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Value models Keeney chapter 5

Value models Keeney chapter 5. Fred Wenstøp. Assumptions. You have identified a set of n performance measures x i , i =1, ... n the x i ’s are a mix of drivers and outcomes You must identify the worst possible and the best possible value for each variable x 0 and x *

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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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