In Plurality, the correct strategy is to vote for the frontrunner that's
closest to your point of view, so as not to split the vote. Now, my
question is: what is the correct strategy with a voting system that
gives you two votes of equal weight? Assume access to a poll so the
voters know who the frontrunners are.
If there are two coalitions, and you (the voter) prefers each coalition
equally (e.g A = B = C > D = E = F), it seems obvious that the two
points should be allocated to the same coalition; otherwise, the vote
for the second coalition diminishes the power of the first vote.
If we consider this in a pairwise fashion, then the point of the
Plurality vote is to contribute maximally to (front runner A) vs (front
runner B) by voting for A (if A's the one you like). A vs others is a
bonus inasfar as they keep the other coalition members out, but not
inasfar as they hurt your favorite (or greater preferred).
This seems to yield two types of strategy. Call the first defensive and
the second offensive. Defensive strategy would have you vote for, among
the candidates you prefer to the least of two evils, the one that has
greatest support (so your A vs all vote doesn't hurt this candidate as
much as it hurts the others). Offensive strategy would have you vote
for, among the candidates you prefer to the worse evil, the one that has
the greatest support ("anyone but the worse evil").
Which one is preferrable? One might, in a way, say that the two are
equivalent. If your preferences are
A > B > C > D
and the poll is
100: C
98: B
90: D
20: A,
then voting {A, B} is an offensive strategy from the point of view of A
(you vote B to increase the force against C), but a defensive strategy
from the point of view of B (you vote for A so your vote of B won't hurt
A). The only real difference is which is the "least of two evils" -
since B is, B's point of view is the true one, and this is a defensive
strategy.
(On the other hand, A isn't going to be providing much of a barrier to
C's victory unless the polls are way wrong.)
A final observation: the extension of this system to the point where you
have as many votes as there are relevant candidates, along with a
write-in option, reduces the system to Approval (approve of some subset
of the relevant candidates, then "waste" the rest on randomly named
write-ins). That's getting a bit ahead of myself, though, because this
particular strategy question is about the system limited to two votes,
which can't really be called Approval.
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