Is law a maximization problem?

08 Dec, 2025

G shared some food for thought. Let us consider the exercise of arguing a case in the court to be an optimization problem where we maximize the convince metric $C$ , such that, beyond a threshold $C \geq C_{t}$ , the bench rules in our favor. Note that the USA is a common law country, i.e. the Supreme Court rulings are typically based on precedents ¹. Now, since ChatGPT is trained on the collective worldly knowledge, and therefore knows all angles and perspectives to a given argument, winning a case simply becomes a RAG problem? It could be solved as:

Retrieve all relevant arguments: every retrieved argument has a convince metric $c_{i}$
Rerank retrieved arguments: s.t., $c_{1} > c_{2} > c_{3} . . .$
Compose final argument: $C = c_{1} + c_{2} . . . c_{n}, s . t . C \geq C_{n}$

The obvious gap in this thought exercise is, how can we derive $C$ ? And the obvious response is, have we tried fitting a network to see if hidden patterns are uncovered to make this work?

What is concerning here is that the common shortcomings of today's AIs that they are only capable of remixing content and not genuinely creative is not necessarily an impediment here. Admittedly, this is only(?) because the idea I propose here is applicable to common law countries. Nevertheless, this certainly makes me wonder what this means for the legal profession in the bigger picture.

Common law relies on judicial precedent (past court decisions) as the primary source of law, while civil law is based on comprehensive, codified statutes. Common law systems are adversarial, with judges acting as impartial referees, and are found in countries like the UK and US. Civil law systems are more investigatory or inquisitorial, and are prevalent in most of Europe, Asia, and South America.↩