Foundations of Algorithmic Decision Making: Probabilistic Reasoning & Representation
Foundations of Algorithmic Decision Making Representation for Probabilistic Reasoning Uncertainty is everywhere. Even systems governed by precise physical laws — like satellite trajectories — can drift because small imprecisions compound over time. Measurements contain noise. Sensors fail. Humans behave unpredictably. A decision-making system that ignores uncertainty is fragile. One that models it explicitly becomes powerful. Probability gives us a structured language for representing uncertainty and reasoning under it. 1. Degrees of Belief Probability can be interpreted as a degree of belief — a numerical way of expressing how plausible we think a proposition is. $$ A \succ B \quad \text{or} \quad P(A) > P(B) $$ To behave rationally, our beliefs must follow two core assumptions: Universal Comparability — Any two events can be ranked. Transitivity — If $$ A \succeq B $$ and $$ B \succeq C $$, then $$ A \succeq C $$. ...