Lottery weighting

From DDL Wiki

Lottery weighting is a method to create weights for use in a additive linear multi-attribute utility function. See also Multiattribute utility theory.

Given is a set of alternatives and a set of attributes. Let N be the number of attributes.

1. Determine the best and worst value of each attribute over the set of alternatives.

2. Construct two fictional alternatives: The first fictional alternative is the "worst-case" and has the worst value on every attribute. The second fictional alternative is the "best-case" and has the best value on every attribute.

3. For each attribute, construct the following decision: there are two choices: A and B. Choice A is a lottery and has a random outcome: the probability that the outcome will be the best-case is p, and the probability that the outcome will be the worst-case is 1-p. Choice is a certain outcome that has the worst value on all of the attributes except the one under consideration and the best value on that attribute. Given this decision, determine the value of p that makes the decision-maker indifferent between the two choices A and B. The weight for the attribute equals this probability.

4. The sum of the weights should equal 1. If the sum is not close to 1, then it may be inappropriate to use an additive utility function.