Here's a scenario I've been thinking about lately.
Say that you have a parliament using proportional representation, and
the voting method is party list. Then say that the situation is so that
after the election, either the left-of-center parties or the
right-of-center parties form a coalition.
Given this, you might get a compromising strategy. Say (WLOG) that
you're a left-wing voter. Then if it's a narrow race, but the polls are
slightly favoring the right-wing group, it might make sense for you to
vote for the most centrist of the right-wing parties. The reasoning
would go that "the right wing is going to win anyway, so if I vote for
the left wing, I get zero influence, but if I vote for the leftmost
right-wing party, I at least pull the right-wing coalition away from its
right extreme".
But if enough people vote this way, then the right-wing wins, even if
the polls were inaccurate and it would not have won if people had voted
honestly.
Is there any way of ameliorating this? The best solution would let
people vote the left parties ahead of the right parties and contribute
both to their left-wing preference, as well as push the right-wing in
their direction.
I suppose the problem is that the coalition makeup is set up after the
election rather than during it. So the voting method has no idea about
how power is distributed and arranged after the election. All the voting
method does is produce a council that is proportional. Thus, if we're to
solve that problem, it would mean either codifying the coalition
structure into the system itself, or make the voters able to react to
coalition setups so that they can redistribute their votes manually.
The former, I'm a bit wary of doing. One of the advantages of
parliamentary rule is that the parliament is fluid. The parliament can
nominate, select, and dissolve executives. The members of parliament can
also ally themselves with others or shift their allegiances, or not have
any fixed coalition allies at all (as is the case with minority
governments). So making the assumption, within the voting system, that
the parliament is going to consist of multiple coalitions and that the
system can redistribute votes to ensure the favored coalition has a
majority... seems intrusive.
That leaves the second option, which sounds more like a form of proxy
voting or liquid democracy. Besides the problems with vote-buying,
there's also the instability. Yes, the voters can now react: left-wing
voters that see that the right-wing is winning can shift their votes to
the most centrist of the right-wing. However, this can cause reactions
in the parliament - e.g. the right-wing wants to exclude the centrists
because the centrists are diluting the unity of power of the coalition -
which in turn would cause reactions among the voters, and so on. There
might even be unstable oscillatory cycles. One such cycle might go that
the right-wing coalition wins. Then the left-wingers move their votes to
the centermost right-wing coalition members. The right-wing splits that
centrist group away because they dilute the "right-wing-ness" of the
right-wing coalition. Then the leftists move their votes back because
nobody has a majority now, so the left-wing could use their support; and
then the right-wing gains a majority. Rinse and repeat.
(One might ask what a deterministic system would do in such a case. The
answer is not obvious!)
So does that mean that we're forced to have some amount of compromising
strategy in parliamentary elections with blocs? Perhaps it's better to
say that the system isn't prepared to handle that kind of problem. Other
systems might, but then they wouldn't be parliamentary in the classical
sense. Or it might be the case that one can make tweaks, but these will
settle on somewhat random outcomes in edge cases like the above. A
proxy/liquid democracy system with damping of noise (e.g. if you move
your vote from X to Y, power gradually seeps from X to Y, not all at
once) might settle on either a minority government or a right-wing
coalition in the cyclical example above -- but there's no objective
reason why it shouldn't settle on the outcome it doesn't settle on.
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