[EM] Condorcet strategy

[James Green-Armytage]

	In this e-mail I’m replying to Markus Schulze, Dave Ketchum, Fan de
Condorcet, Dave Ketchum, Adam Tarr, Eric Gorr, and Mike Ossipoff!!!

	For public elections, I'm recommending the following procedure.
1. Ranked vote. Pairwise tally. If there is a Condorcet winner, they take
office.
2. If there is no Condorcet winner, non-members of the Schwartz set are
eliminated from further consideration. In addition, there is a period of
time between votes where any member of the Schwartz set has the option of
dropping out of the race and removing their name from the second ballot.
3. A second ranked vote takes place. The Condorcet winner or completed
winner of the second vote takes office.

	I’ve discussed this topic on the list before at the following times:
	I first brought up concerns about Condorcet strategy on August 17, in a
thread called "serious strategy problem in Condorcet but not in IRV?" I
don't remember there being any consensus at the time that the strategy
problem was not in fact very serious.
	On December 17th, I re-organized my thoughts on this matter into a
posting called "a strategic problem and possible remedy for
Condorcet-efficient voting methods." (Which also exists on my web pages
now.) At that point I proposed the multiple-round procedure. There wasn't
much comment on it at the time, although some time later Mike Ossipoff and
I discussed it to some extent. He suggested that a two round procedure
would be adequate to solve whatever strategy problems existed in
Condorcet, although such a measure would be basically unnecessary because
such problems are not very severe. I have taken that into consideration,
and I wrote a posting on May 27 saying that while I still believe the
strategy problems to be severe, I am willing to accept a two-round
procedure as the best that we could realistically hope for in a public
election.

	There are basically two things at issue.
1. How serious is the strategy problem in Condorcet? Is it serious enough
to justify another balloting? Is it serious to render single-balloting
Condorcet less stable than IRV?
2. If there is a serious problem, would the second balloting significantly
mitigate that problem?
	At this point I think that the problem is very serious, easily serious
enough to justify another balloting if such a second balloting would help,
and possibly serious enough to render single-balloting Condorcet
critically unreliable as a voting method. I'm not entirely sure about
this, but that's the way it seems to me now. As for whether a second
balloting would significantly mitigate this problem, I'm not sure, but I
*hope* so.
	(Actually there is also a third, namely: is there a way of mitigating the
strategy problem that is both easier (i.e. one ballot) and more
effective... I have my doubts about one-ballot systems, but I suppose it's
possible... anyway, I don't go into those other methods in this e-mail,
although I am open to discussing them.)

	Many people seem to disagree with me on one or both of these questions...
let's see if we can get a meaningful and productive discussion going on
the topic. Myself, I'm open-minded about the issue, and I hope that you
can be open-minded as well. This e-mail is pretty long because I’m
replying to several different messages at once.
	Some people protested the implausibility of my Bush-Gore-Nader example. I
agree that a successful burial strategy in that situation was unlikely,
and I said that at the time. Here is an example in which it takes fewer
insincere votes to execute a burial:

