Odds Law: The Decomposition Algebra On How Intelligence Organizes Itself to Solve Difficult Problems Reliably

The paper introduces a decomposition algebra for organizing unreliable elementary problem-solvers to reliably tackle complex problems. Key contributions include a verification odds law that demonstrates how verification gates can amplify correctness odds, a reliability amplification theorem providing a method to achieve high reliability at logarithmic cost, and a threshold dichotomy that delineates conditions for effective reliability amplification. This work is significant for AI practitioners as it formalizes the relationship between problem-solver organization, reliability, and cost, offering a structured approach to enhance the performance of AI systems through strategic composition.