MultiAttribute Utility

1
Multi-Attribute Utility The Expected Value of
Information
2
Lecture 2 Agenda

• Discussion of Multi-Attribute Utility Assessment
• In Theory
• In Practice

3
Risk (many definitions take your pick)
Variance
Loss

• Risk

Terrorism Risk The expected consequence of an
existent threat, which for a given target,
attack mode, and damage type can be expressed
as (Henry Willis, RAND, p10) Risk P(Attack
Occurs) P(Attack Results in Damage/Attack
Occurs) E(Damage/Attack Occurs, Attack Results
in Damage) Threat Vulnerability
Consequence
4
Assessing Utility for Wealth

• Certainty Equivalent Approach

.5
100,000
.5
A
0
B
CE
Choose a value for B such that youre indifferent
between A and B, thats your Certainty
Equivalent (amount to avoid lottery) U(CE)
.5U(0) 5U(100,000) 50 .51 .5 Continue
this way for other points on your utility curve
5
Assessing Multiattribute Utility Functions

• Utility Function U(x,y,z) A mathematical
  representation of preferences that incorporates
  our attitudes toward risk.
• Steps
• Assess individual utility functions U(x), U(y),
  U(z).
• Check independence assumptions to determine the
  nature of the mathematical function.
• Compute attribute weights kx, ky, kz and
  interaction terms kxy and so forth.

6
Multi-Attribute Utility AssessmentSteps in
Practice

• According to Keeney and von Winterfeldt in
  Advances Practical Value Models (not yet
  released for publication)
• For many decisions it may be reasonable to simply
  assess a value function (Desirability Scale) as
  described in Hammond et al. 1999).
• If Fundamental Objectives have been selected
  correctly a case can be made for assuming an
  Additive Model which greatly simplifies matters.
• According to Clemen Reilly, 2004 an Additive
  Model is often a good approximation.

7
Multi-Attribute Utility AssessmentSteps in
Practice

• For Additive Model
• U(x1,x2,xn)
• k1U1(x1) k2U2(x2) ..knUn(xn)
• Where k1 k2 kn 1
• Assess Utility Function
• Proportional Scoring
• Desirability Scale as in Hammond et al. 1999
• Certainty or Probability Equivalent Approach
• Use Swing Weighting to calculate Attribute
  Weights k1, k2, kn

8
Swing Weighting
9
Swing WeightingMy Surgery Decision