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

[Juho Laatu]

On 22.7.2013, at 23.50, Kristofer Munsterhjelm wrote:

> On 07/22/2013 05:37 PM, Juho Laatu wrote:
>> On 22.7.2013, at 16.43, Vidar Wahlberg wrote:
> 
>>> That might produce a sensible result, I'll see if I can modify the
>>> code to do something like this.
>> 
>> I think that approach is at least quite easy to explain and justify
>> to the voters. A full quota is something that looks pretty much like
>> a certain seat, and quota fractions look like possible seats.
> 
> Yes, a quota is easier to explain. Just consider my attempts at divisor-based STV analogs vs STV itself: the latter is far easier to understand.
> 
> On the other hand, quota-based systems have some peculiar properties. In party list, if you're using a quota method, it might happen that party X gains support while party Y loses support, yet Y gains more seats than X.

Yes, the paradoxes may complicate things (http://en.wikipedia.org/wiki/Apportionment_paradox). Some of the peculiarities can however be quite acceptable and even wanted. We discussed earlier for example the possibility that some seats would go to Condorcet style centrists. Let's say we have three parties, large Left, large Right and small Centre. If there is only one seat, we might give that to the centrist party (since it may be a clear Condorcet winner). But if there are two seats we might give them to Left and Right. And we get Alabama paradox style behaviour (where the centrist party loses a seat when the number of seats grows).

The benefit of divisor methods is that they give a clear order of allocation. The quota methods rather focus on minimizing the "lost votes". Both have their benefits, and their problems, both from the point of view of who should actually be elected, and from the point of view how to explain the behaviour of the methods to the audience.

> 
> I guess that for party list, you could explain a divisor method pretty easily as well -- or rather, the Webster variant (multiply and round) would be fairly easy to explain:
> 
> "We would like each party to get a proportional share. So we divide each party's number of votes by some constant to get the sum to equal the number of seats in parliament.
> But this will give fractional results, so we have to round the results since there's no such thing as a tenth of an MP.
> But now the sum of seats may not add up to the number of seats in parliament. So we adjust the divisor."
> 
> In other words, it's the least possible change from the ideal situation, given that we can't have fractional MPs.
> 

I'd like to test and try fractional MPs too :-).

I note that generally voters need a simple and credible explanation. Very few voters actally understand how the most common divisor methods lead to proportional representation. Some of them may know how to use the algorithm, but I guess most are just happy to have a vague understanding that the used algorithm is most likely ok since people say it is "proportional" and experts, media and one's own party do not complain about it.

The algorithm may thus be complex and it may contain paradoxes as long as there is a consensus that it works well enough. Or the algorithm may simple to help calculations and understanding. Nowadays simple calculations are no more a requirement, but computerized counting may sometimes be presented as a potential source of fraud (not often in real life though, if the calculations can be independently checked).

I note that it is quite common that claimed problems emerge when some interest group wants to attack a method  that is for some reason not beneficial to the interest group. Often the identified flaws are just clever propaganda, not so much about actual meaningful flaws of the system. It is also possible that flaws are real in a situation where someone proposes a biased system that would serve the interest of some interest group (e.g. to keep the current strong parties in power).

After saying all this, I note that the most common divisor and largest remainder methods tend to give very proportional results when compared to what kind of systems are on average used globally. I think they are also all simple enough and easy enough to justify (not to all voters but to many enough experts and politicians to get the consensus that they work fine). Often the vulnerabilities are vulnerabilities to negative marketing, not really vulnerabilities in the actual use of the system.

Juho