This paper argues that in cases of deep judicialization, where highly salient political values are being adjudicated on a regular basis, political attention may shift from national sovereignty costs (the vertical dimension) to distributive conflicts within and between states (the horizontal dimension), creating a multidimensional conflict space. Together with Olof Larsson, we discuss the implications of this setting for judicial behavior, and argue that it may create both opportunities and pitfalls for international judges, depending on how the dimensions are related. If the institutional interests of judges in promoting international law systematically favor some states over others on the horizontal dimension, judicial activism is likely to provoke severe legitimacy problems. If the dimensions are unrelated, on the other hand, arbitrators become further empowered. Empirically, we show how the Court of Justice of the EU has been able to use divisions between states on the Left-Right dimension to enhance the status of European law.
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