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

[Juho Laatu]

On 20.7.2013, at 13.07, Kristofer Munsterhjelm wrote:

> 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.

If new mechanisms are needed in order to avoid using some more problematic mechanisms (like a high threshold), then such mechanisms are needed. But if not absolutely needed, my preference is to go for full proportionality, allowing compromise candidates instead of ones with most unused support (fractional quota) left only when allocating the very last seats. Also in those cases allocation of last seats to compromise candidates would be based on vote transfers (of still unused fractional votes) that give the compromise candidate more support than all extreme candidates have.

One reason for this approach is that voter opinions and majortity are such a strong concepts that one should avoid breaking such majorities. Let's say we have four parties, big left, big right, small extreme left, and small modeate right. L + EL have 51% majority. EL is now a kingmaker in the sense that its support gives majority strength to L. MR is a compromise party in this scenario (preferred over the other big party by many voters). If we give more power to MR (since it is a compromise party, or since it is more moderate than the other small party) would change the left wing majority to a right wing majority. I'm sure this would also not look good in the eyes of the voters and media.

Parties of different size may have "disproportional" voting power with certain distribution of strength among the parties. But I rather see that as a mathematical phenomenon that is natural in the sense that if majorities are that way, then they are that way. It would be difficult to say that some majority grouping does not deserve its majortity status.

I already noted few mails back that at least in Finland I don't see the kingmaker effect giving too much power to the small parties. Typically government coalitions have more than one small party, if one small party would be in a kingmaker position. And generally small parties rather respect the opinions of the big parties. This is because they want to continue co-operation with other parties also in the next governments, and because they probably made some agreements (you get this, I get that, other topics will be decided by majority within the government) when the government was formed.

I thus believe that in many (maybe most) countries the kingmaker position would not be a major problem. But if it causes problems in the discussion, then some modifications may be needed to defend agaist the threat, or the threat of not making any progress otherwise.

> 
> 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.

Yes, in principle we could elect a dictator using Condorcet. Another quite similar approach would be to elect an exactly proportional parliament (in the extreme case, consisting of all the citizens) and then let that parliament vote on every question using Condorcet. Ther resuts could be quite similar, except that in the latter case the opinions would not be those of one chosen individual but compromise opinions of the whole group. (The chosen compromise dictator would probably have some non-compromise opinions too in some topics, while in the latter case all decisions would be compromise decisions.)

In real life multiparty systems it is however typical that some majority forms a govenrment and then votes against the opposition in all questions. This means that one majority takes all power. Parties in the government in a way make (dynamically in time, or when the government was formed) government internal majority decisions and then force others to accept those decisions. Some government parties may vote against their own opinions (that have majorty support in the parliament) in the parliament, but that's how the game goes. This to some extent ties the hands of small parties in the government. (I note that in some countries the discipline within the government is not that high, so there is variation on how mojorities work in different environments and on what effects the kingmaker position has.)

> 
> 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.

Yes (I tried to address similar problems few lines above).

> 
> 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.

One key benefit of multiparty systems is that voters can punish parties that have plotted too much. Humans are clever and tehrefore also always find new way to make deals that are good for themselves but that may bypass the true opinion of the voters. In democratic multiparty systems the promise is that at some point voters will see that things are not right anymore, and that is supposed to led to change in power (not just repretition of the explanations, not just alternating opposition/government role of the old big parties, not just walking in the direction preferred jointly by the top management of all parties (but not by the majority of voters)).

> 
> 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.

Unfortunaltely my best guess is that the strongest power here is maintenance of status quo. Those parties that are now in the parliament are generally happy with the current threshold related rules since they are "above the line". This is one reason why we hear opinions like "having more parties would make the system unstable". I.e. maybe unstable to the current parties in the sense that some of them could lose some of their seats. That is of course not an acceptable argument, so they need to find "better" ones.

If we are talking about typical stable democracies and only few extra seats in the parliament, I can't see any problem in allowing also those opinions to be heard. I note that there may be countries that are not stable and where it would not make sense to risk the current fragile system by introducing more potentially radical opinions in the parliament, but these are exception, not the main rule for (stable) democracies.

> 
> ==
> 
> [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.
> 

The expected lifetime of governments is an important measure. There are countries where govenrmnets usually live from one parliamentary election to the next. In some other countries governments might break every few months. In the first catergory I don't see any need to trade proportionality to stability (by eliminating small parties (= some voters) or their voting power). In the latter case reduced proportionality might help in some cases (or might not).

Juho