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# Introduction to Bayesian Truth Serum

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This is a presentation for introduction on the paper "A Bayesian Truth Serum" by Dražen Prelec

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• The algorithm assigns more points to responses to answers that are &quot;surprisingly common&quot;, that is, answers that are more common that collectively predicted. For example, let&apos;s say you are being asked about which political candidate you support. A candidate who is chosen (in the first question) by 10% of the respondents, but only predicted as being chosen (the second question) by 5% of the respondents is a surprisingly common answer. This technique gets more true opinions because it is believed that people systematically believe that their own views are unique, and hence will underestimate the degree to which other people will predict their own true views.
• example:X_bar = 0.15Y_bar = 0.05 information score = log(3)The Information score measures whether ananswer is surprisingly common
• example:X_bar = 0.15Y_bar = 0.05 information score = log(3)The Information score measures whether ananswer is surprisingly common
• ### Introduction to Bayesian Truth Serum

1. 1. Introduction toBayesian Truth Serum (BTS) presented by Fuming Shih
2. 2. 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)
3. 3. 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
4. 4. 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 Youyour estimation the unknown world (distribution of different opinions)
5. 5. Example Survey
6. 6. How it worksreference: http://internetconferences.net/ipsi/files/CroatiaPrelecVIPSI.pdf
7. 7. Calculate BTS Score reference: http://internetconferences.net/ipsi/files/CroatiaPrelecVIPSI.pdf
8. 8. The Information score: measures surprisingly common ex. log(0.15/0.05) reference: http://internetconferences.net/ipsi/files/CroatiaPrelecVIPSI.pdf
9. 9. prediction score measures prediction accuracy equals zero for a perfect prediction reference: http://internetconferences.net/ipsi/files/CroatiaPrelecVIPSI.pdf
10. 10. Conclusion First• The best strategy for the respondent is to tell the truth Your preference “wins” to the extent that it is more popular than collectively estimated reference: http://internetconferences.net/ipsi/files/CroatiaPrelecVIPSI.pdf
11. 11. The intuitive argument for m=2 reference: http://internetconferences.net/ipsi/files/CroatiaPrelecVIPSI.pdf
12. 12. and I happen to like Red reference: http://internetconferences.net/ipsi/files/CroatiaPrelecVIPSI.pdf
13. 13. This is my best estimate of the Red share (e.g., 50%) reference: http://internetconferences.net/ipsi/files/CroatiaPrelecVIPSI.pdf
14. 14. Bayesian reasoning implies that someone wholikes White will estimate a smaller share for Red reference: http://internetconferences.net/ipsi/files/CroatiaPrelecVIPSI.pdf
15. 15. The average predicted share for Red will fall somewhere between these two estimates reference: http://internetconferences.net/ipsi/files/CroatiaPrelecVIPSI.pdf
16. 16. Hence, if I like Red I should believe thatthe share for Red will be underestimated or ‘surprisingly popular’ My prediction of the average Red share estimate reference: http://internetconferences.net/ipsi/files/CroatiaPrelecVIPSI.pdf
17. 17. The argument holds even if I know that my preferences are unusual reference: http://internetconferences.net/ipsi/files/CroatiaPrelecVIPSI.pdf
18. 18. 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