# [EM] Re: Condorcet's strategy problem

Rob Lanphier robla at robla.net
Wed Sep 14 00:08:48 PDT 2005

```On Tue, 2005-09-13 at 22:51 -0600, Adam Tarr wrote:
> election-methods at electorama.com
> There was an FBC failure example posted recently.  It arises from a
> cycle with a lot of sincere indifference.  It goes like this:
>
> 31% C>A>B
> 9% B>C>A
> 28% B=C>A
> 32% A>B>C

> 68% C > 32% A
> 63% A > 37% B
> 41% B > 31% C
>
> Consider the 32% A>B>C faction.  It takes 12% (38% of the faction) of
> them to win the election for B by "strong" favorite betrayal (B>A>C),
> making B the Condorcet winner.  They can win the election for B by
> "weak" favorite betrayal (A=B>C) if 22% (69% of the faction) vote that
> way, but they have incentive for reversal unless they know for sure
> that that many will act in a similar fashion.

I suspect this would be a rare occurrence.  It's a plausible scenario
using a two-dimensional model of the electorate.  However, one hopes
that a candidate D would emerge that's a reasonable compromise between
the clearly very polarizing A, B, and C candidates.

Note that at least a few of the 31 C>A>B voters would be as motivated to
bury C to keep B out of office.  It would be an interesting game of
chicken that the 31 C>A>B voters would play with the 32 A>B>C voters.  I
strongly suspect the vast majority of attempts to vote strategically
would end in regret for the voters that try it in so many situations,
that conventional wisdom would eventually be to vote sincerely.

Incidentally, this particular scenario presents some nasty strategy
problems for Range and Approval as well.  This is a relatively close
three-way race, so making the decision to approve your second choice is
quite a conundrum.  This is why I'm coming to really dislike Approval as
a method.  It only works well with a unidimensional modeling of the
electorate.

> In my opinion, a method where favorite betrayal scenarios are
> restricted to a very narrow range of situations are not a major
> problem.

I tend to agree.  It seems like diminishingly small number of scenarios
where favorite betrayal actually pays.  It's really easy to construct
many, many scenarios where sincerity pays (including only minor tweaks
to the disaster scenarios).

> If the polls start to look something like this, voters will know well
> in advance.  In the vast majority of situations, there is no incentive

I'm not sure I'd entirely trust the polls to accurately forecast such an
insidious cycle well enough to change my vote based on it.

> Forest has argued recently (with regards to DMC, but the argument
> still applies here) that voters will be very reluctant to vote full
> favorite betrayal unless they know for certain that it is necessary.

I'm inclined to agree with Forest on this point.

>   This runs contrary to what Mike suggest, which is that voters will
> reverse order unless they are absolutely sure it is *not* necessary.

That might be the tendency for newbies backing candidates so far on the
fringe that they know they are going to lose.  I can't imagine those
with long-term experience with the system would continue to vote that
way.

>  Ultimately it is very hard for any of us to predict what effect wv
> Condorcet voting would have on the political climate and people's
> attitudes toward voting.

Agreed...we're all extrapolating on what we'd do personally.  So far, I
haven't seen a scenario that convinces me I'd make favorite betrayal a
routine in my voting patterns.  Of course, I've been known to "throw
away" my vote in the past, so what do I know.

Rob

```