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<p>By defining conditional probabilities as primitives,&#xa0;Rényi (Acta Mathematica Academiae Scientiarum Hungaricae 6(3):285–335, 1955) provides a framework for understanding scenarios that challenge classical probability theory, such as conditioning on events with zero unconditional probability. The paper proposes a notion of equivalence among such <i>conditional probability systems</i> (CPSs) and shows its appealing properties (e.g., the existence of a canonical form). Additionally, we demonstrate an application of the equivalence concept by continuing the work started in&#xa0;Brandenburger et al. (Synthese 201(5):175, 2023) to show that, at some fundamental level, <i>lexicographic probability systems</i> (LPSs) and <i>finitary</i> CPSs are merely different ways of encoding the same probabilistic information.</p>

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Equivalent conditional probability systems

  • 期刊论文

  • 发表日期：

    2026年2月9日

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  • Byung Soo Lee

摘要

By defining conditional probabilities as primitives, Rényi (Acta Mathematica Academiae Scientiarum Hungaricae 6(3):285–335, 1955) provides a framework for understanding scenarios that challenge classical probability theory, such as conditioning on events with zero unconditional probability. The paper proposes a notion of equivalence among such conditional probability systems (CPSs) and shows its appealing properties (e.g., the existence of a canonical form). Additionally, we demonstrate an application of the equivalence concept by continuing the work started in Brandenburger et al. (Synthese 201(5):175, 2023) to show that, at some fundamental level, lexicographic probability systems (LPSs) and finitary CPSs are merely different ways of encoding the same probabilistic information.