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Information Elicitation Sans Verification Bo Waggoner and Yiling Chen 2013-06-16 1 / 33
Information Elicitation SansVerification
Bo Waggoner and Yiling Chen
2013-06-161 / 33
Motivation: human computation
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Motivation: human computation
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Motivation: human computation
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Goal: design systems for eliciting info
Question: How to construct human computationsystems?Approach: Use mechanism design
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Goal: design systems for eliciting info
Question: How to construct human computationsystems?
Approach: Use mechanism design
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Goal: design systems for eliciting info
Question: How to construct human computationsystems?Approach: Use mechanism design
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Mechanism design
Mechanism design:Construct a game to optimize an objective
Game: different actions available; set of actionsmaps to an outcome and payoffs.
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Mechanism design
Mechanism design:Construct a game to optimize an objective
Game: different actions available; set of actionsmaps to an outcome and payoffs.
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Mechanism design
Mechanism design:Construct a game to optimize an objective
Our objective: elicit “useful” information
Our constraints:1 players may not prefer “useful” responses2 designer cannot always verify responses
Our name for this setting:Information Elicitation Without Verification(IEWV)
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Mechanism design
Mechanism design:Construct a game to optimize an objective
Our objective: elicit “useful” information
Our constraints:1 players may not prefer “useful” responses2 designer cannot always verify responses
Our name for this setting:Information Elicitation Without Verification(IEWV)
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Mechanism design
Mechanism design:Construct a game to optimize an objective
Our objective: elicit “useful” information
Our constraints:
1 players may not prefer “useful” responses2 designer cannot always verify responses
Our name for this setting:Information Elicitation Without Verification(IEWV)
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Mechanism design
Mechanism design:Construct a game to optimize an objective
Our objective: elicit “useful” information
Our constraints:1 players may not prefer “useful” responses
2 designer cannot always verify responses
Our name for this setting:Information Elicitation Without Verification(IEWV)
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Mechanism design
Mechanism design:Construct a game to optimize an objective
Our objective: elicit “useful” information
Our constraints:1 players may not prefer “useful” responses2 designer cannot always verify responses
Our name for this setting:Information Elicitation Without Verification(IEWV)
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Mechanism design
Mechanism design:Construct a game to optimize an objective
Our objective: elicit “useful” information
Our constraints:1 players may not prefer “useful” responses2 designer cannot always verify responses
Our name for this setting:Information Elicitation Without Verification(IEWV)
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Agenda
Plan:1 Formally define the setting,
identify limitations of prior work.
2 Prove impossibility results on the setting;demonstrate difficulty of overcominglimitations.
3 Propose new mechanism that overcomes somelimitations, avoids some impossibilities.
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Agenda
Plan:1 Formally define the setting,
identify limitations of prior work.2 Prove impossibility results on the setting;
demonstrate difficulty of overcominglimitations.
3 Propose new mechanism that overcomes somelimitations, avoids some impossibilities.
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Agenda
Plan:1 Formally define the setting,
identify limitations of prior work.2 Prove impossibility results on the setting;
demonstrate difficulty of overcominglimitations.
