The Value of Information with and without Control

1. The Value of Information with and without Control Gordon Hazen, Northwestern University

2. Collaborators • Detlof von WinterfeldtInternational Institute for Applied Systems Analysis • Robert KavetElectric Power Research Institute • MayankMohanLoyola Law School • Stephen PeckElectric Power Research Institute (emeritus)

3. Motivation • An environmental policy decision • e = environmental impact without policy change • D = policy (Strict or No change) • eD = impact under policy D • V = overall value

4. Motivation • The option of gathering more information / doing research • Ie= information from research

5. Motivation: How valuable is commissioning research when another agent acts on it? • Stakeholder considers commissioning research (Choose Ivs. Choose NoI) on environmental impacts e. • Industry or industry consortium • Environmental group • Federal agency implements policy D based on research results Ie. • From stakeholder point of view, Federal policy D is an uncertainty, not a decision.

6. Motivation: How valuable is recommending a medical test? • Governing body considers whether (Choose I vs. Choose NoI) to include a medical test in practice guidelines for potential disease e • Practicing physician implements treatment D based on test results Ie • From governing body’s point of view, treatment D implemented by physician is an uncertainty, not a decision.

7. In general, how valuable is information when another agent acts on it to produce value? • Approaches to the question • Treating the agent’s actions as uncertain • Advantage: Can make qualitative statements about information value with few assumptions on value • Disadvantage: Need a model of uncertain agent choice • Stackelberg leader-follower game • Disadvantage: Need to account for value differences between information-commissioning agent and policy-making agent • Advantage: Need only assume utility maximizing agents. • This talk will focus on the first approach.

8. Information and Control VOIC VOCNoI VOCI VOINoC

9. Relationships • VOINoC can be positive or negative

10. Relationships • Theorem 1: The three quantities VOIC, VOCI, VOCNoI are all nonnegative. Moreover, the incremental value of information (control vs. no control) is equal to the incremental value of control (information vs. no information). VOIC VOINoC = VOCIVOCNoI

11. Additivity • Theorem 2: Suppose V = V1+ V2.Then VOINoC,V=

12. Nonnegativity of VOINoC • VOINoCcan be positive or negative. When is it nonnegative? • Preliminary assumption: • Suppose that uncertainty e is independent of whether or not research concerning e is conducted, that is, e is independent of the events Choose I vs. Choose NoI.

13. Nonnegativity of VOINoC • Theorem 3:A sufficient condition for the nonnegativity (nonpositivity) of the value VOINoCof information on ewithout control is that for all values e and all alternatives d: • that is, for all e and all d: • Given e, the probability of a high-valued decision (i.e. one exceeding d in value) increases (decreases) in expectation when one chooses to obtain information. • Note: The conditioning on e is probabilistic, not informative – there is no assumption one learns e before deciding.

14. Nonnegativity of VOINoC • Case: D can take on only two possible values • E.g., D {Act, Don’t act} • The key condition in Theorem 3 is equivalent to: • The higher-value decision under e is more likely when one chooses to acquire information than when one chooses not to. • (Again, this language is not meant to imply one observes e before deciding.)

15. A Completely Binary Model • Uncertainty quantity e can be High or Low • Decisions D can be Act or Don’t act • Research information Ie can indicate Highe or Lowe.

16. Parameters Type-1 error:  Power:  tH tL DtH DtL

17. Results: Completely binary case • Assumptions • D = Act has higher value V when e = High. • D = Don’t act has higher value V when e = Low • The key condition for VOINoC 0: • The higher-value decision under e is more likely when one chooses to acquire information than when one chooses not to. • Translates to • Under e = Low, the policy D = Don’t act is more likely when one chooses to acquire information than when one chooses not to. • Under e = High, the policy D = Act is more likely when one chooses to acquire information than when one chooses not to.

18. Results: Completely binary case • Under e = Low, the policy D = Don’t act is more likely when one chooses to acquire information than when one chooses not to. • tH =the increase in probability of acting if research indicates Highe. • tL =the increase in probability of not acting if research indicates Low e. • Under e = High, the policy D = Act is more likely when one chooses to acquire information than when one chooses not to. Type-1 error Power

19. Generality of results • One can reach these conclusions knowing almost nothing about the value structure . • The only assumptions used: • D = Act has higher value when e = High. • D = Don’t act has higher value when e = Low

20. Relax assumption of binary research outcome Ie. • Parameters: • P(D = Act | ie, Choose I) = t(ie) • P(D = Act | Choose NoI) = t0 • Same assumptions • D = Act has higher value V when e = High. • D = Don’t act has higher value V when e = Low • Result: A sufficient condition for VOINoC 0 is that obtaining information • increases the probability of acting when e = High, and • decreases the probability of acting when e = Low • that is,

21. VOI Application • D. von Winterfeldt, R.Kavet, S. Peck, M. Mohan, G. Hazen, (2011) “The Value of Environmental Information When Subsequent Decisions are Uncertain”. • What is the value of commissioning research on the health effects of overhead transmission lines? • Stakeholders potentially commissioning research: Research institutes (EPRI), medical foundations, energy facility investors. • Policy makers: Federal agencies. • Potential policy mandates: Undergrounding through residential areas, compaction or split phasing elsewhere.

22. Application parameters

23. Partial results • Value ($millions) of information with and without control

24. Conclusion • VOI without control: • has potentially important applications in policy venues with multiple stakeholders; • has convenient mathematical properties. • Alternate approach not considered here: Stackleberg leader/follower game. • Questions?