[EM] [CES #4429] Looking at Condorcet

Jameson Quinn jameson.quinn at gmail.com
Thu Feb 2 02:13:16 PST 2012

I'm going to continue to take a devil's advocate anti-Condorcet position
here. Of course I still believe that Condorcet systems are good overall,
and much much better than plurality or IRV. But I honestly think that MJ
and SODA are better.

2012/2/1 robert bristow-johnson <rbj at audioimagination.com>

> On 2/1/12 11:28 PM, Jameson Quinn wrote:
>> Dave gives good reasons for Condorcet. I'd like to present the other side.
>> Condorcet systems have many advantages. So what's wrong with Condorcet?
>> It comes in a bewildering array of forms, thus reducing the unity of its
>> supporters. But that's not the real problem.
>> It admits both betrayal and burial strategy, thus encouraging dangerous,
>> negative-sum strategizing from its voters. And that could be significant.
>> But I think that voters will realize that they will almost never have the
>> information and unity to pull off a successful strategy, so that's not the
>> real problem.
>> It is complicated to understand, and impossible to easily visualize, how
>> it works.
> i disagree with that.  i spelled that out (how you would spell it out to
> the average voter) in my just previous post.
> Condorcet is *simple* to understand.  unless there is a cycle, no one
> should be disputing the CW outcome.  the weak-CW with few 1st-choice votes
> is not a strong case.
> you elect the CW, because of the inverse consideration.  if you elect
> someone other than the CW (as we did in Burlington 2009), you are electing
> a candidate when *more* of us voters marked explicitly on our ballots that
> we preferred someone else.  *not* merely someone else in general (the
> "anybody but Jack" vote), but we voter said specifically we want Jill
> instead.  how can it be a democratic decision when more of us choose Jill
> elected to office over Jack than those who choose Jack over Jill, yet Jack
> is elected despite the mandate from the voters?  i have never seen an
> adequate answer to that.  in a simple 2-person race, even if the vote
> margin is close, even if by *one* vote, if more of us want Jill than those
> of us who want Jack, then Jill is elected.  would you have it any other way?
> if you would not have it any other way, you cannot make a consistent
> argument against electing the CW if there is one.  but we can argue about
> what to do about cycles.
>  But that's not the real problem.
>> As a ranked system, it is hopelessly caught in the contradictions of
>> Arrow's theorem.
> sure, and that's the case for any system.

Arrow's Impossibility theorem does not apply to rated systems.
Gibbard-Satterthwaite does; and there are certainly things that are
impossible, even for rated systems.

>  but it's less of a problem than the demonstrated problems (not mere
> theoretical issues with Arrow) of either IRV (as demonstrated in Burlington
> 2009) or FPTP (myriad times when there are spoiler candidates, which might
> happen in Burlington in 1 month).
> the *only* problem (a la Arrow) that i see with Condorcet is the potential
> of a cycle.  but it won't happen often

I agree that an honest cycle will be quite rare. But I believe that
strategic (false) cycles are a problem. More on that later.

> and only when the three top candidate all have roughly equal support.
>  it's the same kind of problem as a tie, and you create rules to deal with
> that difficult situation in some kind of sense that makes sense (and i'm
> not saying that there is a clear winner in which cycle-resolving method
> makes the most sense, but since a cycle is even less likely to involve more
> than three, it's really a moot question).
>  But that's not the real problem.
>> Some voters will mistakenly imagine that it's Borda. But that's not the
>> real problem. (They'll imagine that MJ is Range, too. I don't see how
>> they'd significantly misapprehend SODA, though.)
>> The real problem is that I think that people just don't want to do that
>> much work to vote. Yes, I know, you can just vote approval-style if you
>> want to, but most people would feel guilty about not really doing the whole
>> job then.
> what people don't want to do is to agonize over how to vote to serve their
> political interest when there are multiple outcomes, only one of which is
> the voter's hearts desire.  there often is another outcome which is
> tolerable and another that is intolerable.  what should the voter do to be
> counted among those against the intolerable outcome, yet still support
> his/her sincere favorite candidate?

Condorcet has at least as much of a problem with strategy as MJ, and more
than SODA.