3 Propose new mechanism that overcomes somelimitations, avoids some impossibilities.
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Outline
Information elicitation without verification
Formal setting and prior work
Impossibility results for IEWV
Output agreement mechanisms
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Outline
Information elicitation without verification
Formal setting and prior work
Impossibility results for IEWV
Output agreement mechanisms
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Setting
Game of information elicitation without verification:
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Setting
Game of information elicitation without verification:
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prior
Setting
Game of information elicitation without verification:
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prior events
Setting
Game of information elicitation without verification:
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prior events posterior
Setting
Game of information elicitation without verification:
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prior events posterior report
Setting
Game of information elicitation without verification:
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prior events posterior report payoff
Prior work: themes
Prior work: various mechanisms for instances of thissetting:
Peer prediction (Miller, Resnick, Zeckhauser 2005)
Bayesian truth serum (Prelec 2004)
PP without a common prior, Robust BTS(Witkowski, Parkes 2012a,b)
Collective revelation (Goel, Reeves, Pennock 2009)
Truthful surveys (Lambert, Shoham 2008)
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Prior work: themes
Prior work: various mechanisms for instances of thissetting:
Peer prediction (Miller, Resnick, Zeckhauser 2005)
Bayesian truth serum (Prelec 2004)
PP without a common prior, Robust BTS(Witkowski, Parkes 2012a,b)
Collective revelation (Goel, Reeves, Pennock 2009)
Truthful surveys (Lambert, Shoham 2008)
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Prior work: themes
Prior work: various mechanisms for instances of thissetting:
Peer prediction (Miller, Resnick, Zeckhauser 2005)
Bayesian truth serum (Prelec 2004)
PP without a common prior, Robust BTS(Witkowski, Parkes 2012a,b)
Collective revelation (Goel, Reeves, Pennock 2009)
Truthful surveys (Lambert, Shoham 2008)
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Prior work: themes
Prior work: various mechanisms for instances of thissetting:
Peer prediction (Miller, Resnick, Zeckhauser 2005)
Bayesian truth serum (Prelec 2004)
PP without a common prior, Robust BTS(Witkowski, Parkes 2012a,b)
Collective revelation (Goel, Reeves, Pennock 2009)
Truthful surveys (Lambert, Shoham 2008)
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Prior work: themes
Prior work: various mechanisms for instances of thissetting:
Peer prediction (Miller, Resnick, Zeckhauser 2005)
Bayesian truth serum (Prelec 2004)
PP without a common prior, Robust BTS(Witkowski, Parkes 2012a,b)
Collective revelation (Goel, Reeves, Pennock 2009)
Truthful surveys (Lambert, Shoham 2008)
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Example: peer prediction
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Example: peer prediction
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Πi(ω∗) = A
observation
Example: peer prediction
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Πi(ω∗) = A
observation
Πi(ω∗) = A
report
Example: peer prediction
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Πi(ω∗) = A
observation
Πi(ω∗) = A
report
Pr [Πj(ω∗) | Πi(ω∗) = A]
prediction
Example: peer prediction
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Πi(ω∗) = A
observation
Πi(ω∗) = A
report
Pr [Πj(ω∗) | Πi(ω∗) = A]
prediction
Πj(ω∗) = B
payoff: h a proper scoring rule
h(Pr [Πj(ω∗) | Πi(ω
∗) = A] , B)
Prior work: discussion
Limitations of mechanisms in prior work:
Somewhat complicated to explain
Only applicable in specific settings (e.g. elicitsignals)
“Bad” equilibria exist
Not detail-free (peer prediction)
Restricted domain (all)
Goal: Overcome these limitations.Obstacle: Impossibility results!
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Prior work: discussion
Limitations of mechanisms in prior work:
Somewhat complicated to explain
Only applicable in specific settings (e.g. elicitsignals)
“Bad” equilibria exist
Not detail-free (peer prediction)
Restricted domain (all)
Goal: Overcome these limitations.Obstacle: Impossibility results!
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Prior work: discussion
Limitations of mechanisms in prior work:
Somewhat complicated to explain
Only applicable in specific settings (e.g. elicitsignals)
“Bad” equilibria exist
Not detail-free (peer prediction)
Restricted domain (all)
Goal: Overcome these limitations.Obstacle: Impossibility results!
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Prior work: discussion
Limitations of mechanisms in prior work:
Somewhat complicated to explain
Only applicable in specific settings (e.g. elicitsignals)
“Bad” equilibria exist
Not detail-free (peer prediction)
Restricted domain (all)
Goal: Overcome these limitations.Obstacle: Impossibility results!
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Prior work: discussion
Limitations of mechanisms in prior work:
Somewhat complicated to explain
Only applicable in specific settings (e.g. elicitsignals)
“Bad” equilibria exist
Not detail-free (peer prediction)
Restricted domain (all)
Goal: Overcome these limitations.Obstacle: Impossibility results!
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Prior work: discussion
Limitations of mechanisms in prior work:
Somewhat complicated to explain
Only applicable in specific settings (e.g. elicitsignals)
“Bad” equilibria exist
Not detail-free (peer prediction)
Restricted domain (all)
Goal: Overcome these limitations.Obstacle: Impossibility results!
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Prior work: discussion
Limitations of mechanisms in prior work:
Somewhat complicated to explain
Only applicable in specific settings (e.g. elicitsignals)
“Bad” equilibria exist
Not detail-free (peer prediction)
Restricted domain (all)
Goal: Overcome these limitations.Obstacle: Impossibility results!
