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This is a presentation for introduction on the paper "A Bayesian Truth Serum" by Dražen Prelec
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Introduction to Bayesian Truth Serum (BTS)
presented by Fuming Shih
Ask for true opinion?
• Will you buy Samsung Galaxy S3 when it comes out? (Yes/No)
• Will you vote in the next presidential election?– (definitely/probably/probably not/definitely not)
• Have you had more than 20 sexual partners over the past year (Yes/No)
What is BTS?
• Survey scoring method that provides truth-telling incentives for respondents answering multiple-choice questions
• Respondents to supply not only their own answers, but also percentage estimates of others’ answers.
• The formula then assigns high scores to answers that are surprisingly common
A Bayesian Truth Serum for Subjective Data by Drazen Prelec Science 15 October 2004: Vol. 306 no. 5695 pp. 462-466
BTS simplified
• “The premise behind this approach is the following. If people truly hold a particular belief, they are more likely to think that others agree or have had similar experiences.”
• you are your best estimator– or your estimation reveals you– posterior probability
Youthe unknown world (distribution of different opinions)
your estimation
Example Survey
How it works
reference: http://internetconferences.net/ipsi/files/CroatiaPrelecVIPSI.pdf
Calculate BTS Score
reference: http://internetconferences.net/ipsi/files/CroatiaPrelecVIPSI.pdf
The Information score: measures surprisingly common
ex. log(0.15/0.05)
reference: http://internetconferences.net/ipsi/files/CroatiaPrelecVIPSI.pdf
prediction score measures prediction accuracy
equals zero for a perfect prediction
reference: http://internetconferences.net/ipsi/files/CroatiaPrelecVIPSI.pdf
Conclusion First
• The best strategy for the respondent is to tell the truth
Your preference “wins” to the extent that itis more popular than collectively estimated
reference: http://internetconferences.net/ipsi/files/CroatiaPrelecVIPSI.pdf
The intuitive argument for m=2
reference: http://internetconferences.net/ipsi/files/CroatiaPrelecVIPSI.pdf
and I happen to like Red
reference: http://internetconferences.net/ipsi/files/CroatiaPrelecVIPSI.pdf
This is my best estimate of the Red share (e.g., 50%)
reference: http://internetconferences.net/ipsi/files/CroatiaPrelecVIPSI.pdf
Bayesian reasoning implies that someone wholikes White will estimate a smaller share for Red
reference: http://internetconferences.net/ipsi/files/CroatiaPrelecVIPSI.pdf
The average predicted share for Red will fallsomewhere between these two estimates
reference: http://internetconferences.net/ipsi/files/CroatiaPrelecVIPSI.pdf
Hence, if I like Red I should believe thatthe share for Red will be underestimated
or ‘surprisingly popular’
My prediction of theaverage Red shareestimate
reference: http://internetconferences.net/ipsi/files/CroatiaPrelecVIPSI.pdf
The argument holds even if I know that mypreferences are unusual
reference: http://internetconferences.net/ipsi/files/CroatiaPrelecVIPSI.pdf
Application?
• Honest signals subjective preferences– BTS draws more truth opinions from the users– reality mining captures the objective ground truths
• Are there relations between these two?– I feel stressful when multiple people around me– I feel depressed when I am alone
• A improvement on psychological-social probe– developing an opinion probe on funf-framework– capture preferences and context at the same time