Sincere preferences
27: A>B
25: B>A
24: C>A
24: C>B
Pairwise comparisons
A:B = 51 : 49
A:C = 52 : 48
B:C = 52 : 48
	A is a Condorcet winner. But if just a fraction of the B voters reverse
their preferences, they can steal the election for B. 
27: A>B
21: B>A
4: B>C
24: C>A
24: C>B
Pairwise comparisons
A:B = 51 : 49
A:C = 48 : 52
B:C = 52 : 48
	The C-->A defeat causes a cycle in which the A-->B defeat is dropped. B
wins. I'm assuming that we are using 'winning votes' Condorcet. (I don't
think that switching to margins would ameliorate things here... actually I
think that margins might have worse strategy problems.)
	The only thing that the A voters could have done about this is to somehow
threaten the B voters that they will truncate, causing a result something
like this...
25: A>B
2: A
21: B>A
4: B>C
24: C>A
24: C>B
Pairwise comparisons
A:B = 51 : 49
A:C = 48 : 52
B:C = 50 : 48
	The B-->C defeat is now dropped, and C wins. For the A>B>C voters, this
outcome is not really preferable to B’s victory, and yet it represents the
only change that they can make; the only thing that they could possibly
have done to prevent the B voters from stealing the election.
	But what good is there for the to A>B>C voters to threaten to truncate?
That is, they wouldn’t be able to truncate *in response* to a B voter
order-reversal maneuver, because by the time the maneuver had taken place
the election would be over! 
And if the A voters just truncated no matter what, then they would risk
more trouble. 
Let’s assume that no one is sure before the election who will win the A:B
comparison, and whether both A and B will sincerely beat C. If the A
voters truncate under those circumstances, they are risking giving the
election to C, even if no one else votes insincerely (that is, if B is in
fact the only one who sincerely beats C). 
Plus, even if it turns out that A and B both win their sincere comparisons
against C, but both A and B voters truncate out of suspicion that the
other group will truncate or reverse, then C can easily come away with the
victory. In this sense, the election begins to  resemble a chicken game,
where the worst outcome for A and B voters is for both group to truncate
or reverse, but the best outcome for each group is often for their group
to use strategy but for the other group to vote sincerely.
It’s a mess. What makes it worse is the difficulty of communication. Even
if A and B themselves speak out against strategic voting and encourage
cooperation between the two factions, there might still be some hard-core
A and B fans out there who are willing to take matters into their own
hands on election day, without giving a hint of their intentions at any
polls. A few such B voters could tip the election to B before anyone else
has a chance to do something about it.
	So that’s the point of having another round. Of course, there are a lot
of possibilities for strategic manipulation in a two round system as well.
And that’s something we have to discuss. But at least nothing can happen
as a total surprise to the voters and the candidates. During the interim
period, A and B will have a chance to try to guess what the sincere votes
really were, haggle with each other about it... and hopefully come to some
sort of agreement that one or the other of them is somehow more likely to
be the rightful winner. Perhaps the remaining candidate could make some
sort of concessions to the withdrawing candidate. Of course, it is quite
possible that no arrangement will be reached, but at least there is an
opportunity for it to happen, rather than a sudden surprise that people
have to live with for the next 4 or 5 or 6 years.

Markus wrote:
>When you promote a second balloting then you make the readers
>   mistakenly believe that Condorcet methods have a serious
>   problem when there is no Condorcet winner. However, in my
>   opinion, the currently discussed Condorcet methods (esp.
>   Tideman's ranked pairs method, Heitzig's river method,
>   my beatpath method) are very good single-winner election
>   methods even in the absence of a Condorcet winner, since
>   these methods also satisfy monotonicity, reversal symmetry,
>   independence of clones, majority for solid coalitions, etc.
	
	I don’t mean to make this argument. Even when there is no sincere
Condorcet winner, I usually prefer the completed winner according to wv
minimax, beatpath, etc. to methods like IRV. If people who hear the
argument for two round procedure think that Condorcet’s method is flawed
by the possibility of cycles, I think that they are simply misguided. The
two-round procedure itself can’t be faulted for that.


Markus wrote:
>A very important argument for preferential ballots is that
>   they don't require a second balloting. When you promote
>   a second balloting even for preferential ballots then you
>   lose one of your arguments for preferential ballots.

	Non-ranked methods such as plurality can also be conducted without a
second round. Nevertheless, a second round can be an improvement in both
ranked and unranked methods.

Markus wrote:
>The probability is very large that in the second balloting
>   there are only candidates of the same party. Voters who
>   don't support this party will then be deterred from
>   participating at the second balloting.

	You think that Condorcet cycles usually occur within a single party? I
don’t know of any reason to agree or disagree with that statement. Anyway,
even if all the members of the Schwartz set from the first balloting
happened to be from a party I did not support, I think that I would still
like to have my say in the final balloting. I agree that turnout can be a
problem in runoff systems... but it is at least possible to have a runoff
with approximately equal participation.

Markus wrote:
>A second balloting will encourage the voters to vote
>   insincerely in the first balloting. The voters will believe
>   that they can vote insincerely in the first balloting
>   without any risk; these voters will believe that they can
>   see in the first balloting whether their strategy would
>   strike back so that (when they see that it would strike back)
>   they can still vote sincerely in the second balloting so that
>   they don't risk anything when they vote insincerely in the
>   first balloting. A second balloting will also encourage the
>   voters to vote insincerely in the second balloting because
>   they will believe that they have very precise information
>   about the strengths of the candidates.

