[EM] Blake's margins arguments
Adam Tarr
atarr at purdue.edu
Wed Feb 19 14:35:09 PST 2003
Rob LeGrand wrote:
>In fact, winning-votes often
>encourages *more* drastic strategy: If A>B>C is sincere and voting A=B>C
>helps the voter under margins, winning-votes could make that strategy
>ineffective, forcing a more drastically strategic B>A>C vote.
Really? I have found in examples that I look at, that the exact opposite
is true: equal first ranking works for winning votes in places where
margins requires favorite betrayal.
Here's an example:
48 A>B>C
12 B>A>C
40 C>B>A
B is the Condorcet winner. Now, let's say the 48% that prefer A decide to
truncate:
48 A (insincere truncation)
12 B>A>C
40 C>B>A
Now, we have a cyclic ambiguity. A defeats C 60-40, B defeats A 52-48, and
C defeats B 40-12. In winning votes, B still wins the election (a good
thing, in my opinion - this removes the incentive to falsely
truncate). But in margins, A now wins the election.
In order to create the same effect in winning votes, you need to reverse
preferences (not just truncate). The winning votes results that would be
considered equivalent by margins are:
24 A>C>B (insincere reversal)
24 A>B>C
12 B>A>C
40 C>B>A
A still beats C 60-40, and B still beats A 52-48, But now C beats B
64-36. So now we've put margins and winning votes on a "level playing
field". Now, imagine you're a voter in the C faction. Let's say that only
half of the faction can be convinced to betray C via equal-rankings. We
now have:
24 A>C>B (insincere reversal)
24 A>B>C
12 B>A>C
20 C>B>A
20 C=B>A (insincere equal ranking)
A still beats C 60-40, and B still beats A 52-48. The false equal rankings
brings the B/C tally to 44-36. This is enough in winning votes to carry
the election for B. But in margins, this will not do the trick. You need
the "more drastically strategic" (your term) favorite betrayal.
24 A>C>B (insincere reversal)
24 A>B>C
12 B>A>C
20 C>B>A
20 B>C>A (insincere favorite betrayal)
This more dramatic betrayal makes B the Condorcet winner once again.
So you see, the opposite of what you said is true, at least in this
example. Playing with an example almost exactly like this, long before I
joined the mailing list, was what convinced me that winning votes is better
than margins.
>Besides, any
>strategy that works under margins has an equivalent (maybe probabilistic)
>strategy that works under winning-votes.
As both myself and Mike have argued, the fact that equivalent strategies
exist does not mean they are equally likely to be used.
People currently vote for sure losers in first place in plurality voting,
despite obvious incentives to do otherwise. People want to vote their
natural preferences, and doing anything strikes some as dishonest. There's
a lot of cognitive dissonance in the public when it comes to this issue. I
think it is VERY reasonable to expect that most people won't be wiling to
do anything more strategic than leave candidates off their ballots.
I mean honestly, if you think people can grasp and will employ all the
appropriate order reversal strategies, then I don't see why we need
Condorcet voting at all. An electorate that is that wiling to follow polls
and behave rationally will have an easy time electing the right leaders
using approval, or even IRV, or even our current system. The fact that
this is empirically false, to me, argues strongly for winning votes.
I still have more to say on this, but I don't have time now - perhaps early
next week.
-Adam
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