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![Page 1: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/1.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
Robust Bayesian Truth Serum
Presentation by Mark Bun and Bo Waggoner
2012-12-03
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 2: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/2.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
Outline
1 Introduction and SettingRecap: Human Computation Mechanisms so farThe RBTS ApproachSetting
2 RBTS and ShadowingShadowingRBTS
3 PP Without Common Prior
4 Summary: Human Computation MechanismsAssumptions and Results
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 3: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/3.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
Recap: Human Computation Mechanisms so farThe RBTS ApproachSetting
Recap
Peer prediction:
Elicit?
Rewards?
Bayesian Truth Serum:
Elicit?
Rewards?
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 4: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/4.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
Recap: Human Computation Mechanisms so farThe RBTS ApproachSetting
Recap
Peer prediction:
Elicit?
Rewards?
Bayesian Truth Serum:
Elicit?
Rewards?
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 5: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/5.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
Recap: Human Computation Mechanisms so farThe RBTS ApproachSetting
Big problem with implementing PP?
Mechanism needs to know the information structure!
Big problem with BTS?
Requires n→∞!
Other problems with BTS? Does RBTS resolve them?
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 6: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/6.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
Recap: Human Computation Mechanisms so farThe RBTS ApproachSetting
Big problem with implementing PP?
Mechanism needs to know the information structure!
Big problem with BTS?
Requires n→∞!
Other problems with BTS? Does RBTS resolve them?
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 7: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/7.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
Recap: Human Computation Mechanisms so farThe RBTS ApproachSetting
Big problem with implementing PP?
Mechanism needs to know the information structure!
Big problem with BTS?
Requires n→∞!
Other problems with BTS? Does RBTS resolve them?
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 8: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/8.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
Recap: Human Computation Mechanisms so farThe RBTS ApproachSetting
Big problem with implementing PP?
Mechanism needs to know the information structure!
Big problem with BTS?
Requires n→∞!
Other problems with BTS? Does RBTS resolve them?
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 9: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/9.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
Recap: Human Computation Mechanisms so farThe RBTS ApproachSetting
Big problem with implementing PP?
Mechanism needs to know the information structure!
Big problem with BTS?
Requires n→∞!
Other problems with BTS? Does RBTS resolve them?
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 10: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/10.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
Recap: Human Computation Mechanisms so farThe RBTS ApproachSetting
Goal: Truthful mechanism for any n that doesn’t rely on themechanism knowing the information structure.
Approach:
Recall: Elicit two-part report (prediction and signal)
Which one is easy to incentivize and which is difficult?
To elicit the signal: Use shadowing!
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 11: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/11.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
Recap: Human Computation Mechanisms so farThe RBTS ApproachSetting
Goal: Truthful mechanism for any n that doesn’t rely on themechanism knowing the information structure.
Approach:
Recall: Elicit two-part report (prediction and signal)
Which one is easy to incentivize and which is difficult?
To elicit the signal: Use shadowing!
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 12: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/12.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
Recap: Human Computation Mechanisms so farThe RBTS ApproachSetting
Goal: Truthful mechanism for any n that doesn’t rely on themechanism knowing the information structure.
Approach:
Recall: Elicit two-part report (prediction and signal)
Which one is easy to incentivize and which is difficult?
To elicit the signal: Use shadowing!
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 13: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/13.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
Recap: Human Computation Mechanisms so farThe RBTS ApproachSetting
Belief system
Consists of state T drawn from {1, . . . ,m} and signals Sdrawn from {l , h} = {0, 1}Agents have common prior Pr[T = t] and Pr[S = h|T = t].
“Impersonally informative” : For every i , j , k , write
p{si} = Pr[Sj = h|Si = si ]
p{si ,sj} = Pr[Sk = h|Si = si ,Sj = sj ]
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 14: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/14.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
Recap: Human Computation Mechanisms so farThe RBTS ApproachSetting
Belief system
Consists of state T drawn from {1, . . . ,m} and signals Sdrawn from {l , h} = {0, 1}
Agents have common prior Pr[T = t] and Pr[S = h|T = t].
“Impersonally informative” : For every i , j , k , write
p{si} = Pr[Sj = h|Si = si ]
p{si ,sj} = Pr[Sk = h|Si = si ,Sj = sj ]
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 15: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/15.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
Recap: Human Computation Mechanisms so farThe RBTS ApproachSetting
Belief system
Consists of state T drawn from {1, . . . ,m} and signals Sdrawn from {l , h} = {0, 1}Agents have common prior Pr[T = t] and Pr[S = h|T = t].
