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Constructing Value Models for Applied Systems Analysis

by

Ralph L. Keeney Fuqua School of Business

Duke University Durham, North Carolina, USA

KeeneyR@aol.com

Raiffa’s Opening Comment Looking back to what has been accomplished in systems analysis over the past decades, it seems that there has been less progress than desirable with integrating methodology with real decision making.

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Why did he say this and why does he care?

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Policymakers View of a Complex Policy Decision

Input Policy alternatives

Output Evaluation of the myriad of possible impacts of each policy alternative on human and social wellbeing and the environment

Systems Analysis Policy Model

addresses multiple objectives and risks (uncertainties)

• The only purposeful way to influence policy is by decisions.

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Frame for a Thorough Policy Analysis

Input Policy alternatives

Output Evaluation of the policy alternatives accounting for the myriad of possible impacts of each alternative on human and social wellbeing and the environment

Systems Analysis Policy Model

Why do I say thorough? •This analysis provides insight about the complex relationships from alternatives to impacts.

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Frame of Many Analyses Relevant to Policy

Input Policy alternatives

Output Evaluation of the policy alternatives

Typical Systems Analysis Model

• gaps relating policy

inputs to outputs Input

Scenarios Output Indicators that influence human and social wellbeing and the environment

• There are gaps relating policy inputs to outputs • The typical systems analysis model and its insights are relevant, but to only part of the policy problem

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Gaps Relating Policy Inputs to Outputs

Input Policy alternatives

Output Evaluation of the policy alternatives

Typical Systems Analysis Model

• gaps relating policy

inputs to outputs Input Scenarios

Output Indicators that influence human and social wellbeing and the environment

•Gap relating policy alternatives to scenarios; you can’t choose a scenario

•Gap relating indicators that influence impacts of concern to human and social well-being and the environmental

•Gap aggregating multiple objectives and uncertainties to evaluate alternatives

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Addressing the Gaps

•Policy alternatives to scenarios; alternatives from policymakers, creating alternatives; how governments, organizations, and individuals will act; traditional systems analysis to relate alternatives to scenarios

•Relating indicators to human well-being and the environment; how governments, organizations, and individuals will act; objectives from policymakers; metrics to measure objectives, traditional systems analysis relating indicators to objectives

•Evaluating policy alternatives; build a value model addressing multiple objectives, value tradeoffs, and risk attitudes

Addressing each gap requires interaction with and information from policymakers

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Knowledge Basis for Policy Model Input Policy alternatives

Output Indicators that influence human and social wellbeing and the environment

Typical Systems Analysis Model

Model using hard

sciences: engineering, mathematics, physics,

chemistry, etc.

Value Model Combines multiple objectives and risks

Output Evaluation of alternatives

Models of how policy makers should set policy and how individuals and organizations subsequently act concerns ‘values’ and use soft sciences, such as decision science, political science, sociology, psychology, etc.

Development of typical systems analysis models concern ‘facts’ and use hard sciences

Input Scenarios

Definition of a Value Model

• Value models are often referred to as objective functions

• Value models represent preferences in the mathematical form of an equation

• They can represent preferences of individual or group decision-makers

• Examples are utility functions and value functions

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Why is it a model? It has variables, relationships, parameters, and uses information to specify them.

Steps to Construct a Value Model • generate a list of relevant values • state values as objectives • identify means-ends relationships • select metrics to measure objectives • determine form for a value model • assess components of a value model • assess value tradeoffs

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Terminology for a Value Model Objectives: O1, O2, …, On Measures: X1, X2, …, Xn Level of measures: x1, x2, …, xn Consequences: (x1, x2, …, xn) Want a value model: u(x1, x2, …, xn) Because of uncertainties in the decisions of interest, the value model we will discuss is a utility function. Due to the logical foundations for the existence of the utility function and how it is constructed, one should choose the alternative leading to the highest expected (i.e., average) utility.

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Approach to Construct a Value Model

1. Use value independence or dependence concepts to find a function

u(x1, x2, …,xn) = f[u1(x1), u2(x2), …,un(xn)], where ui, i=1, 2, …, n, are single-objective utility functions. 2. Example: Additive Utility Function

u(x1, x2, …, xn) = Σ kiui(xi)

3. Assess the u(xi) and ki using the value judgments of the decision makers

n

i=1

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Three Independence Concepts

• Preferential Independence

• Utility Independence

• Additive Independence

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Preferential Independence: {X,Y} is preferentially independent of Z if preferences for x,y pairs do not depend on a fixed level of z (x,y,z0) ≥ (x′,y′,z0) ⇒ (x′,y,z) ≥ (y′,z) for all z

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Utility Independence: X is utility independent of Y if preferences over lotteries on x-levels do not depend on a fixed level of y. u(x, y) = g(y) + h(y)u(x, y0) for all y

