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  1. Introduction.
  2. The notion of power and voting power.
  3. The Shapley-Shubik power index.
  4. Decisions at the Council of the CAB.
  5. The advantages of Shapley-Shubik power distribution.
  6. Conclusion.
  7. References.

France is administratively divided in ?communes?, the smallest territorial division of the country, usually corresponding to a city or a village. The number of communes in France, including overseas territories, is 36 782. This high number leads to huge disparities in terms of population and geographical surface. For instance, 90% of the communes have less than 2000 inhabitants and only a hundred have more than 50 000 inhabitants. To make their administrative management easier, the state decided in 1971 with the law ?Marcellin? to give the possibility for neighbouring communes to gather in a collective structure (hereafter called intercommunalité) in order to develop common projects. The idea is that two communes would be financially better-off in supplying together a public good, a swimming-pool for instance, that would be accessible to their inhabitants

[...] is pivotal times in order to pass a decision. What we could finally wonder is whether there are other factors that need to be taken into account in order to measure the exact power of the intercommunalité. First of all, the hypothesis that all voting sequences are equally possible does not hold in reality. Indeed, political preferences often play a crucial role in building coalition. In our case, we could also think that geography is an important element: communes that are next to each other are likely to vote together in order to have the public good supplied in their area (or far away if the good is non- beneficial). [...]

[...] goods. We can indeed expect that the commune with the most power will likely be the one where attractive public goods will be built (crèche, pools, parks ) and unattractive public goods will be settled further away from it (rubbish dump). However, it is not because a commune has more delegates than others that it has the most power. This is the idea underlying theories of voting power index. All of these theories (Penrose, Banzhaf, Shapley and Shubik ) have in common the notion of ?pivotal agent' as the most important player in a cooperative game. [...]

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