“Impersonally informative” : For every i , j , k , write
p{si} = Pr[Sj = h|Si = si ]
p{si ,sj} = Pr[Sk = h|Si = si ,Sj = sj ]
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 16: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/16.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
Recap: Human Computation Mechanisms so farThe RBTS ApproachSetting
Belief system
Consists of state T drawn from {1, . . . ,m} and signals Sdrawn from {l , h} = {0, 1}Agents have common prior Pr[T = t] and Pr[S = h|T = t].
“Impersonally informative”
: For every i , j , k , write
p{si} = Pr[Sj = h|Si = si ]
p{si ,sj} = Pr[Sk = h|Si = si ,Sj = sj ]
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 17: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/17.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
Recap: Human Computation Mechanisms so farThe RBTS ApproachSetting
Belief system
Consists of state T drawn from {1, . . . ,m} and signals Sdrawn from {l , h} = {0, 1}Agents have common prior Pr[T = t] and Pr[S = h|T = t].
“Impersonally informative” : For every i , j , k , write
p{si} = Pr[Sj = h|Si = si ]
p{si ,sj} = Pr[Sk = h|Si = si ,Sj = sj ]
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 18: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/18.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
Recap: Human Computation Mechanisms so farThe RBTS ApproachSetting
Belief system
Consists of state T drawn from {1, . . . ,m} and signals Sdrawn from {l , h} = {0, 1}Agents have common prior Pr[T = t] and Pr[S = h|T = t].
“Impersonally informative” : For every i , j , k , write
p{si} = Pr[Sj = h|Si = si ]
p{si ,sj} = Pr[Sk = h|Si = si ,Sj = sj ]
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 19: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/19.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
Recap: Human Computation Mechanisms so farThe RBTS ApproachSetting
Admissibility
Admissible prior:
1 At least two states (m ≥ 2)
2 Every state has positive probability (Pr[T = t] > 0)
3 Assortative property:Pr[S = h|T = 1] < · · · < Pr[S = h|T = m]
4 Fully mixed: 0 < Pr[S = h|T = t] < 1
Lemma 6: For an admissible prior,
1 > p{h,h} > p{h} > p{h,l} = p{l ,h} > p{l} > p{l ,l} > 0
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 20: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/20.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
Recap: Human Computation Mechanisms so farThe RBTS ApproachSetting
Admissibility
Admissible prior:
1 At least two states (m ≥ 2)
2 Every state has positive probability (Pr[T = t] > 0)
3 Assortative property:Pr[S = h|T = 1] < · · · < Pr[S = h|T = m]
4 Fully mixed: 0 < Pr[S = h|T = t] < 1
Lemma 6: For an admissible prior,
1 > p{h,h} > p{h} > p{h,l} = p{l ,h} > p{l} > p{l ,l} > 0
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 21: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/21.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
Recap: Human Computation Mechanisms so farThe RBTS ApproachSetting
Admissibility
Admissible prior:
1 At least two states (m ≥ 2)
2 Every state has positive probability (Pr[T = t] > 0)
3 Assortative property:Pr[S = h|T = 1] < · · · < Pr[S = h|T = m]
4 Fully mixed: 0 < Pr[S = h|T = t] < 1
Lemma 6: For an admissible prior,
1 > p{h,h} > p{h} > p{h,l} = p{l ,h} > p{l} > p{l ,l} > 0
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 22: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/22.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
Recap: Human Computation Mechanisms so farThe RBTS ApproachSetting
Admissibility
Admissible prior:
1 At least two states (m ≥ 2)
2 Every state has positive probability (Pr[T = t] > 0)
3 Assortative property:Pr[S = h|T = 1] < · · · < Pr[S = h|T = m]
4 Fully mixed: 0 < Pr[S = h|T = t] < 1
Lemma 6: For an admissible prior,
1 > p{h,h} > p{h} > p{h,l} = p{l ,h} > p{l} > p{l ,l} > 0
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 23: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/23.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
Recap: Human Computation Mechanisms so farThe RBTS ApproachSetting
Admissibility
Admissible prior:
1 At least two states (m ≥ 2)
2 Every state has positive probability (Pr[T = t] > 0)
3 Assortative property:Pr[S = h|T = 1] < · · · < Pr[S = h|T = m]
4 Fully mixed: 0 < Pr[S = h|T = t] < 1
Lemma 6: For an admissible prior,
1 > p{h,h} > p{h} > p{h,l} = p{l ,h} > p{l} > p{l ,l} > 0
