[EM] Condorcet strategy and anti-reversal enhancements

James Green-Armytage jarmyta at antioch-college.edu
Fri Jan 16 20:59:02 PST 2004

Dear election methods fans,

	Does anyone remember my proposal for a voting procedure which I posted on
December 17th, titled "a strategic problem and possible remedy for
Condorcet-efficient voting methods"? Here is the link, to make it

	Anyway, Chris Benham and Mike Ossipoff wrote replies, and now I am
*finally* replying to their replies. 
	Right now I'm just getting out of college, starting a new job, trying to
find a place to live, etc. So I'm afraid that my replies may be on a sort
of delay action as a result. Anyway, thank you to Mike and Chris, as well
as Rob LeGrand, for taking the time to read my proposal and respond. I'm
sorry if I forgot anyone.
	I'd really appreciate for any of you to read this, and/or the original
proposal, if you have the time. If not, of course I understand, since I am
pressed myself these days. Hopefully I will have more time in the near
	I'm putting the reply to Chris Benham first, because it goes over the
basics of my proposal. The reply to Mike is more of a response to a
critique, so I go into the justification for the rules to some degree. If
anyone is still confused, either about the rules or the justification for
them, I will be happy to answer their questions.


>I am a bit confused as to exactly what you mean. Do you mean that the
>Condorcet completion method
>is decided on in advance, 

	Yes, the completion method is decided in advance

>and that the voters as well as rank the candidates also vote Yes or No
>to each candidate?

	No. Let me try to explain it in brief. The initial ranked vote is just a
normal ranked vote. 
	In a public election, if a Condorcet winner exists from the ranked vote,
then they win. If no Condorcet winner exists, then whichever candidate
wins according to the given completion method is submitted to the public
for a yes or no vote. If the majority of those who vote vote yes, then
that candidate is elected. If the majority votes no, then another round of
ranked voting is triggered. 
	In a public election, simply to save time, I would put the subsequent
ranked vote on the same ballot with the yes or no vote which determines
whether that ranked vote is needed in the first place. So, if the majority
votes yes, then the ranked vote that has already been taken turns out to
be unnecessary. Weird, maybe, but clearly a time and money saver.

	The use-in-legislative-bodies/councils proposal is pretty similar except
for a couple things. One, a Condorcet winner in the first balloting is
still subject to a yes-no vote, although the majority should vote yes
nearly always. Also, legislators will know the results of a yes-no vote
before they take a subsequent ranked vote, unlike in a public election
where they are on the same ballot.
	The other difference is in how many rounds can occur. For councils, there
is no limit to this. The council can go on rejecting the potential winner
by majority and holding more ranked votes indefinitely, or until they get
sick of it and move onto something else without resolving the issue. In
public elections, some other way of limiting the number of rounds may need
to be found. The way which I like best so far is to automatically select
an outcome that reoccurs a certain number of times from the ranked vote.
For example, if candidate A is the completed winner of the ranked vote
twice, but is rejected in the yes-no vote, then wins yet another ranked
vote, candidate A is elected without having to do another yes-no vote.

> (BTW, Does "relative majority" mean a majority of those voters who chose
>give a Yes or a No to the provisional winner?

	Yes, that's how I meant it. Sorry if my usage was unclear.

> I have seen "relative majority" mean a plurality.)
>And then (if there is no CW) the ranked-ballot completion method winner
>gets a "Yes" from a 
>"relative majority" then that result is final?
>And if not, there is a period of "discussion",
>during which some candidates might withdraw, and then maybe the initial
>ranked-ballot winner is 
>eliminated, and then repeat?

	No. See above. Sorry if my paper was unclear. Any suggestions as to how I
can word it to make it more clear?
>BTW, have you read the excellent paper by Woodall that M.Schulze
>uploaded? There is a link from
>If so, you will know that Condorcet is incompatible with Later-no-help
>and Later-no-harm, as well
>as 5 other what Woodall classifies as "monotonicity properties".

