False Consensus, Information Theory, and Prediction Markets
summary
Proves that when private signals are conditional independence (substitutes), any epsilon-approximate consensus (agents’ mutual information with outcome ≤ ε given history) implies ε·n approximate aggregation: the remaining information about the outcome is ≤ nε by mutual information subadditivity via interaction information and chain rules. Uses a potential function (mutual information of public history with outcome) to rederive fast convergence, and links to prediction markets where trades under the log scoring rule payments equal conditional mutual information.
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chapters (12)
- 0:00Intro
- 1:09Agreement Protocol Example
- 2:49Agreement Theorem
- 3:15Questions
- 6:34Main Theorem
- 7:29High-Level Proof
- 9:41Information Theory Background
- 12:04Approximate Agreement
- 13:24Subadditivity for substitutes
- 16:20No False Consensus with Substitutes
- 18:52Quick Consensus
- 21:49Connection to Prediction Market
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