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 24: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/24.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
Recap: Human Computation Mechanisms so farThe RBTS ApproachSetting
Admissibility
Admissible prior:
1 At least two states (m ≥ 2)
2 Every state has positive probability (Pr[T = t] > 0)
3 Assortative property:Pr[S = h|T = 1] < · · · < Pr[S = h|T = m]
4 Fully mixed: 0 < Pr[S = h|T = t] < 1
Lemma 6: For an admissible prior,
1 > p{h,h} > p{h} > p{h,l} = p{l ,h} > p{l} > p{l ,l} > 0
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 25: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/25.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
Recap: Human Computation Mechanisms so farThe RBTS ApproachSetting
Admissibility
Admissible prior:
1 At least two states (m ≥ 2)
2 Every state has positive probability (Pr[T = t] > 0)
3 Assortative property:Pr[S = h|T = 1] < · · · < Pr[S = h|T = m]
4 Fully mixed: 0 < Pr[S = h|T = t] < 1
Lemma 6: For an admissible prior,
1 > p{h,h} > p{h} > p{h,l} = p{l ,h} > p{l} > p{l ,l} > 0
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 26: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/26.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
ShadowingRBTS
What does shadowing solve?
Truthfully elicit signals instead of beliefs
ω ∈ {0, 1} a binary future event
Agent i draws a signal Si ∈ {0, 1} = {l , h}How do we get agent i to truthfully reveal Si?
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 27: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/27.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
ShadowingRBTS
What does shadowing solve?
Truthfully elicit signals instead of beliefs
ω ∈ {0, 1} a binary future event
Agent i draws a signal Si ∈ {0, 1} = {l , h}How do we get agent i to truthfully reveal Si?
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 28: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/28.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
ShadowingRBTS
What does shadowing solve?
Truthfully elicit signals instead of beliefs
ω ∈ {0, 1} a binary future event
Agent i draws a signal Si ∈ {0, 1} = {l , h}How do we get agent i to truthfully reveal Si?
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 29: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/29.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
ShadowingRBTS
What does shadowing solve?
Truthfully elicit signals instead of beliefs
ω ∈ {0, 1} a binary future event
Agent i draws a signal Si ∈ {0, 1} = {l , h}
How do we get agent i to truthfully reveal Si?
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 30: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/30.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
ShadowingRBTS
What does shadowing solve?
Truthfully elicit signals instead of beliefs
ω ∈ {0, 1} a binary future event
Agent i draws a signal Si ∈ {0, 1} = {l , h}How do we get agent i to truthfully reveal Si?
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 31: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/31.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
ShadowingRBTS
Naıve approach
1 Choose a strictly proper binary scoring rule R(y , ω)
2 Ask agent i for signal report xi ∈ {0, 1} using R(xi , ω)
Might not work if i ’s beliefs p{Si} about ω are far from xi !
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 32: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/32.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
ShadowingRBTS
Naıve approach
1 Choose a strictly proper binary scoring rule R(y , ω)
2 Ask agent i for signal report xi ∈ {0, 1} using R(xi , ω)
Might not work if i ’s beliefs p{Si} about ω are far from xi !
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 33: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/33.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
ShadowingRBTS
Naıve approach
1 Choose a strictly proper binary scoring rule R(y , ω)
2 Ask agent i for signal report xi ∈ {0, 1} using R(xi , ω)
Might not work if i ’s beliefs p{Si} about ω are far from xi !
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 34: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/34.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
ShadowingRBTS
Naıve approach
1 Choose a strictly proper binary scoring rule R(y , ω)
2 Ask agent i for signal report xi ∈ {0, 1} using R(xi , ω)
Might not work if i ’s beliefs p{Si} about ω are far from xi !
