Abstract
The approaching exit of Great Britain from the European Union raises many questions about the changing relations between other member states. In this work, we propose a new fuzzy game for multicriteria voting. We use this game to show changes in Shapley’s values in a situation where the weights of individual member countries are not determined and we describe non-determinism with fuzzy sets. In particular, this concerns considerations related to pre-coalitions.
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Notes
- 1.
It is worth noting that in Gładysz and Mercik (2018) the condition of superadditiveness is not met for simple fuzzy games. The condition can be modified for the so-called partial superadditiveness.
- 2.
There are several theorems related to additional properties of the Shapley value, e.g. Young (1985) proved that the Shapley value is the only value satisfying the properties of effectiveness, symmetry and strong monotonicity; van den Brink (2001) showed that it is the only value preserving a fairness condition according to a modification of marginal contributions to a coalition; Myerson (1977) showed that it preserves fairness based on balanced contributions to a coalition.
- 3.
We will notice that although the authors of the treaty rather did not expect Brexit to happen, the decision-making rules were formulated to be work regardless of the number of Member States.
- 4.
You can also show that after Brexit Ireland will join the group led by France.
- 5.
This approach can be referred to as optimistic approach. The pessimistic approach in this case means the Left spread equal to the population of the largest country from a given cluster (except the leading country), and the right spread equal to the population of the smallest of the other countries. Probably a mixed approach should be used, but we have no premises to propose such an approach.
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Gładysz, B., Mercik, J., Ramsey, D.M. (2018). The Effect of Brexit on the Balance of Power in the European Union Council Revisited: A Fuzzy Multicriteria Attempt. In: Nguyen, N., Kowalczyk, R., Mercik, J., Motylska-Kuźma, A. (eds) Transactions on Computational Collective Intelligence XXXI. Lecture Notes in Computer Science(), vol 11290. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-58464-4_8
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