[EM] Preferential voting system where a candidate may win multiple seats

[Kristofer Munsterhjelm]

On 07/19/2013 11:50 PM, Juho Laatu wrote:
> On 19.7.2013, at 10.18, Kristofer Munsterhjelm wrote:

>> In such cases, I would also suggest a few of the seats of the
>> parliament be given by a centrist- or minmax-based method (e.g.
>> Condorcet, CPO-SL with few seats, or possibly even minmax approval
>> or something like it). The idea would be that there shouldn't be
>> any kingmakers, but if there's a near-tie, that tie is broken by a
>> moderate group.
>
> In proportional systems one should distribute most of the seats
> directly to different parties without seeking for compromise
> candidates. I mean that also extreme parties should get their
> proportional share of the seats. Only in the allocaton of the very
> last seats (=last seats at national level) one can take the second
> preferences of the voters into account. The second preferences often
> point to compromise oriented candidates (by definition). The idea of
> favouring compromise candidates thus means taking the second
> preferences of the voters into account when allocating the very last
> seats.
>
> Sometimes the voters may prefer giving the last seat to a compromise
> party (with only a small fraction of quota of first preference votes
> supporting this decision) to giving it to one of the main parties
> (that might have close to 0.5 quota of first preference votes left
> supporting their candidate). The CPO approach is a good way to
> estimate which allocation of seats would get wide support among the
> electorate.

I was more thinking of doing so as a way of heading off the kingmaker 
objection. The objection goes something like: "we need to have a 
threshold, because otherwise a very small party might be in position to 
make or break a coalition and so would get undue power". A threshold is 
an absolute way of avoiding this unless the party is at least to some 
extent large enough, but one could also avoid it by giving the 
tiebreaker spot to a centrist or broad appeal group. If complexity is 
not an issue, having a centrist tiebreaker group might even be 
preferable, since a threshold is indiscriminate about where it gives 
that tiebreaker power: a medium sized party could still become kingmaker 
were it lucky enough, given a threshold.

Now that I think about it, that might be a way to improve the inequality 
between proportional representation and coalition voting power. This 
could be done in one of two ways.

One could just state it as a constraint problem: "given n adjustable 
seats, allocate so as to minimize the difference between coalition power 
and representation according to some metric". Like biproportional 
apportionment, this can be done by either departing from perfect 
representation of from perfect coalition power proportionality, and 
probably would meet somewhere in the middle.

The other option is to use parties or candidates with centrist positions 
or broad appeal as tiebreakers by themselves. If these are elected 
separately[1] to the main body of PR representatives, this would be more 
understandable to the voter, I think. The designer could say "we used to 
have a 2% threshold to keep radicals from getting undue power; now we 
give 2% of the seats to a moderating body instead, which is more 
consistent and doesn't necessarily deprive the minor parties of a voice".

The former option is pretty straightforward in the explanatory sense (if 
difficult to actually implement because of the computational cost). But 
the second might require some more thought.

I often find it useful to consider extremes to determine the underlying 
logic. The extreme of the second option would be to give the entire 
parliament to a compromise group. In effect, that's what a single-winner 
rule does. If we consider a single-winner election as a "council" with 
only one seat and put it into the logic of the second option, then the 
single-winner election should give a candidate with broad support 
because the alternatives give a less accurate result. If one gives the 
single seat to a wing candidate, then the other voters are left 
unrepresented.

So what happens as we increase the number of seats? On the one hand, the 
quantization error due to the limited number of seats goes down. This is 
what permits PR in the first place. On the other, to the degree that the 
various members of the council are going to engage in coalition games, 
power starts to move from the center of the opinion space given by those 
members.

So, ideally speaking, PR opposes the tendency for the leadership of the 
central group to impose its views on the rest of the group (which when 
taken to its extreme can lead to the kind of corruption and inefficiency 
associated with one-party states). This it does by giving the different 
groups a voice and by making negotiation public. It is not perfect, 
because negotiation can still be concealed through backroom deals, but 
it's better than having no public negotiation at all.

And similarly, again ideally speaking, giving tiebreaker powers to a 
broad group counters disproportionality in power. While I don't know of 
any councils arranged in that way, I'd think that if implemented 
properly, it would limit swings that would otherwise happen due to the 
composition of the council (instead of due to swings in voter opinion). 
Smaller groups can lead to greater disproportionality in power because 
they can align in many directions - one can see that by considering the 
extreme where there's only one very large group. So thresholds might be 
present to limit disproportionality in power, and if so, one would not 
need thresholds if the second option were used instead.

But it doesn't seem we can get further or derive an intuitive reason for 
how much of the council to give to the tiebreaker group. It depends on 
many things: how corruptible the center group is (which factors in as 
cost of giving power to it), how static and unresponsive the center 
group is (ditto), how unified the parties are (less unified means 
power-bloc analysis is not as appropriate and PR is more likely to also 
grant proportionality of power), and whether there are limits to what 
alliances may happen (a point Wahlberg expressed quite well: the smaller 
left-wing parties are not likely to ally themselves with right-wing 
parties, for instance[2]).

Perhaps there's a sharp bend to the Pareto frontier, i.e. that giving no 
seats to a center group would mean disproportionality of power would be 
quite common, while giving just a few would significantly decrease the 
chance of unrepresentative kingmaker parties, and giving more seats 
don't noticeably decrease the chance further before the whole council 
consists of centrists. If so, one can just place the trade-off at that 
sharp bend and be done with it; but even finding it would require 
further research.

For that matter, the same reasoning applies to thresholds. How can one 
tell whether the threshold should be 2% absolute, 4% absolute, or 4% for 
leveling seats only? There does not seem to be any "mathematical" way of 
determining why. Instead, it's a political decision.

==

[1] Here I mean that the process uses additional seats instead of 
redistributing; it may not need a different ballot. But by using 
additional seats, I think there's a lesser chance that it would be seen 
as somehow "tampering with the proper result".
[2] Parties that absolutely don't like each other can be considered 
within this category as well; and so one reaches the conclusion that in 
a country where parties just can't form coalitions and the government 
changes very rapidly, a majoritarian system is preferable. If the 
paralysis is too bad, then that kind of adjustment happens de facto 
anyway: the bureaucracy or civil service decides to govern as the only 
stable component in a system that can't otherwise decide. But the 
bureaucracy might have biases of its own: it tends to be very interested 
in its own perpetuation, for one. Thus that is not desirable.