	I took your suggestion and read the paper. So far I'm not impressed with
the method which Woodall proposed in that paper, but I liked the way he
organized his "impossibility theorems" into that cool chart. You're right
that he did cover this incompatibility. Maybe therefore I should shorten
the part of my paper where I'm talking about that, since it's already
public knowledge after a kind.


	My most general reply is this: You give a number of reasons why offensive
order reversal is unlikely to succeed in a public Condorcet election, and
why a sort of chicken-car crash scenario is unlikely to occur in a public
Condorcet election. For the most part, I agree that these things are
reasonably unlikely. However, as I wrote before, I think that if they do
happen, then it is a real disaster, and will utterly undermine the
credibility of the system. 
	The question then becomes a matter of *how* unlikely these scenarios are
in a public election. Are they astronomically improbable (say, one in a
million)? If so, then I would be willing to let it slide and back
Condorcet without any backup mechanism. Are they improbable on the order
of one in a hundred? If so, then I would start to get somewhat
uncomfortable with the raw, unprotected Condorcet being used for a
serious, high-stakes public election. The cost of a backup mechanism
begins to be less important to me that the risk of one of these scenarios.
If it is more like one in fifty, then this continues to increase my
concern. And so on. At a certain point, I will refuse to back Condorcet at
all without some backup mechanism. Although I don't expect that such tidy
number values can be put on this matter, I use them to illustrate the
point that a odds-against risk of a major disaster is still a major
	My general opinion is that the offensive order reversal / burying problem
is more of a 1/100 problem (or worse) than a 1/1,000,000 problem, even in
a public election. I will try to back this intuition up at least a little
bit, although I'm not quite sure whether it can be quantified in any
meaningful way. In an election with fewer voters, then it becomes
substantially more significant.
	Back in August, there was an EM thread called "serious strategy problem
in Condorcet..." A lot of people were arguing that the problem was not as
serious as I was making it out to be. So I suppose that I made a few
points then in support of it actually being a critical problem. I don't
think that we came to any real consensus on the point, though. I am still
of the opinion that it is a critical problem, and I hope I am not doing
too bad a job of supplying reasons why I think this.

Mike Ossipoff wrote:
>That's a big subject.

	I agree.
>You correctly point out that defensive strategy is a worse problem with 
>margins than with winning-votes (wv).
>Additionally, with wv, truncation can't steal the election from a 
>well-supported CW, a CW who has a majority defeat against the truncators' 

	Good point.

>That's the subject of the criterion SFC. GSFC generalizes SFC to 
>situations where there's no CW. When defeats are measured by wv, then SSD 
>and Ranked-Pairs meet the powerful GSFC. Plain Condorcet (PC) meets SFC.
>In fact, SFC and GSFC describe plausible conditions under which, with 
>complying methods (Condorcet wv), the majority who don't want X can be
>X won't win, _without having to do anything other than vote sincerel_. 

	I don't understand what you mean by this. Could you clarify?

>That's what I most like about Condorcet wv.
>Your iniltial wording of the Condorcet count implies that defeats are 
>measured by margins. That probably isn't intentional.
>To put the problem in perspective, Condorcet wv has no defensive strategy 
>need unless someone is going to try offensive order-reversal strategy. At 
>its very worst, under less-than-likely worst-case conditions, Condorcet
>begins to share the strategy need that the other methods have all the
>And, with Condorcet wv, in order for you to successfully steal the
>it's only possible if the people from whom you're stealing the election
>tried to help you. Doesn't that make you feel proud of yourself? :-)
>P.S. Don't expect them to rank your cxandidate again. Don't expect your 
>winner to be able to show his face in public.

	The problem with this is the way most public elections are staggered
several years apart. This makes it hard for the threat of retaliation in
the next election to have much effect on people's strategies in the
current election.
	Also, in a high-stakes election, victory might matter more than the
reputation of the candidate. For example, Bush stopped at nothing to steal
the 2000 election. It is clear to many people that the result was unfair,
but Gore doesn't seem to be running against him in '04. The fake winner is
the president of the U.S., with all the power that implies, while the real
winner is sort of a political ghost who comes around to haunt the media
every so often. By your logic (as far as an unfair winner not being able
to show his face in public) I would expect Gore to run again and to smash
Bush in '04. But it seems that the power that Bush seized was able to
override the concerns of fairness in a way.
>As you mentioned, it's like a game of chicken, when defensive truncation
>threatened against would-be offensive order-reversers.
>But please note that the supporters of the middle CW who is being
>will suffer less if no one chickens out, compared to how much the
>order-reversers would suffer then. That's because, in your example, the C
>farther away from the order-reversers than from the defenders.