	This is a point that is very important to look at. I can’t pretend that I
understand all the strategic implications of a two-round Condorcet system
at this stage of the game. Would voters be more likely to vote
strategically in the first balloting if they knew that a second one would
follow in the event of a cycle? Maybe so, maybe so. It’s a tough question.
We should come back to this one. I am well aware that a two round system
still has ongoing strategy problems, which is why I initially proposed a
multiple-round system. The question is whether the two round system is an
improvement over a single-round system.

Dave Ketchum wrote:
>If this argument managed to kill Condorcet, 

	This is definitely not my intention.

Dave Ketchum wrote:
>Conceded that a private group might contain the ability and willingness 
>for strategies of this sort, public elections have to be about immune.
>Potential strategists have to predict the expectable results with no 
>effort and what effort will promote a better result without going into 
>something worse.

	In the example above, the B order-reversing voters should be confident
that B will beat C in pairwise comparison by a greater magnitude than A
will beat B. That way, the A-->B defeat is dropped before the B-->C
defeat. 
How hard is this to guess at? Well, I concede that it’s not terribly easy
in the example above. But you can alter the example so that C is a weaker
candidate. The weaker C is, the more likely it is that a burial strategy
will not backfire, and yet the more voters it will take to make the
strategy a success. For example...

Sincere votes
28: A>B
27: B>A
23: C>A
22: C>B
	A is a Condorcet winner. If 7 voters change from B>A>C to B>C>A, B will
win instead of A.
28: A>B
20: B>A
7: B>C
23: C>A
22: C>B
Pairwise comparisons
A:B = 51:49
A:C = 48:52
B:C = 55:45
	So the B voters face relatively little risk in reversing, unless the A
voters are using some kind of strategy as well. And 7/27 is still not a
very large portion of the B voters.
	Perhaps the situation tends toward the chaos point where the A voters’
and B voters’ strategy are just about to cause each other to backfire? I
don’t know. Anyway, if the B voters happen to be much more risk-tolerant
than the A voters, then that can win the election for B. Which is an
undemocratic way to decide things!

Fan de Condorcet wrote:
>Give some other important role to the runner-up.  
and
>(2) Elect the top two candidates to the office.  That is, there could be a
>planned split term, with the people's first choice holding office for the
>first part of the term and the second choice holding office for the latter
>part.  (If Shulze's method were used, the strength of the beatpaths could
>be
>used to determine how the term would be split.)

	How do you define the runner up? How would beatpath strength translate
into a time-share?

Adam Tarr wrote:
>This problem is in no way limited to winning votes Condorcet.  The exact 
>same strategy works in margins Condorcet.  

	Oh, I quite agree. I’m not trying to make an argument for margins. At
this point I think that margins is even more strategy-prone. I went into
that a little bit when I was on this topic in August.

Adam Tarr wrote:
>I see it as extremely unlikely that burial strategy would 
>be successful on a large scale without public coordination, which would
>be 
>easy to counter and would create a big scandal.

	This is one of my newer points. I don’t think that coordination is
necessary. As long as voters understand the system, and are aware that
strategy can bring both risk and a possible advantage, I think that they
can make up their minds individually when they go to the ballot box. 

Adam Tarr wrote:
>Remember that there are lots of people who have a sense of obligation
>that 
>pushes them towards voting sincerely.

	I hope you’re right about that. Politics can be a pretty brutal sport,
though. And we should be designing these methods to be able to stand up to
the test when an election is very hotly contested and there’s a lot on the
line.

>What if no candidate is willing to drop out?

	Yes, as I said, that is a concern. Still, I’d like to offer them the
opportunity to do so.

Eric Gorr wrote:
>The only potential place for this strategy to work would be in 
>relatively small groups where everyone knows everyone else and how 
>they are going to vote, but then one cannot discount the potential 
>for counter-strategies to be employed in which case nearly anything 
>could happen and again the only rational choice for the voters would 
>be to vote sincerely.

	I am hoping that everyone will agree that my multiple-round proposal is
suitable for small-group voting, such as use within legislatures. That is,
basically, to have a ranked vote, and follow it with an up-or-down vote on
the Condorcet or completed winner... repeating this until some option wins
the up-or-down vote... True majority rule.
	I think that in a single-balloting, there would have to be a lot of
guesswork involved in employing counter-strategy. Things could get
extremely confident in a senate-type situation where people are employing
strategy and counter-strategy and counter-counter strategy. Thus I
wouldn’t like to settle it all in a single, binding vote. I’d like the
process to continue until there is a stable winner that wouldn’t be likely
to suddenly change in a subsequent round of voting.
	Can everyone agree on a multiple-round system for small group voting?

