I study endogenous learning dynamics for people expecting systematic reversals from random sequences - the "gambler's fallacy." Biased agents face an optimal-stopping problem , such as managers conducting sequential interviews . They are uncertain about the underlying distribution (e.g. talent distribution in the labor pool) and learn its parameters from their predecesors . Agents stop when early draws are deemed "good enough," so predecessors' experience contain negative streaks but not positive streaks. Since biased agents understate the likelihood of consecutive below-average draws, society converges to over-pessimistic beliefs about the distribution's mean . When early agents decrease their acceptance thresholds due to pessimism, later agents will become more surprised by the lack of positive reversals in their predecessors' histories, leading to more pessimistic inferences and lower acceptance thresholds -- a positive-feedback cycle. Agents who are additionally uncertain about the distribution's variance believe in fictitious variation (exaggerated variance) to an extent depending on the severity of data censoring .
I study endogenous learning dynamics for people expecting systematic reversals from random sequences - the "gambler's fallacy." Biased agents face an optimal-stopping problem . They are uncertain about the underlying distribution and learn its parameters from predecessors . Agents stop when early draws are "good enough," so predecessors' experience contain negative streaks but not positive streaks. Since biased agents understate the likelihood of consecutive below-average draws, society converges to over-pessimistic beliefs about the distribution's mean and stops too early. Agents uncertain about the distribution's variance overestimate it to an extent that depends on predecessors' stopping thresholds. Subsidizing search partially mitigates long-run belief distortions .
D
, such as managers conducting sequential interviews
D
(e.g. talent distribution in the labor pool)
R
their predecesors
predecessors
D
deemed
R
. When early agents decrease their acceptance thresholds due to pessimism, later agents will become more surprised by the lack of positive reversals in their predecessors' histories, leading to more pessimistic inferences and lower acceptance thresholds -- a positive-feedback cycle. Agents who are additionally
and stops too early. Agents
R
believe in fictitious variation (exaggerated variance)
overestimate it
R
depending on the severity of data censoring
that depends on predecessors' stopping thresholds. Subsidizing search partially mitigates long-run belief distortions