	You mean in this example?:

46: A>B>C
44: B>A>C
5: C>A>B
5: C>B>A

	How so?
>Additionally, a defender has a more credible threat. A cat defending its 
>territory has a more credible threat against an interloper than the other 
>cat has. The defender, it's understood, is more willing to fight and risk 
>getting hurt when defending what's rightfully his. This adds to the 
>defenders' advantage in the game of chicken.
>Sure, if no one chickens out, the result isn't desirable for the
>either. Defensive truncation is a dominated strategy for them: But note
>dominated deterrent strategies are common in legal systrems and in the 
>animal kingdom. They wouldn't be used so much if they didn't work.

	Interesting point. I think I agree with you, but I would enjoy hearing a
couple of examples. I like game theory. Also, again, the ability of the
"defenders" to punish the "reversers" is severely limited if they have to
wait another four years to cast a vote. 
>In public elections, effective offensive order-reversal would require
>organizing. There' s just no way it could be done without its intended 
>victims hearing about it and using defensive truncation.
>So in public elections, offensive order-reversal is a losing proposition.

	A couple points here. One, which we will probably agree on, is that this
kind of strategic organizing is much easier in a voting situation with
fewer voters, for example a vote within a legislature or council. Hence, I
think that offensive order reversal / burying would be much more of a
problem in such situations. Also, the cost of implementing an
anti-reversal enhancement such as the one I proposed would be
substantially smaller in such situations, since the voters will still be
gathered together and in a position to vote again when the result of the
first vote is announced. Do you agree that my proposal is marginally more
relevant for use within legislatures, councils, etc.? Since you frequently
qualify with the word 'public,' I assume that you do.
	Secondly, burial strategies don't have to be entirely conscious. Given
ranked ballots I think you might find that many voters will rank a
candidate last not because that candidate is their sincere last favorite,
but because the candidate is the main competition for their favorite. This
can just be a matter of instinct, and can happen whether voters really
know how the tally system works or not. With IRV, (or any system where the
burial strategy doesn't work), people doing voter ed. can say "listen,
there's *no way* that burying your second favorite going to help your
favorite candidate, so why mess with it." With Condorcet, unfortunately,
this wouldn't be true, so this impulse will not necessarily disappear
given good voter education.

>For all the above reasons, I don't consider offensive order-reversal a 
>problem. Effectively, then, Condorcet wv is practically strategy-free. 
>Remarkably strategy-free. No other method of comparable simplicity even 
>comes close.
>So, for that reason, I don't feel that it's necessary to include 
>enhancements to further reduce that already near-nonexistent problem.
>Of course, when Condorcet wv has been in use for a long time, and if by
>people are discussing the order-reversal possibility, then, at that time, 
>the anti-reversal enhancements could be proposed.
>Even though I claim that they aren't needed in public Condorcet wv 
>proposals, I'm going to discuss anti-reversal enhancements in a
>Mike Ossipoff

	By the way, in my original paper I used this example:

46: A>B>C
44: B>A>C
5: C>A>B
5: C>B>A

	But this example is even trickier:

28: A>B>C
27: B>A>C
23: C>A>B
22: C>B>A

	It's trickier because mutual truncation in the first example leads to the
sincere Condorcet winner winning anyway, but in this example the second
preference votes are essential for both A and B.