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 35: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/35.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
ShadowingRBTS
Solution: Use a reference prediction
1 Let y ∈ (0, 1) be an arbitrary prediction report
2 Set δ = min(y , 1− y)
3 Create a shadow report for i :
y ′i =
{y + δ if xi = 1y − δ if xi = 0
4 Score agent xi using the quadratic scoring rule Rq(y ′i , ω)
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 36: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/36.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
ShadowingRBTS
Solution: Use a reference prediction
1 Let y ∈ (0, 1) be an arbitrary prediction report
2 Set δ = min(y , 1− y)
3 Create a shadow report for i :
y ′i =
{y + δ if xi = 1y − δ if xi = 0
4 Score agent xi using the quadratic scoring rule Rq(y ′i , ω)
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 37: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/37.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
ShadowingRBTS
Solution: Use a reference prediction
1 Let y ∈ (0, 1) be an arbitrary prediction report
2 Set δ = min(y , 1− y)
3 Create a shadow report for i :
y ′i =
{y + δ if xi = 1y − δ if xi = 0
4 Score agent xi using the quadratic scoring rule Rq(y ′i , ω)
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 38: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/38.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
ShadowingRBTS
Solution: Use a reference prediction
1 Let y ∈ (0, 1) be an arbitrary prediction report
2 Set δ = min(y , 1− y)
3 Create a shadow report for i :
y ′i =
{y + δ if xi = 1y − δ if xi = 0
4 Score agent xi using the quadratic scoring rule Rq(y ′i , ω)
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 39: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/39.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
ShadowingRBTS
Solution: Use a reference prediction
1 Let y ∈ (0, 1) be an arbitrary prediction report
2 Set δ = min(y , 1− y)
3 Create a shadow report for i :
y ′i =
{y + δ if xi = 1y − δ if xi = 0
4 Score agent xi using the quadratic scoring rule Rq(y ′i , ω)
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 40: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/40.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
ShadowingRBTS
When and why does shadowing work?
Intuition: Truthfully reporting xi = Si pulls the referenceprediction toward i ’s posterior
Selten ’98: Let Y ⊂ [0, 1]. If agent i has beliefs p, then shemaximizes her expected score Rq(y , ω) over y ∈ Y byminimizing |y − p|.Lemma 8: Suppose agent i has observed signals I ∈ {l , h}kand Si . If p{l ,I} < y < p{h,I}, then agent i should truthfullyreport xi = Si .
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 41: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/41.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
ShadowingRBTS
When and why does shadowing work?
Intuition: Truthfully reporting xi = Si pulls the referenceprediction toward i ’s posterior
Selten ’98: Let Y ⊂ [0, 1]. If agent i has beliefs p, then shemaximizes her expected score Rq(y , ω) over y ∈ Y byminimizing |y − p|.Lemma 8: Suppose agent i has observed signals I ∈ {l , h}kand Si . If p{l ,I} < y < p{h,I}, then agent i should truthfullyreport xi = Si .
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 42: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/42.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
ShadowingRBTS
When and why does shadowing work?
Intuition: Truthfully reporting xi = Si pulls the referenceprediction toward i ’s posterior
Selten ’98: Let Y ⊂ [0, 1]. If agent i has beliefs p, then shemaximizes her expected score Rq(y , ω) over y ∈ Y byminimizing |y − p|.
Lemma 8: Suppose agent i has observed signals I ∈ {l , h}kand Si . If p{l ,I} < y < p{h,I}, then agent i should truthfullyreport xi = Si .
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 43: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/43.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
ShadowingRBTS
When and why does shadowing work?
Intuition: Truthfully reporting xi = Si pulls the referenceprediction toward i ’s posterior
Selten ’98: Let Y ⊂ [0, 1]. If agent i has beliefs p, then shemaximizes her expected score Rq(y , ω) over y ∈ Y byminimizing |y − p|.Lemma 8: Suppose agent i has observed signals I ∈ {l , h}kand Si . If p{l ,I} < y < p{h,I}, then agent i should truthfullyreport xi = Si .
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 44: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/44.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
ShadowingRBTS
What’s missing?
How do we pick y to guarantee p{l ,I} < y < p{h,I}?
How do we pick ω when there is no ground truth?
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 45: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/45.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
ShadowingRBTS
What’s missing?
How do we pick y to guarantee p{l ,I} < y < p{h,I}?
How do we pick ω when there is no ground truth?
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 46: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/46.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
ShadowingRBTS
What’s missing?
How do we pick y to guarantee p{l ,I} < y < p{h,I}?
How do we pick ω when there is no ground truth?
