[EM] Quick and Clean Burial Resistant Smith, compromise

[Daniel Carrera]

On Mon, Jan 17, 2022 at 4:29 AM Colin Champion
<colin.champion at routemaster.app> wrote:

> On the magnitude of errors, my own figures suggest that Condorcet/Hare
> makes fewer but larger errors than minimax when confronted with false cycle
> tactics, and therefore looks marginally better in terms of accuracy (and no
> doubt much better in terms of strategy resistance) but significantly worse
> in terms of Euclidean loss. See
> http://www.masterlyinactivity.com/condorcet/condorcet.html#results
> (where Condorcet/Hare=Condorcet+AV).
>


Thanks for the link. I'm going to need time to digest all of that. I just
updated my program to compute the Eucledian loss. I'm sure I can't compare
my numbers to yours; there will be a lot of implementation differences, and
you implement a lot more strategies than I do. But here it goes anyway:

Method   , suscep, new winner is ...
MiniMax  , 0.412 , better=0.134, worse=0.866
Hare     , 0.066 , better=0.655, worse=0.345
Benham   , 0.047 , better=0.135, worse=0.865
Smith_IRV, 0.047 , better=0.120, worse=0.880
Range    , 0.787 , better=0.072, worse=0.928
STAR     , 0.750 , better=0.061, worse=0.939


The first column ("suscep") is how often the method is susceptible to
strategy. It's basically the same number I've been posting here lately. The
next two numbers tell you how often the new winner (i.e. after strategy) is
better (i.e. smaller Eucledian distance to the mean voter) or worse than
the original winner. I was surprised to see that with Hare / IRV tactical
voting actually seems to make candidates better. I wonder how many of those
would be similar to the centre squeeze scenario you were just telling me
about. For other methods, strategy seems to be universally unhelpful.

Here is the Eucledian loss (gain?) for each case:

Method   , Change in Eucledian distance
MiniMax  , better=0.067, worse=0.196
Hare     , better=0.157, worse=0.172
Benham   , better=0.081, worse=0.228
Smith_IRV, better=0.081, worse=0.241
Range    , better=0.077, worse=0.355
STAR     , better=0.068, worse=0.335

The units are a bit different from yours. The mean voter is at a distance
~2.0 from the center, and ditto for candidates. Overall, these don't look
like very big jumps in either direction. That said, for all systems except
Hare, the downside of using strategy is significantly greater than the
upside.

You said that Condorcet/Hare makes fewer but larger errors than minimax
when confronted with false cycle tactics. I cannot confirm that because I
have not implemented false cycle tactics. But for the strategies I have
implemented, they look pretty similar.

Cheers
-- 
Dr. Daniel Carrera
Postdoctoral Research Associate
Iowa State University
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