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CATEGORIES:Optimization and Incentives Seminar
SUMMARY:Elicitation for Aggregation - Ian Kash (MSR Cambri
dge)
DTSTART;TZID=Europe/London:20141111T140000
DTEND;TZID=Europe/London:20141111T150000
UID:TALK56041AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/56041
DESCRIPTION:We study the problem of eliciting and aggregating
probabilistic information from multiple agents. In
order to successfully aggregate the predictions o
f agents\, the principal needs to elicit some noti
on of confidence from agents\, capturing how much
experience or knowledge led to their predictions.
To formalize this\, we consider a principal who wi
shes to elicit predictions about a random variable
from a group of Bayesian agents\, each of whom ha
ve privately observed some independent samples of
the random variable\, and hopes to aggregate the p
redictions as if she had directly observed the sam
ples of all agents. Leveraging techniques from Bay
esian statistics\, we represent confidence as the
number of samples an agent has observed\, which is
quantified by a hyperparameter from a conjugate f
amily of prior distributions. This then allows us
to show that if the principal has access to a few
samples\, she can achieve her aggregation goal by
eliciting predictions from agents using proper sco
ring rules. In particular\, if she has access to o
ne sample\, she can successfully aggregate the age
nts' predictions if and only if every posterior pr
edictive distribution corresponds to a unique valu
e of the hyperparameter. Furthermore\, this unique
ness holds for many common distributions of intere
st. When this uniqueness property does not hold\,
we construct a novel and intuitive mechanism where
a principal with two samples can elicit and optim
ally aggregate the agents' predictions.
LOCATION:MR4\, Centre for Mathematical Sciences\, Wilberfor
ce Road\, Cambridge
CONTACT:Felix Fischer
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