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Value models Keeney chapter 5

Identify performance measures, worst and best values, build a value model with utility functions, risk attitudes, and separability. Explore additive and multiplicative functions for comprehensive utility. Ensure utility independence and preference independence. Balanced scorecard assumption of balanced performance and identification of the value model with relative weights and positive synergy specification.

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Value models Keeney chapter 5

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  1. Value modelsKeeney chapter 5 Fred Wenstøp Fred Wenstøp: Value models

  2. Assumptions • You have identified a set of n performance measures • xi, i =1, ... n • the xi’s are a mix of drivers and outcomes • You must identify the worst possible and the best possible value for each variable • x0 and x* • You want to build a value model • U(x1,x2, ... ,xn) • so that • U(x10,x20, ... ,xn0)=0 • U(x1*,x2*, ... ,xn*)=1 Fred Wenstøp: Value models

  3. Primary utility functions • Build a von Neumann Morgenstern utility function u(x) for each x to represent risk attitude and to make attachement of weights possible • a linear utility function is risk neutral • a concave function is risk averse • a convex function is risk prone • You may use the technique in synergy.xls to identify a and b when you specify a subjective middle value Fred Wenstøp: Value models

  4. Separability • You would like a comprehensive utility function • that is easy to interpret • and easy to identify by eliciting the decision maker • That requires separability • an additive function is an example • U(x1,x2, ... ,xn) = w1u1(x1) + w2u2(x2)+ ... wnun(xn) • here, the w’s are simply weights or importances • another example is the multiplicative function • U(x1,x2, ... ,xn) = • here, k is the synergy coefficient Fred Wenstøp: Value models

  5. Requirements for separability • Both functions obviously require • that the primary u-functions are independent of the x-scores • meaning that risk attitude is independent of performance • this is called utility independence • it is unrealistic if you become desperate in a tight corner • that the relative weights are independent of performance • this is called preference independence • it may be unrealistic in some situations (income and vacation) • we shall assume that the requirements are met Fred Wenstøp: Value models

  6. Choice of function • A basic assumption of the balanced scorecard is that the performance must be balanced • we should not score badly in one area and well in others • therefore the additive function may be inadequate • a multiplicative function with k > 0 may be better Fred Wenstøp: Value models

  7. Identification of the value model • The multiplicative value model • identify first the relative weights • specify the weights after thoughtful consideration so that the sum is 1 • or use Pro&Con • specify the degree of positive synergy 0 < k • find w so that Fred Wenstøp: Value models

  8. Example • n = 3 • weight-spesification: w1 = 0.3, w2 = 0.2, w3 = 0.5 • synergy spesification: k = 2 • solve for w: • Use Excel’s solver • result • w = 0,68 • final weights • 0.20334 • 0.13556 • 0.338899 Fred Wenstøp: Value models

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