Axiomatic Choice
Ben Abramowitz, Nicholas Mattei
TL;DR
Axiomatic Choice offers a domain-agnostic formalism for decision-making that encodes normative positions as axioms over decisions defined by profiles, rules, and outcomes, bridging and extending beyond classical Social Choice. The approach defines a rich taxonomy of axioms, formalizes transparency and deception, and introduces the Decision-Evaluation Paradox, which shows that decisions following an axiom’s implied rule may fail to obey the axiom itself. It also provides a minimal, language-independent definition of intraprofile axioms and analyzes how combining axioms via set operations can yield impasses or impossibilities, affecting methods like Voting by Axioms. The work highlights fundamental limits of axiom-based decision procedures, emphasizes the importance of auditable explanations, and offers a domain-agnostic path for future research in normative decision-making and value alignment.
Abstract
People care about decision outcomes and how decisions get made, both when making decisions and reflecting on decisions. But formalizing the full range of normative concerns that drive decisions is an open challenge. We introduce Axiomatic Choice as a framework for making and evaluating decisions based on formal normative statements about decisions. These statements, or axioms, capture a wide array of desiderata, e.g., ethical constraints, beyond the typical treatment in Social Choice. Using our model of axioms and decisions we define key properties and introduce a taxonomy of axioms which may be of general interest. We then use these properties and our taxonomy to define the Decision-Evaluation Paradox, formalize the concepts of transparency and deception in explaining and justifying decisions, and reveal the limits of existing methods using axioms to make decisions.