[EM] Strategic voting in Condorcet & Range N-canddt elections

[Warren Smith]

>Venzke:
>There is another scenario of interest to me, where you can only break a
>tie between two candidates, but it isn't certain which two candidates they
>will be, at the time you're voting.
>  If we'll always be limited to two frontrunners, then I'm not all that
>interested in reform.

--Well, in major elections, we usually have a pretty good idea who A & B are.
If we genuinely had no idea and the V-1 other votes were totally
random, then probably
in the V=huge limit best Condorcet strategy would be honesty (though
I've never seen a proof) and best range strategy is
mean-utility-as-threshold approval voting.
   If all voters do that, then compare system 16 vs system 2 here
http://www.math.temple.edu/~wds/homepage/voFdata

E.g regrets using random-normal utilities & 200 voters:
system|2 canddts 3 canddts 4 canddts 5 canddts
------+--------- --------- --------- ---------
Cond|  1.61631   2.18396   2.43847   2.57293
Appv|  1.61631   1.85211   2.40181   2.83800

so in this experiment approval voting does better than Condorcet
with N=3,4 candidates; Condorcet does better with N=5; and both same with N=2.

>> 5. In a monotone Condorcet method (such as Schulze, Tideman
> ranked
> pairs, etc) you cannot go wrong by ranking A top and B
> bottom (both of
> which, in general, will be dishonest, but this is always
> strategically
> correct).

>Venzke: What assumptions are you making? This doesn't seem to be demonstrated.

--it is just the monotonicity and the asumption only A & B can win.

If you think some other vote is more strategic, then fine, use it,
then I will raise A to top, which never hurts me due to monotonicity
assumption, and drop B to bottom, same argument, thus proving my vote
is at least as strategic as yours.

So for the rest let us assume voters will cast votes with A,B top &
bottom (or reverse)
only, due to them being strategically wise and also due to them
wanting to simplify
their lives if they can (and they can, here).


-- 
Warren D. Smith
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