>You described an anti-reversal enhancement that involved a 2nd balloting. 
>Sure, a 2nd balloting can further reduce wv's already tiny offensive 
>strategy problem, assuming that it ever becomes a problem.
>But it's not necessary to hold a 2nd balloting anytime there's a circular 
>tie, though that's one solution.
>If a CW's support isn't indifferent, s/he'll be ranked over the
>candidate by a majority, meaning that for the reversers' candidate to
>everyone else must have even bigger majority against them.
>So the 2nd balloting should only be triggered if there's an 
>all-majority-defeats circular tie.

	That's an interesting idea for a modification of my proposal.
>Here's what I've propsed as a 2nd ballot solution:
>If there's a circular tie all of whose members have another member ranked 
>over them by a majorith, then a 2nd balloting is held.
>Before the 2nd balloting, the pairwise defeats will have been published,
>order-reversal, if it happened, can be noticed.
>In the 2nd balloting, the reversal can be countered. It can be punished
>defensive truncation. Or, as in your example, the C voters could rank B 
>equal to C. Note that, with wv, they only need rank B equal to C. In
>they'd often have to rank B _over_ C. That's a lot more to ask.

	Are the results of the second balloting final? This can be a problem
because, if a burial strategy has happened in the first balloting, then
the chicken game is already in full swing at the time of the second
balloting. If neither voting bloc swerves, and the car crash candidate is
elected in the second balloting, then the result has gone from bad to
worse. If such a result is locked in, then it'd be bad. 
	In this case I'd say that the result is still highly unstable as of the
end of the second balloting. The goal of the method I'm proposing is to
find a relatively stable outcome. It offers three definitions of
stability. One is a clear Condorcet winner on the initial balloting. The
second definition is an outcome that the majority votes in favor of when
they are given the choice between that outcome and a re-vote. That is, a
majority perceives it as a fair outcome, a majority doesn't think that
they can get a better outcome without risking a worse outcome and
considering the cost of an extra election, or whatever. The last resort
definition of stability is to pick an outcome that reoccurs from a certain
number of ballotings, e.g. an outcome that repeats 3 times. This last rule
is not necessary for use within legislatures, because deadlock on some
issues is acceptable in the legislative process. This rule is only
necessary when an election absolutely needs to produce a positive result
by a certain date. A car crash candidate or a burial-strategy beneficiary
may still conceivably win, but not all at once and by surprise, as can
happen when a specific round of ranked voting is automatically locked in.
Instead, the voters will necessarily see the result coming and must make
repeated conscious choices to affirm it. 
	This rule strikes me as the best way to break deadlock, but I mentioned a
few other possibilities before, along with their shortcomings.
	Going back to your suggestion, I'm also not sure that there should
automatically be a whole 'nother ranked vote in the event of a majority
rule cycle. In my proposal, if a majority accepts the completed winner as
legitimate, then there is no need for a second balloting. (Indeed a
binding second balloting could lead to an unfair result, and could cause
difficult strategic incentives in both ballotings). 

>But another possibilit for the 2nd balloting is an Approval balloting.
>simpler method won't produce another cycle, and the defense against the 
>reversers would consist of their victimes not voting for the reversers' 
>candidate. In that case the defensive truncation elects the CW.

	I see no reason to assume that a subsequent approval balloting will pick
the sincere Condorcet winner if one exists, or the sincere completion
winner. So I can't accept this as a solution.
>The 2nd balloting pretty much eliminates whatever amount of reversal
>Something similar can be used for committees. I'd suggest it for an EM
>for instance.
>To a poll, I'd add the rule that, after the result is announced, there's 
>about a week or half-week period during which anyone can truncate their 
>ranking if they choose to, or can uprank an alternative to 1st place.
>(I prefer open polls in which voters post their ballots. That's the way
>have proven security.
>But, as these ballots come in, reversal opportunities could be obvious to 
>those who haven't voted yet. The defdensive strategy option avoids that 
>reversal problem).

	I don't quite understand this. Is the second balloting still an approval
>Either of those 2 enhanhancements, or something similar, could be used
>Tom Roiund and Steve Eppley separately independently proposed the 
>candidate-withdrawal option:
>After an election result, any candidate can declare that he withdraws,
>call for another count of the same ballots with his name deleted from
>That also thwarts offensive order-reversal.
>I notice that candidate-withdrawal is part of your proposal.

