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In the area of the law applicable to investment arbitration disputes, there has been a certain doctrinal indifference since the 1990s, when arbitrations on the sole basis of investment protection treaties began to emerge in the wake of the AAPL v. Sri Lanka award. The new arbitral trend seems to have blurred the boundaries between contractual and treaty-based arbitration. But arbitral practice has shown that the applicable law still contains significant issues. The arbitral jurisprudence is far from unanimous on the identification of the applicable law depending on whether or not there is a choice of law. The article examines the way in which arbitral tribunals deal with the parties’ will regarding the applicable law and the absence of such a will. Starting from a summa divisio modelled on the implementation of article 42 (1) of the ICSID Convention by arbitral tribunals, the conclusion is drawn that in many situations party autonomy tends before to yield to the arbitrator’s office.