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 47: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/47.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
ShadowingRBTS
Robust Bayesian Truth Serum
Idea: Shadowing + reference raters
Information report: xi ∈ {0, 1} represents agent i ’s signal
Prediction report: yi ∈ [0, 1] represents agent i ’s predictionfor the frequency of h signals
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 48: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/48.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
ShadowingRBTS
Robust Bayesian Truth Serum
Idea: Shadowing + reference raters
Information report: xi ∈ {0, 1} represents agent i ’s signal
Prediction report: yi ∈ [0, 1] represents agent i ’s predictionfor the frequency of h signals
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 49: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/49.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
ShadowingRBTS
Robust Bayesian Truth Serum
Idea: Shadowing + reference raters
Information report: xi ∈ {0, 1} represents agent i ’s signal
Prediction report: yi ∈ [0, 1] represents agent i ’s predictionfor the frequency of h signals
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 50: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/50.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
ShadowingRBTS
Robust Bayesian Truth Serum
Idea: Shadowing + reference raters
Information report: xi ∈ {0, 1} represents agent i ’s signal
Prediction report: yi ∈ [0, 1] represents agent i ’s predictionfor the frequency of h signals
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 51: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/51.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
ShadowingRBTS
Scoring
For each agent i , pick reference raters j , k
Set y = yj and ω = xk .
Create a shadow report for i :
y ′i =
{yj + δ if xi = 1yj − δ if xi = 0
where δ = min(yj , 1− yj)
RBTS score:
Rq(y ′i , xk)︸ ︷︷ ︸information score
+ Rq(yi , xk)︸ ︷︷ ︸prediction score
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 52: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/52.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
ShadowingRBTS
Scoring
For each agent i , pick reference raters j , k
Set y = yj and ω = xk .
Create a shadow report for i :
y ′i =
{yj + δ if xi = 1yj − δ if xi = 0
where δ = min(yj , 1− yj)
RBTS score:
Rq(y ′i , xk)︸ ︷︷ ︸information score
+ Rq(yi , xk)︸ ︷︷ ︸prediction score
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 53: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/53.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
ShadowingRBTS
Scoring
For each agent i , pick reference raters j , k
Set y = yj and ω = xk .
Create a shadow report for i :
y ′i =
{yj + δ if xi = 1yj − δ if xi = 0
where δ = min(yj , 1− yj)
RBTS score:
Rq(y ′i , xk)︸ ︷︷ ︸information score
+ Rq(yi , xk)︸ ︷︷ ︸prediction score
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 54: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/54.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
ShadowingRBTS
Scoring
For each agent i , pick reference raters j , k
Set y = yj and ω = xk .
Create a shadow report for i :
y ′i =
{yj + δ if xi = 1yj − δ if xi = 0
where δ = min(yj , 1− yj)
RBTS score:
Rq(y ′i , xk)︸ ︷︷ ︸information score
+ Rq(yi , xk)︸ ︷︷ ︸prediction score
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 55: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/55.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
ShadowingRBTS
Scoring
For each agent i , pick reference raters j , k
Set y = yj and ω = xk .
Create a shadow report for i :
y ′i =
{yj + δ if xi = 1yj − δ if xi = 0
where δ = min(yj , 1− yj)
RBTS score:
Rq(y ′i , xk)︸ ︷︷ ︸information score
+ Rq(yi , xk)︸ ︷︷ ︸prediction score
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 56: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/56.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
ShadowingRBTS
Incentive compatibility
If n ≥ 3 agents have signals drawn from an admissiblecommon prior, then reporting truthfully is a strictBayes-Nash equilibrium.
Why should agents report their predictions truthfully?
How about signals? Enough to show that admissibility=⇒ p{l ,I} < yj < p{h,I}.
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 57: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/57.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
ShadowingRBTS
Incentive compatibility
If n ≥ 3 agents have signals drawn from an admissiblecommon prior, then reporting truthfully is a strictBayes-Nash equilibrium.
Why should agents report their predictions truthfully?
How about signals? Enough to show that admissibility=⇒ p{l ,I} < yj < p{h,I}.
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 58: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/58.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
ShadowingRBTS
Incentive compatibility
If n ≥ 3 agents have signals drawn from an admissiblecommon prior, then reporting truthfully is a strictBayes-Nash equilibrium.
Why should agents report their predictions truthfully?
How about signals? Enough to show that admissibility=⇒ p{l ,I} < yj < p{h,I}.