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Prior work: discussion
Limitations of mechanisms in prior work:
Somewhat complicated to explain
Only applicable in specific settings (e.g. elicitsignals)
“Bad” equilibria exist
Not detail-free (peer prediction)
Restricted domain (all)
Goal: Overcome these limitations.
Obstacle: Impossibility results!
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Prior work: discussion
Limitations of mechanisms in prior work:
Somewhat complicated to explain
Only applicable in specific settings (e.g. elicitsignals)
“Bad” equilibria exist
Not detail-free (peer prediction)
Restricted domain (all)
Goal: Overcome these limitations.Obstacle: Impossibility results!
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Outline
Information elicitation without verification
Formal setting and prior work
Impossibility results for IEWV
Output agreement mechanisms
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Existence of uninformative equilibria
DefinitionA strategy is uninformative if it draws a reportfrom the same distribution in every state of theworld.
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Existence of uninformative equilibria
DefinitionA strategy is uninformative if it draws a reportfrom the same distribution in every state of theworld.
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Existence of uninformative equilibria
Proposition
The following mechanisms for IEWV always haveuninformative equilibria:
Those with compact action spaces andcontinuous reward functions;
Those that: (a) are detail-free and (b) alwayshave an equilibrium.
=⇒ All mechanisms we know of; all “reasonable”mechanisms.
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Existence of uninformative equilibria
Proposition
The following mechanisms for IEWV always haveuninformative equilibria:
Those with compact action spaces andcontinuous reward functions;
Those that: (a) are detail-free and (b) alwayshave an equilibrium.
=⇒ All mechanisms we know of; all “reasonable”mechanisms.
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Impossibility for truthful equilibria
Q: What is “truthful”?
A: define a query T specifying the truthful responsefor a given posterior belief.
truthful strategy: si(Πi(ω∗)) = T (Πi(ω
∗)).truthful equilibrium: (Given T ) one in which eachsi is truthful.
TheoremFor all detail-free M and all queries T , there existsI such that G = (M, I) has no strict truthfulequilibrium.
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Impossibility for truthful equilibria
Q: What is “truthful”?
A: define a query T specifying the truthful responsefor a given posterior belief.
truthful strategy: si(Πi(ω∗)) = T (Πi(ω
∗)).truthful equilibrium: (Given T ) one in which eachsi is truthful.
TheoremFor all detail-free M and all queries T , there existsI such that G = (M, I) has no strict truthfulequilibrium.
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Impossibility for truthful equilibria
Q: What is “truthful”?
A: define a query T specifying the truthful responsefor a given posterior belief.
truthful strategy: si(Πi(ω∗)) = T (Πi(ω
∗)).truthful equilibrium: (Given T ) one in which eachsi is truthful.
TheoremFor all detail-free M and all queries T , there existsI such that G = (M, I) has no strict truthfulequilibrium.
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Impossibility for truthful equilibria
Q: What is “truthful”?
A: define a query T specifying the truthful responsefor a given posterior belief.
truthful strategy: si(Πi(ω∗)) = T (Πi(ω
∗)).
truthful equilibrium: (Given T ) one in which eachsi is truthful.
TheoremFor all detail-free M and all queries T , there existsI such that G = (M, I) has no strict truthfulequilibrium.
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Impossibility for truthful equilibria
Q: What is “truthful”?
A: define a query T specifying the truthful responsefor a given posterior belief.
truthful strategy: si(Πi(ω∗)) = T (Πi(ω
∗)).truthful equilibrium: (Given T ) one in which eachsi is truthful.
TheoremFor all detail-free M and all queries T , there existsI such that G = (M, I) has no strict truthfulequilibrium.
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Impossibility for truthful equilibria
Q: What is “truthful”?
A: define a query T specifying the truthful responsefor a given posterior belief.
truthful strategy: si(Πi(ω∗)) = T (Πi(ω
∗)).truthful equilibrium: (Given T ) one in which eachsi is truthful.
TheoremFor all detail-free M and all queries T , there existsI such that G = (M, I) has no strict truthfulequilibrium.
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How to get around this result?
Goal: overcome limitations of prior mechanisms.
Obstacle: Impossibility result!
Proposed solution: Output agreementmechanisms.
simple to explain and implement
applicable in variety of complex domains
detail-free
unrestricted domain
... but not truthful!
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How to get around this result?
