[EM] Parliamentary compromising strategy

[Kristofer Munsterhjelm]

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.