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 59: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/59.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
ShadowingRBTS
Incentive compatibility
If n ≥ 3 agents have signals drawn from an admissiblecommon prior, then reporting truthfully is a strictBayes-Nash equilibrium.
Why should agents report their predictions truthfully?
How about signals?
Enough to show that admissibility=⇒ p{l ,I} < yj < p{h,I}.
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 60: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/60.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
ShadowingRBTS
Incentive compatibility
If n ≥ 3 agents have signals drawn from an admissiblecommon prior, then reporting truthfully is a strictBayes-Nash equilibrium.
Why should agents report their predictions truthfully?
How about signals? Enough to show that admissibility=⇒ p{l ,I} < yj < p{h,I}.
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 61: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/61.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
ShadowingRBTS
Incentive compatibility
Lemma 6: For an admissible prior,
1 > p{h,h} > p{h} > p{h,l} = p{l ,h} > p{l} > p{l ,l} > 0
Case 1: yj = p{h} =⇒ p{l ,h} < yj = p{h} < p{h,h}
Case 2: yj = p{l} =⇒ p{l ,l} < yj = p{l} < p{h,l}
Recap: p{l ,Sj} < yj < p{h,Sj}, so agent i should truthfullyreveal xi = Si
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 62: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/62.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
ShadowingRBTS
Incentive compatibility
Lemma 6: For an admissible prior,
1 > p{h,h} > p{h} > p{h,l} = p{l ,h} > p{l} > p{l ,l} > 0
Case 1: yj = p{h} =⇒ p{l ,h} < yj = p{h} < p{h,h}
Case 2: yj = p{l} =⇒ p{l ,l} < yj = p{l} < p{h,l}
Recap: p{l ,Sj} < yj < p{h,Sj}, so agent i should truthfullyreveal xi = Si
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 63: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/63.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
ShadowingRBTS
Incentive compatibility
Lemma 6: For an admissible prior,
1 > p{h,h} > p{h} > p{h,l} = p{l ,h} > p{l} > p{l ,l} > 0
Case 1: yj = p{h} =⇒ p{l ,h} < yj = p{h} < p{h,h}
Case 2: yj = p{l} =⇒ p{l ,l} < yj = p{l} < p{h,l}
Recap: p{l ,Sj} < yj < p{h,Sj}, so agent i should truthfullyreveal xi = Si
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 64: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/64.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
ShadowingRBTS
Incentive compatibility
Lemma 6: For an admissible prior,
1 > p{h,h} > p{h} > p{h,l} = p{l ,h} > p{l} > p{l ,l} > 0
Case 1: yj = p{h} =⇒ p{l ,h} < yj = p{h} < p{h,h}
Case 2: yj = p{l} =⇒ p{l ,l} < yj = p{l} < p{h,l}
Recap: p{l ,Sj} < yj < p{h,Sj}, so agent i should truthfullyreveal xi = Si
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 65: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/65.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
ShadowingRBTS
Incentive compatibility
Lemma 6: For an admissible prior,
1 > p{h,h} > p{h} > p{h,l} = p{l ,h} > p{l} > p{l ,l} > 0
Case 1: yj = p{h} =⇒ p{l ,h} < yj = p{h} < p{h,h}
Case 2: yj = p{l} =⇒ p{l ,l} < yj = p{l} < p{h,l}
Recap: p{l ,Sj} < yj < p{h,Sj}, so agent i should truthfullyreveal xi = Si
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 66: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/66.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
ShadowingRBTS
Properties of RBTS
Works for any number of agents n ≥ 3
Scores are well-defined between 0 and 2. Participation is “expost individually rational”.
Numerically robust
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 67: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/67.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
ShadowingRBTS
Properties of RBTS
Works for any number of agents n ≥ 3
Scores are well-defined between 0 and 2. Participation is “expost individually rational”.
Numerically robust
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 68: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/68.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
ShadowingRBTS
Properties of RBTS
Works for any number of agents n ≥ 3
Scores are well-defined between 0 and 2.
Participation is “expost individually rational”.
Numerically robust
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 69: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/69.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
ShadowingRBTS
Properties of RBTS
Works for any number of agents n ≥ 3
Scores are well-defined between 0 and 2. Participation is “expost individually rational”.
Numerically robust
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 70: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/70.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
ShadowingRBTS
Properties of RBTS
Works for any number of agents n ≥ 3
Scores are well-defined between 0 and 2. Participation is “expost individually rational”.
