[EM] Smith//Score ?

[Kevin Venzke]

Hi Daniel,

> Could Smith//Score be the ideal strategy-resistant Condorcet method?
> 
> The ballot would look like a Score ballot. To process the ballots, the scores
> are converted into rankings (equal rankings allowed), and the highest scoring
> candidate inside the Smith set is elected.
> 
> I'm hoping to make a Condorcet method that is very resistant to strategy. It's
> not 100% resistant ---- you can devise an example where there is a unique CW and
> a group of voters alter their ballots to produce a different CW that they
> prefer. Fair enough. But in general the voter has to contend with the fact that
> Score gives you a clear motivation to put your preferred candidate on top and
> your least preferred candidate at the bottom. Trying to alter the Smith set by
> ranking Y>X when you really prefer X>Y is a strategy that could work, but it
> could also backfire if X was going to get to the Smith set anyway. My intuition
> is that any strategy that works for Smith//Score (and they do exist) should also
> work for any other Condorcet method. So in that sense, this may be the most
> strategy-proof Smith-efficient Condorcet method.

I'm not sure what it is you're saying will differentiate Smith//Score.

My concern is this scenario:

A is the CW, but might not be the Score winner. B may also be the Score winner,
and they want to use a weaker candidate C as a "pawn" against A. So they vote
A 0/10, B 10/10, C 1/10. They may succeed in creating a C>A win, and which
should be a cycle. And they have done this without giving much support to C.

Possible outcomes:
1. C is actually voted as CW, because the A voters use the same strategy as the
B voters. Or for whatever reason, C beats B pairwise.
2. A is actually the Score winner and still wins.
3. B is the Score winner and B wins, strategy successful.

I prefer a version of this method where an X>Y preference implies you are giving
X the maximum rating, so that you can't create a cycle using a pawn candidate
without having a meaningful commitment to the pawn during the cycle resolution.

It might be interesting to look at Stensholt BPW, which is among the most
burial-resistant Condorcet methods. It's defined on first preferences, but a
Score adaptation should still work OK. In BPW, in a three-candidate cycle, the
winner is that candidate who defeats the "strongest" candidate. Of course, this
is not monotone, since it can penalize "strength" in whatever metric you are
using.

But the effect of this rule is that no matter whether it's an A>B>C>A or A>C>B>A
cycle, burial against the CW using a "pawn" candidate, will only give the
desired outcome to the strategists when the pawn candidate is the strongest one
of the three!

So in the above scenario that I described, if either A or B is the Score winner,
B will not win the (artificially created) cycle. The strategy either leaves the
win with A or gives it to C.

Kevin