Abstract
Ideals are used to provide necessary and sufficient conditions for classes of choice functions satisfying the Strong Axiom of Preference, the Weak Axiom of Revealed Preference, or Path Independence. Semigroups whose choice functions are not path independent are demonstrated to lack proper ideal structures. A subsemigroup which is a monoid is identified. A motivation for interest in these structures is that the semigroup property is required of all finite state automata. Search-process foundations to choice functions facilitate applying automata results to economics and direct tests of whether an automaton is economic. Journal of Economic Literature Classification Numbers: C69, D00, D83.
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