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Beyond Unbounded Beliefs: How Preferences and Information Interplay in Social Learning

Navin KartikSangMok LeeTianhao LiuDaniel Rappoport
Mar 2021
摘要
When does society eventually learn the truth, or take the correct action, viaobservational learning? In a general model of sequential learning over socialnetworks, we identify a simple sufficient -- and, in a sense, necessary --condition for learning dubbed \emph{excludability}. Excludability is a jointproperty of agents' preferences and their information. When required to holdfor all preferences, it is equivalent to information having "unboundedbeliefs", which demands that any agent can individually identify the truth,even if only with small probability. But unbounded beliefs may be untenablewith more than two states: e.g., it is incompatible with the monotonelikelihood ratio property. Excludability reveals that what is crucial forlearning, instead, is that a single agent must be able to rule out any wrongaction, even if she cannot take the correct action. Consequently, excludabilityhelps study classes of preferences and information that mutually ensurelearning. We develop two such pairs: (i) for a one-dimensional state,preferences with single-crossing differences and a new informational condition,directionally unbounded beliefs; and (ii) for a multi-dimensional state,Euclidean preferences and subexponential location-shift information.
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