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

Collaborators 2 Detlof von Winterfeldt International Institute for Applied Systems Analysis Robert Kavet Electric Power Research Institute Mayank Mohan Loyola Law School Stephen Peck Electric Power Research Institute (emeritus)

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

Motivation 4 The option of gathering more information / doing research I e = information from research

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

Motivation: How valuable is recommending a medical test? 6 Choose I Choose NoI 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 I e From governing bodys point of view, treatment D implemented by physician is an uncertainty, not a decision.

In general, how valuable is information when another agent acts on it to produce value? 7 Approaches to the question 1. Treating the agents actions as uncertain Advantage: Can make qualitative statements about information value with few assumptions on value Disadvantage: Need a model of uncertain agent choice 2. 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.

Information and Control 8 No InformationInformation Control No Control VOI C VOI NoC VOC I VOC NoI

Relationships 9 VOI NoC can be positive or negative

Relationships 10 Theorem 1: The three quantities VOI C, VOC I, VOC NoI 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). VOI C VOI NoC = VOC I VOC NoI

Additivity 11

Nonnegativity of VOI NoC 12 VOI NoC can 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.

Nonnegativity of VOI NoC 13

Nonnegativity of VOI NoC 14 Case: D can take on only two possible values E.g., D {Act, Dont 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.)

A Completely Binary Model 15 Uncertainty quantity e can be High or Low Decisions D can be Act or Dont act Research information I e can indicate High e or Low e.

Parameters 16

Results: Completely binary case 17 Assumptions D = Act has higher value V when e = High. D = Dont act has higher value V when e = Low The key condition for VOI NoC 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 = Dont 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.

Results: Completely binary case 18 Under e = Low, the policy D = Dont 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. t H = the increase in probability of acting if research indicates High e. t L = the increase in probability of not acting if research indicates Low e. Type-1 error Power

Generality of results 19 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 = Dont act has higher value when e = Low

Relax assumption of binary research outcome I e. 20

VOI Application 21 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.

Application parameters 22

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

Conclusion 24 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?