Numerically robust
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 71: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/71.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
ShadowingRBTS
Extensions
Adapting to a budget constraint. Scaling, randomizedexclusion.
More than two outcomes?
Other proper scoring rules?
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 72: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/72.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
ShadowingRBTS
Extensions
Adapting to a budget constraint.
Scaling, randomizedexclusion.
More than two outcomes?
Other proper scoring rules?
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 73: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/73.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
ShadowingRBTS
Extensions
Adapting to a budget constraint. Scaling, randomizedexclusion.
More than two outcomes?
Other proper scoring rules?
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 74: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/74.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
ShadowingRBTS
Extensions
Adapting to a budget constraint. Scaling, randomizedexclusion.
More than two outcomes?
Other proper scoring rules?
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 75: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/75.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
ShadowingRBTS
Extensions
Adapting to a budget constraint. Scaling, randomizedexclusion.
More than two outcomes?
Other proper scoring rules?
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 76: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/76.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
Peer Prediction Without a Common Prior. Witkowski, Parkes.EC-2012.
Same setting as RBTS except each agent may have a differentinformation structure.
Elicit both the agent’s prior and posterior probability thatanother agent will get a high signal.
Infer whether agent’s signal was high or low
Score = score(prior) + score(posterior)
OR elicit prior and signal, and shadow to get a posterior(complicated)
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 77: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/77.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
Peer Prediction Without a Common Prior. Witkowski, Parkes.EC-2012.
Same setting as RBTS except each agent may have a differentinformation structure.
Elicit both the agent’s prior and posterior probability thatanother agent will get a high signal.
Infer whether agent’s signal was high or low
Score = score(prior) + score(posterior)
OR elicit prior and signal, and shadow to get a posterior(complicated)
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 78: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/78.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
Peer Prediction Without a Common Prior. Witkowski, Parkes.EC-2012.
Same setting as RBTS except each agent may have a differentinformation structure.
Elicit both the agent’s prior and posterior probability thatanother agent will get a high signal.
Infer whether agent’s signal was high or low
Score = score(prior) + score(posterior)
OR elicit prior and signal, and shadow to get a posterior(complicated)
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 79: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/79.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
Peer Prediction Without a Common Prior. Witkowski, Parkes.EC-2012.
Same setting as RBTS except each agent may have a differentinformation structure.
Elicit both the agent’s prior and posterior probability thatanother agent will get a high signal.
Infer whether agent’s signal was high or low
Score = score(prior) + score(posterior)
OR elicit prior and signal, and shadow to get a posterior(complicated)
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 80: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/80.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
Peer Prediction Without a Common Prior. Witkowski, Parkes.EC-2012.
Same setting as RBTS except each agent may have a differentinformation structure.
Elicit both the agent’s prior and posterior probability thatanother agent will get a high signal.
Infer whether agent’s signal was high or low
Score = score(prior) + score(posterior)
OR elicit prior and signal, and shadow to get a posterior(complicated)
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 81: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/81.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
Peer Prediction Without a Common Prior. Witkowski, Parkes.EC-2012.
Same setting as RBTS except each agent may have a differentinformation structure.
Elicit both the agent’s prior and posterior probability thatanother agent will get a high signal.
Infer whether agent’s signal was high or low
Score = score(prior) + score(posterior)
OR elicit prior and signal, and shadow to get a posterior(complicated)
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 82: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/82.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
Assumptions and Results
PP PP-CP BTS RBTS
common prior exists
designer knows CP
information structure
# of players
# of signals
designer learns?
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum
![Page 83: Robust Bayesian Truth Serum - Harvard · PDF fileRobust Bayesian Truth Serum Presentation by Mark Bun and Bo Waggoner 2012-12-03 Presentation by Mark Bun and Bo Waggoner Robust Bayesian](https://reader031.vdocument.in/reader031/viewer/2022022505/5ab8bf277f8b9ac1058d066e/html5/thumbnails/83.jpg)
Introduction and SettingRBTS and Shadowing
PP Without Common PriorSummary: Human Computation Mechanisms
Assumptions and Results
PP PP-CP BTS RBTS
common prior exists
designer knows CP
information structure
# of players
# of signals
designer learns?
Presentation by Mark Bun and Bo Waggoner Robust Bayesian Truth Serum