Sensitivity Analysis

As you can see, coming up with a utility function isn't easy, especially if there are many people involved. The value I place on a particular outcome is likely to be different from yours. The actions themselves may change my personal utility function.⁸ Still, coming up with a utility function may be a useful exercise to get us to think carefully about the alternatives and their consequences.

There is still the danger that we will be captured by the apparent precision of the numerical results. One way of combating this, and sometimes of producing agreement where there was none, is through a sensitivity analysis. The idea is exactly the same as we saw with sensitivity and elasticity coefficients in demographic matrices. Which aspects of the decision tree and the utility function have a big impact on the decision.

• Use the existing utility function
  • change probability that captive breeding is successful to 0.5
    
    $$(0.5)(U(0)) + (0.5)(U(0.95)) = 0.511$$
    
    

  • change probability that new reserve prevents timber harvest to 0.8
    
    $$(0.05)(U(0.9)) + (0.15)(U(0.9)) + (0.8)(U(0.37)) = 0.67$$
    
    

• Exercise: Use Maguire's probabilities change the utility function and calculate utility of captive breeding versus new reserve.

Sensitivity analysis allows us to explore how different things would have to be for us to change our minds about the decision. Indicates how robust our decision is and points out areas where uncertainty is particularly problematic.