<p>AI systems are widely applied in many different areas of life. It is also possible to create automated judicial decision-making systems to support or even replace human judges. Because the entry into force of regulation that enables the application of fully automated judicial decision-making systems would be a Copernican revolution in the execution of judicial power, it would be necessary to organise referenda and public consultations concerning issues discussed in this work and make constitutional amendments. The scope of public consultations and main referendum questions are proposed in this article. The paper also considers proposals for constitutional principles concerning judicial AI systems, such as the right to human intervention, the right to know the logic of automated judicial decision-making systems, the right to know about the application of AI systems for executing judicial power purposes, the right to obtain meaningful information on automated judicial systems, the right to know the logic of these systems, and the right not to be subject to automated judicial proceedings. The article also discusses non-constitutional amendments of judicial orders concerning AI decision-making systems. There is a proposal for benchmark constitutional regulation concerning automated judicial decision-making systems in the work. This proposal includes the main fundamental principles that are discussed in theoretical part of the article. This work can be helpful in adjusting constitutional law and judicial orders to the future application of fully automated judicial decision-making systems. Furthermore, this paper's conclusions can be valuable for legal researchers and lawmakers. This stems from the fact that the article includes theoretical considerations on proposals for fundamental principles concerning AI judicial systems and the way of entering these rules into force.</p>