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DN Debate. Game theory shows that S+C+L+MP gives the strongest government

What are the power relations in the parliament? What is the political strength of different partikonstellationer have in office? Because small parties can sometimes act vågmästare so it is not only a question of the number of seats in the parliament. Therefore need other methods to determine a party or a partigrupperings political strength in the parliament.

In this post, we present what we found by applying a certain spelteoretisk method. The method was invented by Lloyd Shapley and further developed later by Roger Myerson. Both are laureate, however for other game theoretic contributions than these. The method is general and abstract, but gives precise results in applications. Shapley's original method has had many and varied applications, ranging from the political analysis of the strength of individual countries within the federations to the economic analysis of the cost-sharing between the airlines regarding the airport charges. Our results are based on the Myersons generalization.

; the shapley value enter in a systematic and overall power between individuals and groups in situations where these can form the value-creating coalitions among themselves. An individual's or group's strength, its Shapleyvärde, is defined as the added value of the individual or group adds by connecting to a randomly selected existing group. Applied in the majority decision in a political assembly; the shapley value of a party, the probability that the party will be vågmästare at a randomly selected vote. For example, every party in parliament that stands outside of a given partigruppering with, say, 143 (or 144) of the mandate, added value for the grouping if the party has at least 32 (or 31) seats in the parliament.

perhaps The most important missing aspect is the parties ' ideological similarities and differences. We have recently begun an analysis in which we introduce these in an extended version of the shapley's model.

Myerson generalizes; the shapley value by allowing certain individuals or groups are reluctant to engage in cooperation with some other groups. The starting point for the analysis then becomes a matrix that consists of ones and zeros, where a one corresponds to the mutual willingness to cooperate and a zero the absence of such mutual willingness.

the poll SVT conducted before the parliamentary elections , in which all parties were asked about their willingness or unwillingness to cooperate with the other parties. The resulting matrix contains the most ones, and, unsurprisingly, the zeros of certain pairs of batches when a batch is SD or V.

Based on this matrix, we calculate the intensity values captured for different partikonstellationer that have occurred in the debate. Styrkevärdet for such a constellation, we define as its Shapley-Myerson value under two assumptions: first, that partigruppen stick together at the polls in the Swedish parliament as a party, and that the other parties behave as individual actors (not form coalitions). Styrkevärdena for all parties will then lie between zero and one.

The strongest of the opposition parties against the red-green would be M and C, both with a strength index of 0.17. The strongest opposition parties against the alliance would be S and SD, both with the strength index to 0.12. The alliance is thus a stronger partigruppering than the red and green, both in terms of its own strength and in terms of the individual opposition parties strength.

A measure of the incentive for a party to be included in a coalition is the difference between the party's share of the strength of the group and how great its strength would be if all of the parties in parliament had acted individually. So defined is the incentive for the parties in the red-green coalition to 0.15, while the incentive within the Alliance is of 0.55. The parties in the Alliance have stronger incentives than parties in the red-green.

For example, S+M have styrkevärde 0,71 and incentives from 0.37 for participation. Against this group, all the other parties to be equally weak in the face of opposition, weaker than the opposition to the Alliance and the red-green. This partikoalition would, therefore, be slightly stronger than the Alliance and face a weaker opposition, but have weaker deltagarincitament for the opening parties.

What is the partikoalition of all of the discussed would be the greatest under this method of measurement? By allowing the computer to calculate a large amount of the potential partikonstellationer as mentioned in the media, we found that the maximum value, was 0.75, achieved both of the S+C+L+MP, and of the Alliance+MP. The first of these two coalitions would have the highest deltagandeincitament, 0,54 v to 0.47 for the other. The coalition S+C+L+MP would have M, V and KD as the equally strong opposition parties, while the SD would then miss oppositionsstyrka. Against the Alliance+MP would all the other parties have the same strength in the opposition.

Since none of the discussed partikoalitionerna have the majority playing the opposition's strength and political orientation to a certain role when the governing power is to be exercised.

Finally, we want to point out that these results should be taken with a pinch of salt because they do not capture all relevant aspects of the situation in the parliament. Perhaps the most important missing aspect is the parties ' ideological similarities and differences. We have recently begun an analysis in which we introduce these in an extended version of the shapley's model. It is too early to comment on the general results, but it seems that the following partikoalitioner would have very high values, even in the new analysis: S+C+L+MP, P+C+MP, and S+M.

in Summary, we find S+C+L+MP to be the strongest potential regeringsalternativet of that discussed.

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