Goal: overcome limitations of prior mechanisms.Obstacle: Impossibility result!
Proposed solution: Output agreementmechanisms.
simple to explain and implement
applicable in variety of complex domains
detail-free
unrestricted domain
... but not truthful!
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How to get around this result?
Goal: overcome limitations of prior mechanisms.Obstacle: Impossibility result!
Proposed solution: Output agreementmechanisms.
simple to explain and implement
applicable in variety of complex domains
detail-free
unrestricted domain
... but not truthful!
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How to get around this result?
Goal: overcome limitations of prior mechanisms.Obstacle: Impossibility result!
Proposed solution: Output agreementmechanisms.
simple to explain and implement
applicable in variety of complex domains
detail-free
unrestricted domain
... but not truthful!
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How to get around this result?
Goal: overcome limitations of prior mechanisms.Obstacle: Impossibility result!
Proposed solution: Output agreementmechanisms.
simple to explain and implement
applicable in variety of complex domains
detail-free
unrestricted domain
... but not truthful!
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How to get around this result?
Goal: overcome limitations of prior mechanisms.Obstacle: Impossibility result!
Proposed solution: Output agreementmechanisms.
simple to explain and implement
applicable in variety of complex domains
detail-free
unrestricted domain
... but not truthful!
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How to get around this result?
Goal: overcome limitations of prior mechanisms.Obstacle: Impossibility result!
Proposed solution: Output agreementmechanisms.
simple to explain and implement
applicable in variety of complex domains
detail-free
unrestricted domain
... but not truthful!
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Outline
Information elicitation without verification
Formal setting and prior work
Impossibility results for IEWV
Output agreement mechanisms
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Output agreement
Truthful → common-knowledge truthful:
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Common Knowledge
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Ω: possible states of the world
Common Knowledge
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Ω: possible states of the world
P [ω]: common prior
Common Knowledge
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Π1: player 1’s partition
Common Knowledge
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Π1
ω∗: true state selected by nature
Common Knowledge
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Π1
Π1(ω∗): player 1’s signal
Pr [ω | Π1(ω∗)]: player 1’s posterior
Common Knowledge
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Π1 Π2
Common Knowledge
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Π1 Π2
Π: common-knowledge partition
Output agreement
Truthful → common-knowledge truthful:si(Πi(ω
∗)) = T (Π(ω∗)).Previously: = T (Πi(ω
∗)).
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Output agreement: Origins
Output agreement: informally coined by von Ahn,Dabbish 2004.
Game-theoretic analysis of ESP Game: Jain, Parkes2008. (Specific agent model, not general output agreement
framework.)
Here: first general formalization of outputagreement.
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Output agreement: Origins
Output agreement: informally coined by von Ahn,Dabbish 2004.
Game-theoretic analysis of ESP Game: Jain, Parkes2008. (Specific agent model, not general output agreement
framework.)
Here: first general formalization of outputagreement.
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Output agreement: Origins
Output agreement: informally coined by von Ahn,Dabbish 2004.
Game-theoretic analysis of ESP Game: Jain, Parkes2008. (Specific agent model, not general output agreement
framework.)
Here: first general formalization of outputagreement.
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Output agreement
An output agreement mechanism:
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Output agreement
An output agreement mechanism:
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report space: A
a1 a2
Output agreement
An output agreement mechanism:
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d(a1, a2)
report space: (A, d)
a1 a2
Output agreement
An output agreement mechanism:
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d(a1, a2)
report space: (A, d)
payoff: h strictlydecreasing
h(d) h(d)
a1 a2
Output agreement
TheoremFor any query T , there is an output agreementmechanism M eliciting a strictcommon-knowledge-truthful equilibrium.
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Proof by picture
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Π1 Π2 Π
Are “good” equilibria played?
What is “focal” in output agreement?
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Are “good” equilibria played?
What is “focal” in output agreement?One approach: player inference, beginning withtruthful strategy.
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Are “good” equilibria played?
What is “focal” in output agreement?One approach: player inference, beginning withtruthful strategy.
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Are “good” equilibria played?
What is “focal” in output agreement?One approach: player inference, beginning withtruthful strategy.
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Are “good” equilibria played?
What is “focal” in output agreement?One approach: player inference, beginning withtruthful strategy.
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Output agreement
Inference: iteratively compute strategy thatmaximizes expected utility.
