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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.30017 |
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| _version_ | 1866914614335242240 |
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| author | Yang, Erya Brandenburger, Adam |
| author_facet | Yang, Erya Brandenburger, Adam |
| contents | We use the machinery of a conditional probability space (Rényi, 1955) to obtain an Agreement Theorem (Aumann, 1976) under general conditions. A conditional probability space (CPS) is a family of probability measures defined relative to a family of conditioning events that satisfies concentration and a chain rule. Using this apparatus, we derive an Agreement Theorem that dispenses with the traditional assumptions of a common prior, information partitions, positivity of measure, and knowledge operators. Our treatment can be viewed as ``deconstructing" the classic Agreement Theorem, by showing how it can be built up from local probabilistic-epistemic ingredients. The main technical contribution is to define an augmentation procedure for CPS's that adds into the conditioning family all (sub)events that receive probability $1$ -- thereby achieving consistency between an agent's information and subjective certainty of events. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_30017 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Conditional Probability Spaces and the Structure of Agreement Yang, Erya Brandenburger, Adam Probability 60A05 We use the machinery of a conditional probability space (Rényi, 1955) to obtain an Agreement Theorem (Aumann, 1976) under general conditions. A conditional probability space (CPS) is a family of probability measures defined relative to a family of conditioning events that satisfies concentration and a chain rule. Using this apparatus, we derive an Agreement Theorem that dispenses with the traditional assumptions of a common prior, information partitions, positivity of measure, and knowledge operators. Our treatment can be viewed as ``deconstructing" the classic Agreement Theorem, by showing how it can be built up from local probabilistic-epistemic ingredients. The main technical contribution is to define an augmentation procedure for CPS's that adds into the conditioning family all (sub)events that receive probability $1$ -- thereby achieving consistency between an agent's information and subjective certainty of events. |
| title | Conditional Probability Spaces and the Structure of Agreement |
| topic | Probability 60A05 |
| url | https://arxiv.org/abs/2605.30017 |