[EM] Efforts to improve on CR's strategy

[Bart Ingles]

Ken Johnson wrote:
> 
> >Date: Mon, 24 May 2004 21:55:40 -0700
> >From: Bart Ingles <bartman at netgate.net>
> >...
> >IRNR seems equivalent to repeated runoff elections.  In a zero-info
> >election with five candidates, where my preferences are A>B>C>D>E, I
> >would vote something like:
> >
> >A(1.0) > B(0.001) > C(0.000001) > D(0.000000001) > E(0.0)
> >
> >The idea is that subsequent ratings are low enough that they don't
> >detract much from my first-choice vote in each round.  And if my first
> >choice is ever eliminated, the bulk of my voting power always goes to my
> >highest remaining choice.
> >
> >...
> >
> Bart,
> 
> It seems to me that a limitation of this strategy is that if candidate A
> is left standing in the last round, then you have very little say in who
> A is running against. What if you have very high, and nearly equal,
> sincere ratings of A, B, C, and D, and a very low rating for E? Your
> highest priority is to ensure that E is eliminated. What then would be
> your strategy?

The same.  The method at each round is equivalent to Cumulative Voting,
which is known to be strategically equivalent to Plurality Voting.  In
other words, throw all of your voting power behind one candidate (to do
otherwise would be analogous to a group of like-minded voters in a
Plurality election splitting their vote by failing to back the same
candidate).

Since the iterative elimination process is the same as IRV's, my initial
belief (unless someone can show otherwise) is that the method is
strategically equivalent to IRV.

If the election is "zero-info" (no polling or similar data available),
you are forced to assume that all candidates are equally likely to
defeat your least favorite, so you might as well try to insure that your
favorite survives to the final round.  I chose the values above so that
I could give near-maximum support to my favorite, while ensuring that
the remaining votes would normalize to the same strategy if A is
eliminated.  I would use the same strategy even if I liked A-D nearly
equally, and hated E.

If I knew that B and E were the two major candidates, the fact that I
ranked A first above would imply that I was sure A would be eliminated
before B.  As soon as A is eliminated, my voted ratings normalize to
B(.999) > C(.001) > D(.000001) > E(0).  If I had any doubts about this,
I would have ranked "lesser evil" B first (especially if I only slightly
preferred A over B).


There may be situations where a different strategy is called for, but
these would be identical under IRV (except with pure rankings, of
course).  These are fairly obscure though.  For example, suppose the
candidates are Extreme Right, Solid Right, Center Right, and Far Left. 
Say I prefer Solid Right, but I want to make sure that Far Left loses,
so my strategic choice (the probable CW) is Center Right.  I am
concerned that Center Right may not emerge as strong contender among
right-wing voters until Solid Right (the probable CW among Right voters)
is eliminated.  If polls show that Extreme Right is stronger than Center
Right in the first round, I might rank Extreme Right first under IRV in
the hope that (1) ExtremeR can eliminate SolidR and (2) most of SolidR's
voters will do the sensible thing and rank CenterR second, thus
defeating ExtremeR in the 2nd round.  Under IRNR, my vote would be in
the same order, with the Cardinal values shown above.  In other words:

Sincere:
SolidR(1.0) > CenterR(0.5) > ExtemeR(0.3) > FarL(0)

Strategic:
ExtR(1.0) > CenterR(.001) > SolidR(.000001) > FarL(0)

Under Approval, I would approve both SolidR and CenterR given the
sincere ratings above).
Under Condorcet, I would probably just rank sincerely, but might
truncate below CenterR for non-strategic reasons.

Bart