'd do it.  However, if instead I was put in charge of a foundation
with a budget of $250 million (i.e. large, but not infinite...Kerry
spent more and lost), I'd spend all of that money on a good Condorcet
method.  I think Condorcet methods are at least as politically viable as
Approval or Range, for reasons I describe below.  Given that I think
that Condorcet methods are superior, that's the tiebreaker in my mind.

On Sat, 2005-09-17 at 04:52 +0000, MIKE OSSIPOFF wrote:
> [SFC, GSFC, Condorcet's Criterion, and Smith Criterion compliance is]
> why I suggest BeatpathWinner or CSSD for organizations and committees.
> 
> But Condorcet has two problems with the public: 1) It doesn't have RV's 
> familiarity and obviousness; and 2) It doesn't meet FBC, so you can't 
> emphatically assure someone that they have absolutely no reason to vote 
> someone over their favorite

Range Voting is more mechanically obvious than Condorcet.  However, it's
not morally more obvious.  The moral justification is bound up in the
abstract concept of "utility", which is very difficult to measure fairly
in aggregate.  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.  

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.

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.

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.  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.  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.

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.  ;-)

4.  Strategically speaking, it's not simple to explain what the optimal
strategy is.  There's an interesting conversation occuring on Wikipedia
which indicates that Range strategy isn't the same as Approval:
http://en.wikipedia.org/wiki/Talk:Range_voting#My_Sep_12_edit

The implication from the simulation that Boris Alexeev posted is that,
given a utility "u" ranging 0-1, and a range "r" ranging 0-1 (where
fractional votes are acceptable) you should vote r=u^2.  Of course, it's
very dangerous to come up with a formula based on just this example, and
probably doesn't hold when negative utilities are involved, but it's
interesting food for thought.

> [Rob:]
> 
> [Voting sincerely is] certainly not nearly as risky to
> vote sincerely for your favorite in Schulze(wv) than it is in Plurality.
> 
> [Mike replies:]
> 
> Yes, that's for sure. The threat that that will let the greater-evil win 
> isn't as great when it only happens in rare examples. Surely there will be 
> many who won't be compelled by that threat. And equally surely there will be 
> some who will be. No one can say how many. Maybe  what I've observed of LO2E 
> progressive Condorcet voting would actually be rare, and has unduly scared 
> me. Who knows? But one can only go by what one has observed.

I think you should attempt to make more observations before entirely
discounting Condorcet methods for public elections.

> Good enough, and maybe many others would feel that way. But what's wrong 
> with the FBC-complying rank methods? ...Aside from the fact that no rank 
> method has RV's familiarity or simplicity?

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.

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.

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 will be willing to bet that there's some element of this problem in
any FBC complying method.

> [Rob replies:]
> 
> It's a matter of degrees.  Under Approval, the voter is saying that both
> Kerry and Nader are equally acceptable.  For that matter, they may even
> have to say McCain or Giuliani is just as acceptable if it means beating
> Bush.
[...]
> While that may not seem as bad as saying that Kerry is better than
> Nader, in my mind, it's only a question of degree of insincerity.
> 
> [Mike replies:]
> 
> Of course. I haven't denied that either. But do you want a higher degree of 
> insincerity, or a lower degree of insincerity? 

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.

> Besides, there's a very big 
> difference between the results of those two levels of insincerity. For one 
> thing, when the defensive strategy involves voting someone over your 
> favorite, it only takes half as many mistaken compromisers to give away an 
> election, as compared to Approval or RV.

This is an interesting argument, that I'll have to consider further.
However, it also points to the reason why I believe that burying your
favorite in a Condorcet election is not as compelling as you make it out
to be.  It just doesn't seem like a good strategy.

> And, when voters are burying their favorite, they're completely concealing 
> their support for him/her.

Not true.  Ranking a non-frontrunner over any frontrunner is quite a
visible statement.  If a majority of voters do it, then the election
results could yield the surprising result of:

1st place:  B: Compromise frontrunner candidate
2nd place:  A: "Non-frontrunner" candidate, who just beat one of the
frontrunners
3rd place:  C: Supposed frontrunner, who was so bad that he/she/it
couldn't even beat A

For example, if Nader would have pairwise beat Bush in 2000, that in and
of itself would have been a pretty big deal, even if Gore had won.  The
closer that a non-frontrunner comes to beating a frontrunner, the
stronger the statement, despite any burying that goes on. 

>  In Approval or RV, they'll still give full 
> support to their favorite. No, your LO2E compromisers won't express that 
> they like Nader better than McCain. But they'll show that at least they're 
> supporting Nader as much as anyone. That allows Nader to maybe outpoll the 
> Republican, giving progressives information about whether or not they really 
> need the Democrat. That doesn't happen when they've completely buried their 
> favorite.

I suspect there will be a strong tendency to "bullet poll" if Approval
ever becomes the norm.  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) 

>     [Rob continues]:
> >We'll have to agree to disagree, because [absolute avoidance of favorite 
> >betrayal] is not my goal.
> 
> [Mike replies:]
> Ok, but when people are afraid to show full support for their favorite, 
> "Democracy" becomes a joke.
> 
> [Rob replies]:
> 
> "Full support" means being able to express which candidate I
> like /better/ than any other.
> 
> [Mike replies]:
> 
> That's a semantics quibble. If you give Nader the highest possible rating, 
> that could be called full support, even if you give that full support to 
> McCain too. If you don't call that full support, then maybe I should find 
> another word for what I mean. Maybe just "highest rating".

Taken to its logical conclusion, you're saying "under Condorcet,
Democracy becomes a joke".  I know you don't mean that, but I find it
hard to concede that it's a mere semantic quibble in the face of that
conclusion.

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.

> But sure, the McCain & Nader Approval vote doesn't fully express how much 
> you prefer Nader. But it does so better than the McCain>Nader>Cheney 
> Condorcet ballot. As you said, it's a matter of degree.

I really find it /extremely/ unlikely that it would ever come to that.
There would be at least one "so-called liberal" in the running.  So, the
worst case for progressives would be Kerry>Nader>McCain>Cheney, and
would likely be something like Feingold>Nader>Kerry>McCain>Cheney.  It
would be hard to imagine that McCain would be the most likable credible
frontrunner for a hard-core progressive to vote for as a compromise.

I also think someone whose sincere preferences are
Nader>Feingold>Kerry>McCain>Cheney should vote that way in a Condorcet
election.  In all but the rarest of situations, it's the right decision,
and as you've pointed out, it doesn't take much of a strategic
mis-compromise to give away an election.

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.

Rob