[EM] Automatic algorithm for coalition building

Peter Gustafsson miningphd at hotmail.com
Tue Sep 3 06:36:34 PDT 2013

> From: juho4880 at yahoo.co.uk
> Date: Mon, 2 Sep 2013 00:08:38 +0300
> To: election-methods at lists.electorama.com
> Subject: Re: [EM] Sociological issues of elections
> On 1.9.2013, at 22.02, Vidar Wahlberg wrote:
>> On Sun, Sep 01, 2013 at 07:05:12PM +0300, Juho Laatu wrote:
>>> I tried to outline some scenarios where the voters could more or less directly determine the composition of the coalition. I guess this is too "dynamic" for you, and you actually like the current Norwegian practice where there are two rather fixed government alternatives, and voters know exactly which coalition each candidate/party belongs to?
>> I apologize for answering so briefly on your message.
>> I find the idea that letting the voters vote for their preferred
>> coalition quite interesting
> I agee with interesting. But probably they are not very pracical, and probably will not be used. I just wanted to analyze the prospects a bit further on the path taht you seemed to point out. :-)
>> And I can't fully
>> visualize how such an election would work, and it seems to me that this
>> may quickly become a fairly complex system?
> Yes. Even the simplest approaches could get quite complex since one can not allow a mechanical algorithm to>determine the coalition anyway. Maybe the parties will not agree, and it is not easy to agree what coalition>size is optimal etc. So, maybe voter opinions would be used olny as one input in the negotiations.

One simple (in theory, good luck getting parties to agree with it!) way of dealing with that would be that parties must agree to enter whichever coalition the voters prefer. That would be a prerequisite for entering the election. Parties that balk, once the coalition is decided upon by the voters, get their parliamentary seats revoked, but no other party gets those seats - they go empty until the next general election. That kind of potential punishment ought to concentrate their minds.

> We can see the sizes of the parties after the election anyway, and we can see which parties lost votes and which ones gained new votes. Based on this we can quite well already see which coalitions are the favourite ones. Explicit voter given information on different coalitions could be just additional opinion poll style information. Maybe a Condorcet poll where different coalition core partner combinatons are listed as candidates. Maybe a poll on one's favourite party and one's favourite second party for the coalition. The latter example is easier since it is easier to agree what the candidates are. But the additional information that these polls would offer is not very essential anyway.

Let me suggest a method for how to create coalitions based upon voter preferences:
1. Voters vote for primary party. They also are given the option to rank all other parties in order of preference.
2. Parties get seats according to the usual proportional parliamentary election procedure.
3. If any one party gets an outright majority of the seats, they get to form a 1-party govt.
4. Otherwise, all possible party pairs are investigated. If N voters from party A rank party B as the 2nd best party, and M voters from party B rank party A as the 2nd best party, then the sum N+M is designated the Mutual 2nd preference number (M2PN) for the party pair AB.
5. The M2PN is found for all party pairs.
6. The party pair which is has the highest M2PN is put together into the first coalition.
7. If that party pair has an outright majority of the parliamentary seats, they form a 2-party coalition govt.
8. If there still is no majority coalition, a new party pair is put together by using the 2nd highest M2PN number. However, for the voters who voted for either of the two parties in the first coalition, their 3rd party preference is used, so that party pair AB can be coalitioned with party C, if many of the AB voters thought that party C was their 3rd preference, and many of the C voters thought that either A or B were their 2nd preference.
9. Coalitions are formed and extended until one coalition has an outright majority of the seats, and then that coalition gets to form the govt.

This method is simple for the voter that does not want to do anything complicated - just vote as usual. If that voter does not state any 2nd and lower preferences, then he simply does not have any say in coalition building.
The more sophisticated voter simply has to add preferences, until he reaches a party that he can not stand at all, or that he is sure that any further party preferences will not change the outcome.
It is also simple for political parties - they simply have to agree on coalitions beforehand, and instruct their voters to vote for all the coalition parties Before any other party.

This system would only really come into play if none of the coalitions would amass a majority. In that case, it would be the job of the voters to put together one of the preannounced coalitions with one or more parties that they did not want. I think that such enforced nearness would sharpen the minds of the politicians.
An example of this would be the most recent parliamentary election in Sweden. Before it, the conservatives, liberals, farmer party, and christian democrats announced that they were a 4-party coalition. On the other side, the labor party, the greens, and the left party were in it together, but in a somewhat less formalized structure. Beside those 7 parties, there was one more party with a reasonable chance of getting into the parliament - the Sweden Democrats. None of the 7 old parties would touch the SD party, and the latter was harshly treated in media. What happened was that the 4-party coalition got the largest bloc of seats, and they now form a minority govt which is not toppled by the SD party, even if the latter could do so at any time by Calling a no confidence vote.

Under the system outlined above, there would be some coalition building, so that at one point 3 plocs would be formed. None of those would have a majority of seats. Then, in the next stage of automated coalition-building, one of the 3 possible coalitions would gain a majority, and politicians would be forced to work together with people that they do not like. That would be something that I would like to see.
One county In Sweden had at one time 8 parties in the county parliament, which had 33 seats. The labor party had 16 of those, but the other 7 parties formed a coalition govt. with 17 seats. That had required quite a bit of haggling, and it was difficult to keep the coalition together for the entire period. If there would have been an automated coalition building system in place, and no form of premature elections, then it would have held together with less work.

Peter Gustafsson 

> Juho
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