Mike Ossipoff wrote:
>wv's problem 
>when offensive order-reversal is being attempted is no worse than the 
>problem that IRV has without anyone attempting offensive strategy.
>You can call wv's offensive order-reversal problem a serious problem if
>you 
>want to, but then you should also say that all the other voting systems
>have 
>a more serious problem. A similar problem that exists all the time,
>instead 
>of just when some voters attempt a very risky offensive strategy.

	I don’t agree with this. The burial strategy enables people to “rip off”
elections in much more severe and startling ways than would be possible in
IRV. Sure, it’s pretty hard to do, but the possibility is there.
	IRV’s strategy problems are quite different. Rather than vulnerability to
burying, IRV suffers from the need for compromising strategy. 
It is difficult to say which problem is worse, because they are very
different. IRV’s problem results in a lack of accountability that tends to
support the status quo. Condorcet opens the way for more genuine
participation, but the possibility remains for a really violent election
steal, or a really bizarre chicken game.
I don’t know which problem is worse. They’re both bad. If no one uses
strategy, Condorcet is by far the better system. Any hope of really
vibrant single-winner elections has to come from Condorcet. So I’d much
rather try to address the strategy concerns in Condorcet rather than throw
it over for the rather uninspiring IRV.

Mike wrote:
>And no, they don't have to know that the offensive order-reversal is
>being 
>done. They can do the defensive truncation, and, without the offensive 
>order-reversal, the defensivse truncation will have no effect, no harm.

	If supporters of the CW truncate, yes, the CW will still win. However,
people do not always know who the CW will be ahead of time, or if there is
one. If supporters of more than one candidate truncate with the notion
that their candidate is probably the CW and they don’t want the election
stolen by supporters of the other candidate, then it is quite possible for
this to result in the election of the sincere Condorcet loser.

I wrote:
>It is also possible that a combination of
>mutual burial and mutual truncation (due to either aggressive or paranoid
>voting) could lead to the election of the car crash candidate.
Mike replied:
>Mutual truncation won't do that. 

	In my examples in this posting, if both A voters and B voters truncate,
it will result in the election of C, the sincere Condorcet loser.

Mike wrote:
>And, given a particular set of polling 
>data, there won't be candidates who'd both try offensive order-reversal 
>against each other.

	There might be, if they don’t know which one of the two candidates wins
the pairwise comparison.

Mike wrote:
>Don't forget that 2nd balloting methods should only trigger a 2nd
>balloting 
>when there' s a circular tie all of whose membes are _majority_ beaten.

	You’re probably right about that. I’ll let you know if I ever disagree
with it, but for now it seems to make sense.

Mike wrote:
>It can have a BeatsAll candidate, and some losers who are in a 
>cycle. So it's better to say "circular tie" or "top cycle" than just 
>"cycle".

	Fair enough.

Mike wrote:
>And this discussion has been assuming that Kerry is CW. Let's remember
>that 
>that is only an assumption for the sake of discussion. There's no
>particuar 
>reason to believe that it's true, except for what your tv commentators
>have 
>been drumming into you all this time.

	This is a valid point in general: In a two round system, it is possible
or even likely that more than one candidate will make the claim to be the
sincere CW. How do you know which votes are sincere and which aren’t? You
don’t, of course. But at least the candidates have a chance to talk it out
and maybe make some bargains.
	In the *totally hypothetical, non-real* example from my last posting, I
think that Nader should drop out because there doesn’t seem to be any
realistic way that he can win. Basically his presence in the election only
serves Bush voters with a weapon to gouge at Kerry. Since it’s a Condorcet
election, voters had a very very fair chance to vote sincerely and support
Nader if that’s who they really like best. Only 8% chose them as their
first choice, and the 44% Bush > Nader > Kerry voters are highly suspect.
However, I wouldn’t fault Nader for trying to wrest some concessions from
Kerry in exchange for his withdrawal. I’d like to keep talking about this
real, upcoming election, since we both have strong opinions about it, but
I think that we should make that another thread, as it’s a very separate
issue.

Mike wrote:
>What if 
>you use Condorcet for the 2nd balloting, and again there's a circular tie 
>with all majorilty defeats?

	Take the completed winner (wv beatpath, ranked pairs, etc.). 

Sincerely,
James