Swing weighting

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Revision as of 14:24, 5 February 2009

Swing weighting is a method for setting the weights in a linear multiattribute 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. Create N+1 fictional alternatives. The first fictional alternative is the "worst-case" and has the worst value on every attribute. The next N fictional alternatives have the worst value on all but one of the attributes; on the remaining attribute, each alternative has the best value on one attribute. (Each of these alternatives has a different best than any of the others.)

3. Rank order the N+1 fictional alternatives. The ranks are determined by the decision-maker. The rank of the worst-case alternative will be N+1, and the rank of the best of the fictional alternatives will be 1.

4. Rate the N+1 fictional alternatives. The rating of the worst-case alternative will be 0, and the rating of the best of the fictional alternatives will be 100. The decision-maker must rate the others and these ratings should be coherent with the rankings. That is, if one fictional alternatives has a better rank than a second, the first should have a higher rating as well. An alternative's rating is the decision-maker's increase in satisfaction if he gives up the worst-case alternative and chooses this one instead.

5. Normalize the ratings by dividing each one by the sum of all the ratings. The normalized rating of the worst-case alternative will still be 0, and the sum of all the normalized ratings will equal 1.

6. The weight for each attribute is the normalized rating of the fictional alternative that has the best value on that attribute.

Consider the following example:

A design team needs to select a cooling technology for a microprocessor cooling system. There are N = 3 attributes: chip temperature, power consumption, and volume (lower is better on all three).

Among all the alternatives, the best temperature is 55 degrees, and the worst is 75 degrees. The best power is 1, and the worst is 10. The best volume is 300, and the worst is 1200.

The swing weighting method constructs four fictional alternatives:

	temperature	power	volume
1. (benchmark)	75	10	1200
2. Temperature	55	10	1200
3. Power	75	1	1200
4. Volume	75	10	300

The decision-maker's name is Joe. Joe cares a lot about temperature and some about volume and power. He ranks alternative 2 as best, then 4 and 3.

	temperature	power	volume	rank
1. (benchmark)	75	10	1200	4
2. Temperature	55	10	1200	1
3. Power	75	1	1200	3
4. Volume	75	10	300	2

Joe then gives a rating of 25 to alternative 4 because that would satisfy him only 25% as much as alternative 1, and he gives a rating of 20 to alternative 3.

	temperature	power	volume	rank	rating
1. (benchmark)	75	10	1200	4	0
2. Temperature	55	10	1200	1	100
3. Power	75	1	1200	3	20
4. Volume	75	10	300	2	25

Based on Joe's input, the normalized ratings can be calculated, as shown in the following table. These become the weights in the utility function.

	temperature	power	volume	rank	rating	weight
1. (benchmark)	75	10	1200	4	0	0
2. Temperature	55	10	1200	1	100	100/145 = 0.69
3. Power	75	1	1200	3	20	20/145 = 0.14
4. Volume	75	10	300	2	25	25/145 = 0.17

A real alternative that has a utility of 0.5 on temperature, 0.2 on power, and 0.9 on volume will have a combined utility of 0.69(0.5) + 0.14(0.2) + 0.17(0.9) = 0.526.