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Additive Independence: X and Y are additive independent if lotteries are indifferent for all x, y, x′, y′.

and

1/2

1/2

(x,y)

(x’,y’)

1/2

1/2

(x’,y)

(x,y’) L1: L2:

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• If X and Y are additive independent, u(x, y) = kXuX(x) + kYuY(y), where u, uX, and uY are scaled 0 to 1 and kX and kY are

scaling factors. • If X and Y are each utility independent of each other, u(x, y) = kXuX(x) + kYuY(y) + kXYuX(x)uY(x), where u, uX, and uY are scaled 0 to 1 and kX, kY, and kXY are scaling factors. Note: If kXY ≠ 0, there is an interaction of values between X and Y and the utility function is not ‘additive’.

Results for Two Objectives

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A Result for n Objectives: Multiplicative Utility Function

If {X1, Xi} is preferentially independent of the other measures for i = 2, …, n, and if X1 is utility independent of {X2, …, Xn}, then either n u(x1, x2, …, xn) = ∑ kiui(xi), ∑ ki = 1 or i=1

n 1+ku(x1, x2, …, xn) = Π (1+ kkiui(xi)), ∑ ki ≠ 1, i=1 where u and ui are scaled independently from 0 to 1, 0 < ki < 1, and k is calculated from the ki’s.

Practical Value Models

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You have a travel decision: c is the cost of the travel and t is the time of the travel Is u(c, t) = kCuC(c)+kTuT(t) an additive utility function? Is u(c, t) = kCuC(c)+kTuT(t)+kCTuC(c)uT(t) additive? In practice: • If you use only fundamental objectives, and additive

utility function is often reasonable • Component utility functions can often be linear or

exponential • Value tradeoffs require assessing the relative values of

changes in the levels of different objectives, and consistency checks.

Policy to Address a Forest Pest

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• Case study of managing the spruce budworm in New Brunswick, Canada

• How to best manage a forest over time • Decision-maker: Canadian Forestry Commission • Developed a value model to evaluate

preferences over time to address identified stakeholders (the logging industry, regional employment, and individuals concerned about the environmental and recreational value of the forest)

• Work with Buzz Holling and Bill Clark • Reference: David E. Bell, A Decision Analysis of

Objectives for a Forest Pest Problem, in Conflicting Objectives in Decisions, David E Bell, Ralph L Keeney, and Howard Raiffa (editors), Wiley-Interscience, Chichester, 389-421, 1977.

Skeena River Salmon Fishing Policy

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• Who can fish where, when, and how for salmon on the Skeena River

• Decision-maker: Department of the Environment, Canada

• Developed a value model to address economic costs and stakeholder concerns:

• Work with Ray Hilborn and Carl Walters • Reference: Ralph L. Keeney, "A Utility

Function for Examining Policy Affecting Salmon in the Skeena River," Journal of the Fisheries Board of Canada, 34, 1977, 49-63.

uD(x1, x2,…, x12) = u[uN(x1, x2, x3), uL(x4, x5, x6), uS(x7), uR(x8, x9, x10), uF(x11), x12]

Developing Water Resources of the Tisza River Basin in Hungary

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• What water resources infrastructure should be developed

• Decision-maker: Hungarian National Water Authority

• Developed a value model to evaluate five distinct water resources development plans for the Tisza River Basin in Hungary

• Work with Eric Wood, L. David, K. Csontos, and I. Bogart

• Reference: Ralph L. Keeney and Eric F. Wood, "An Illustrative Application of the Use of Multiattribute Utility Theory for Water Resource Planning," with E.F. Wood. Water Resources Research, 13, 705-716.

Setting Standards for Offshore Oil Discharges

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• Setting standards for oil discharges in the North Sea under British authority

• Decision-maker: Petroleum Production Division, UK

• Developed a value model to evaluate oil discharge standards accounting for decisions of offshore oil operators and impacts on fisherman and the environment

• The analysis identified many dominated standards and a few non-dominated contenders

• Reference: Detlof von Winterfeldt, Setting Standards for Offshore Oil Discharges: A Regulatory Decision Analysis. Operations Research 30(5), 867-886, 1982.

What Could Be Done

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• Working with policymakers and stakeholders to articulate and model their values and concerns requires knowledge and skills different than, and yet analogous to, those needed to build traditional systems analysis models

• Any group doing traditional systems analysis to provide insight about policy could benefit by including such individuals on their team

Benefits: Why Howard Raiffa Cares

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• The effort required to build value models is very small relative to that to build traditional systems analysis models

• Including policymakers in this explicit manner enhances their interest in the analysis, since it addresses their decisions and their values

• Such analyses provide more insight for the decisions that may be made

• This increases the influence of the overall policy analysis, which should lead to more informed and hopefully better decisions

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Thank You

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