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SUMMARY:Elicitation for Aggregation - Ian Kash (MSR Cambridge)
DTSTART:20141111T140000Z
DTEND:20141111T150000Z
UID:TALK56041@talks.cam.ac.uk
CONTACT:Felix Fischer
DESCRIPTION:We study the problem of eliciting and aggregating probabilisti
 c information from multiple agents. In order to successfully aggregate the
  predictions of agents\, the principal needs to elicit some notion of conf
 idence from agents\, capturing how much experience or knowledge led to the
 ir predictions. To formalize this\, we consider a principal who wishes to 
 elicit predictions about a random variable from a group of Bayesian agents
 \, each of whom have privately observed some independent samples of the ra
 ndom variable\, and hopes to aggregate the predictions as if she had direc
 tly observed the samples of all agents. Leveraging techniques from Bayesia
 n statistics\, we represent confidence as the number of samples an agent h
 as observed\, which is quantified by a hyperparameter from a conjugate fam
 ily of prior distributions. This then allows us to show that if the princi
 pal has access to a few samples\, she can achieve her aggregation goal by 
 eliciting predictions from agents using proper scoring rules. In particula
 r\, if she has access to one sample\, she can successfully aggregate the a
 gents' predictions if and only if every posterior predictive distribution 
 corresponds to a unique value of the hyperparameter. Furthermore\, this un
 iqueness holds for many common distributions of interest. When this unique
 ness property does not hold\, we construct a novel and intuitive mechanism
  where a principal with two samples can elicit and optimally aggregate the
  agents' predictions.
LOCATION:MR4\, Centre for Mathematical Sciences\, Wilberforce Road\, Cambr
 idge
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