The basic strategic issue with MJ is the chicken dilemma. And this
strategic dilemma applies also to Condorcet:

35: A>B
25: B>A
40: C

A wins

35: A>B
14: B>A
11: B>C
40: C

Now B wins. But if the A voters had used a similar defensive strategy, then
the B voters' strategy would make C win.

Yes, you can definitely argue that this is less of a slippery slope in
Condorcet than it is under Approval or Range. But you can make that same
kind of argument for MJ, and SODA completely resolves the chicken dilemma.

There's another generally-applicable strategy in Condorcet. Consider a
typical one-dimensional scenario:

30: A>B
9: B>A
21: B>C
40: C>B

B wins

30: A>B
9: B>A
21: B>C
40: C>A

Now C wins in most Condorcet systems. Yes, this strategy is dangerous, but
it will be applicable in real-world elections. MJ and SODA have no problems
with this scenario.

Note that in both of these scenarios, there is a plausible argument that
Condorcet could fail to elect the honest CW, while MJ and SODA could
succeed. Condorcet is not necessarily the most Condorcet-efficient system
(which seems to be your highest priority).

> that is the real problem, Jameson.  i don't think feeling guilty is a
> problem.  but voter regret is, especially after helping elect someone like
> George W Bush to office because one voted for Ralph Nader.  that, in a
> nutshell, is the problem.

I agree that strategic regret is a big problem. I just disagree that
Condorcet resolves it better than MJ or SODA.

>  I honestly think that honest rating is easier than honest ranking. (How's
>> that for honesty per square word?) MJ is the only system which allows
>> honest rating to be full-strength in practice; and SODA is the only good
>> system which allows anything easier. (And no, approval is not easier than
>> MJ, because approval forces some amount of strategizing.)
>> Most voters are lazy. And they'll resent any system which rubs their nose
>> in that fact. Which Condorcet does.
>>  i don't see that.  it's no worse than IRV, which is
>              "as easy as 1-2-3!"  :-)

A slogan with which I disagree.

> ranking is not hard.

And rating is easier. And picking a favorite you trust (as in SODA) is even

>  Condorcet does not ask anything more from the voter, lazy or not, than
> does IRV.  all it requires is for the voters to make up their minds about
> the candidates by Election Day.  how is that an unreasonable expectation of
> voters?
>  (SODA, on the other hand, brings lazy voters together, and gives their
>> representative as much negotiating power as possible without diluting the
>> winner's leadership mandate.)
> my issue with SODA is only that regarding any* non-Condorcet method.

SODA meets the Condorcet criterion for any expressed preferences. That is,
if you assume that all candidates actually try to get the best result
according to their predeclared preference order, then SODA will give the
same result as a Condorcet system would with the same ballots, taking any
delegated ballot to be the candidate's predeclared preference order.

Yes, that means that undelegated ballots only can express approval ballots,
not full rankings. So there could, in theory, be an honest Condorcet winner
who does not show up on the ballots. But that is unlikely. Candidates will
tend to declare an order which satisfies most of their voters, so
undelegated ballots will be a minority. And if it is known beforehand that
only one or two candidates have a chance of being the honest Condorcet
winner, then any undelegated ballots have enough expressive power to ensure
that the true Condorcet winner will win.

In provable terms: for both MJ and SODA, as with approval, the true
Condorcet winner will win in a strong Nash equilibrium, and if it is a
majority Condorcet winner then there can be no strong Nash equilibrium for
any other winner.)

>  if SODA does not elect the CW, if IRV does not elect the CW, if Borda or
> Bucklin do not elect the CW, then we are electing a candidate to office
> when more voters explicitly preferred (as marked on their ballots) a
> different *specific* candidate. how is that democratic?

If Condorcet does not elect the CW because of strategy, then we are
electing a candidate to office when more voters honestly preferred a
different *specific* candidate; and only doing so because the voters who
favored that winner were more unscrupulous than other voters. How is that


PS: I don't here a lot of Bucklin advocacy around here lately; it seems
that MJ is the median-based system of choice. And certainly nobody but
Donald Saari thinks Borda is a good idea.

PPS: In this thread I haven't even mentioned the weak Condorcet winner
problem, where there is an apparent CW who, with a little more scrutiny,
would actually lose support and lose in a runoff. I think this is a serious
concern for an incumbent, and thus a significant problem for Condorcet's
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20120202/0283eff5/attachment-0004.htm>

More information about the Election-Methods mailing list