	Sort of. In the proposal I made, candidates can withdraw in between
ballotings, but they can't order a recount of the previous balloting with
their name deleted. I think that candidate withdrawal option is an
interesting idea, but it's not exactly what I proposed here.

>For 1-balloting elections, the voter could have the option of drawing a
>in his ranking, to indicate that, in the event of an all-majority-beaten 
>circular tie involving candidates above and below that line, he wants to 
>drop the candidates below the line. Then the same ballots, with the 
>candiddates dropped, would be recounted. That would be a powerful
>to offensive order-reversal.
>I don't claim to have covered all the possible anti-reversal
>We've discussed a few other ones.
>For instance, a tentative possible solution involves giving the voter the 
>option to indicate that, if there's an all-majority-beaten circular tie,
>if groups of voters sharing the same 1st  choices have certain patterns
>unanimity and non-unanimity within those groups, in their subsequent 
>choices, that voter wants do delete certain candidates. That may catch be 
>able to catch some offensive order-reversals. Obviously that isn't a 
>complete detailed proposal.

	Ahhhhh! Yes, this is a crazy and fascinating direction that I haven't
seen explored much. That is, a vote which changes in response to the other
votes cast! I tried to get a proposal together along these lines in the
fall, but it is difficult stuff! With three candidates it is perhaps
manageable, but with a lot more than that, tremendous complexities seem to
emerge from whatever method I consider. Still, it is an interesting
direction to take with further discussion, even if it ultimately turns out
to be a goose chase.
	I was working on a method with a "variable fraction ballot" before I
threw up my hands in frustration and decided to stick with the simpler
proposal that I made. The basic idea was that the strength of an A>B>C
voter's vote in favor of B over C can depend--according to some equation
that the voter is able to determine--on the percentage of B voters who
vote B>A>C rather than B>C>A or B>A=C. The strength could be 1 (ordinary /
full), 0 (equivalent to truncation, or somewhere in between. Maybe even a
range from zero to negative one as well.
	Using this for the final binding vote was the original deadlock breaker
in my procedure. (Note that in the midst of deadlock after several rounds
of voting, voters would have a great deal of information to base their
equations on, which is of course helpful.) But aside from the extreme
complexity required of voters and voting machines, I am still not sure
what kinds of equations would be effective in situations with several
	Of course there could be ballot options to just trust the equation
offered by a particular candidate, party, organization, etc., which would
mean that not all voters would have to devise their own equations from
scratch. But still, it's very problematic.

>Methods more fancy and complicated than Condorcet are discussed. Though
>methods have strategy, there's always the possibility that one of those 
>fancier methods will get rid of defensive strategy need, as I've defined
>here. Or at least let defensive truncation elect the CW, without the use
>a 2nd ballotiong.

	Of course, I would be interested in hearing about as many of these as
possible. I would be very impressed to see a Condorcet efficient
single-balloting method that is more strategy resistant the winning votes
ranked pairs & beatpath. It seems that whichever way you slice Condorcet,
you end up giving voters a chance to overrule a real majority with a fake
majority, unless you complete with a totally different method, which gives
you all the strategic problems of that method. So far, I don't think a
really mechanistic system can weed out offensive strategy, which is why my
proposal relies on fairly subjective human judgement. Of course, if I can
be proven wrong, that will be a good thing.

	By the way, I think that my proposal can conceivably be extended to use
with multiple winner CPO-STV, although the process might be somewhat
unwieldy. Basically, if there is a cycle between outcomes, there would be
a yes or no vote on whether to approve the completion-method-winning
outcome. If the majority votes to keep it, then it's done. If they decide
on a re-vote, then it is once again a CPO-STV re-vote, rather than a
single-winner Condorcet re-vote among the different outcomes. Thus, a
majority can't use the procedure to crowd out minority-supported winners
and thus subvert the proportionality of the election. All they can do is
delay the outcome, which means they will be delaying the majority
candidates they like from taking office as well.

	If you made it down this far, thanks for reading!

all my best,
James Green-Armytage

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