The law applicable to arbitration is different from the law applicable in arbitration. The latter leads arbitrators to decide as they do. The former refers to the source of their authority and the effect of their decision – the legal order that governs arbitration. According to the territorialist thesis, an arbitration can have no foundation other than that of the legal order of the particular state where the arbitration takes place. This outdated conception is disproved by the simple factual observation that a plurality of legal orders may give effect to arbitration. Some French scholars promote the notion of an autonomous arbitral order. Inasmuch as they ultimately seek to establish this order by positing its recognition by the very state orders from which they claim autonomy, their idea is circular and in effect no more than a dressed-up variant of ordinary horizontal pluralism. But the model of horizontal pluralism fails to account for important orderings of arbitral activity. Arbitration in modern society is accurately perceived as a complex, three-dimensional form of pluralism, in which legal orders (i) are not exclusively those of states and (ii) frequently overlap
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