When does inference, starting with truthfulness,converge to common-knowledge truthfulness?
Eliciting the mean: Yes!
Eliciting the median, mode: No!(arbitrarily bad examples)
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Output agreement
Inference: iteratively compute strategy thatmaximizes expected utility.
When does inference, starting with truthfulness,converge to common-knowledge truthfulness?
Eliciting the mean: Yes!
Eliciting the median, mode: No!(arbitrarily bad examples)
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Output agreement
Inference: iteratively compute strategy thatmaximizes expected utility.
When does inference, starting with truthfulness,converge to common-knowledge truthfulness?
Eliciting the mean: Yes!
Eliciting the median, mode: No!(arbitrarily bad examples)
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Output agreement
Inference: iteratively compute strategy thatmaximizes expected utility.
When does inference, starting with truthfulness,converge to common-knowledge truthfulness?
Eliciting the mean: Yes!
Eliciting the median, mode: No!
(arbitrarily bad examples)
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Output agreement
Inference: iteratively compute strategy thatmaximizes expected utility.
When does inference, starting with truthfulness,converge to common-knowledge truthfulness?
Eliciting the mean: Yes!
Eliciting the median, mode: No!(arbitrarily bad examples)
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Output agreement
Mechanisms on many players?
(Yes)
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Output agreement
Mechanisms on many players? (Yes)
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Outline
Information elicitation without verification
Setting
Impossibility results
Output agreement
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Summary
IEWV: formalized mechanism design setting.
(Almost) all mechanisms have bad equilibria.
There are no detail-free, unrestricted-domain,truthful mechanisms.
Output agreement:simpleapplicable in complex domainsdetail-free, unrestricted-domainelicits common knowledge
Thanks!
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Summary
IEWV: formalized mechanism design setting.
(Almost) all mechanisms have bad equilibria.
There are no detail-free, unrestricted-domain,truthful mechanisms.
Output agreement:simpleapplicable in complex domainsdetail-free, unrestricted-domainelicits common knowledge
Thanks!
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Summary
IEWV: formalized mechanism design setting.
(Almost) all mechanisms have bad equilibria.
There are no detail-free, unrestricted-domain,truthful mechanisms.
Output agreement:simpleapplicable in complex domainsdetail-free, unrestricted-domainelicits common knowledge
Thanks!
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Summary
IEWV: formalized mechanism design setting.
(Almost) all mechanisms have bad equilibria.
There are no detail-free, unrestricted-domain,truthful mechanisms.
Output agreement:simpleapplicable in complex domainsdetail-free, unrestricted-domainelicits common knowledge
Thanks!
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Summary
IEWV: formalized mechanism design setting.
(Almost) all mechanisms have bad equilibria.
There are no detail-free, unrestricted-domain,truthful mechanisms.
Output agreement:
simpleapplicable in complex domainsdetail-free, unrestricted-domainelicits common knowledge
Thanks!
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Summary
IEWV: formalized mechanism design setting.
(Almost) all mechanisms have bad equilibria.
There are no detail-free, unrestricted-domain,truthful mechanisms.
Output agreement:simple
applicable in complex domainsdetail-free, unrestricted-domainelicits common knowledge
Thanks!
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Summary
IEWV: formalized mechanism design setting.
(Almost) all mechanisms have bad equilibria.
There are no detail-free, unrestricted-domain,truthful mechanisms.
Output agreement:simpleapplicable in complex domains
detail-free, unrestricted-domainelicits common knowledge
Thanks!
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Summary
IEWV: formalized mechanism design setting.
(Almost) all mechanisms have bad equilibria.
There are no detail-free, unrestricted-domain,truthful mechanisms.
Output agreement:simpleapplicable in complex domainsdetail-free, unrestricted-domain
elicits common knowledge
Thanks!
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Summary
IEWV: formalized mechanism design setting.
(Almost) all mechanisms have bad equilibria.
There are no detail-free, unrestricted-domain,truthful mechanisms.
Output agreement:simpleapplicable in complex domainsdetail-free, unrestricted-domainelicits common knowledge
Thanks!
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Summary
IEWV: formalized mechanism design setting.
(Almost) all mechanisms have bad equilibria.
There are no detail-free, unrestricted-domain,truthful mechanisms.
Output agreement:simpleapplicable in complex domainsdetail-free, unrestricted-domainelicits common knowledge
Thanks!
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