Lecture 3: Determination of Weights

Question 1

Interpretation of weights within an attribute

Answer 1

1. Attribute weights reflect the additional value generated by increasing the attribute from its least-preferred to the most-preferred level
2. Attribute weights relate the valuations of different attributes to each other

Question 2

Methods to determine attribute weights

Answer 2

1. Swing method
2. Trade-off method
3. Direct-ratio method

Question 3

Swing Method (Steps)

Answer 3

1. Set the worst alternative (e.g. a_- = (40 €, 12 days, 80 hours) and the artificial alternatives to be ranked (b_1, b_2, …)
2. Ask the DM to rank the alternatives and assign points from 1 to 100
3. Divide the points by the total sum of assigned points (normalise) to get the weights

Question 4

Trade-off Method (Steps)

Answer 4

1. Produce equations by considering indifference statements for different alternatives
2. Generate m-1 non-redundant equations plus the normalisation condition (sum of weights = 1)
3. Solve the system of linear equations to drive the weights

Question 5

Why is it called trade-off method?

Answer 5

• We make pairwise comparisons where trade-offs concern 2 attributes at a time
• The number of indifference statements = number of attributes - 1

Question 6

Differences between Swing Method and Trade-off Method

Answer 6

Swing Method:

• point assignments
• simpler
• no value function needed
• no problems with discrete attributes
• does not allow for consistency check within method

Trade-off Method:

• Preference-based
• More complicated
• Attribute value function needed
• Discrete attributes are problematic
• Consistency check within method possible

Question 7

Direct Ratio Method

Answer 7

1. Rank the attributes according to their importance
2. Compare the least important attribute with all other attributes: E.g. If working hours has importance 1, how important is days off? -> 1.2 -> w2/w3 = 1.2
3. Derive objective weights by solving the system of equations

Question 8

Problems with the Direct Ratio Method

Answer 8

• Approach tries to derive weights from general statements about the importance of attributes without considering their range -> no credible result
• Better ask if the DM prefers an increase in salary from X to Y or an increase of holiday time from A to B

Question 9

Experiment by Fischer (1995)

Answer 9

• 45 students divided into two groups (2 scenarios)
• Both groups have the same range regarding starting salary but different ranges regarding vacation days (low and high range)
• Result: with the direct ratio method the difference between the low and high range scenario was very small while it was larger for the trade-off method (range sensitivity increases a lot for trade-off method)

Question 10

Range Effect

Answer 10

• Cognitive bias
• Dependence of decision weights on attribute range -> If the attribute range changes, the decisions weights have to change
• The greater the range of outcomes for attribute X the greater the weight for attribute X should be
• Experiments show that DM’s do not sufficiently adjust their importance statements in direct ratio method even if the assumed intervals were made transparent (meaning of attribute weights is unclear to the DM’s)

-> Don’t use the direct ratio method!

Question 11

Range effect: What can you do to make two decisions consistent?

Answer 11

2 equations:
w1 * [v1 (x’+) - v1 (x’-)] = w’1’ * [v’1 (x’+) - v’1 (x’-)]
w2 * [v1 (x’+) - v1 (x’-)] = w’2’ * [v’1 (x’+) - v’1 (x’-)]
-> [v’1 (x’+) - v’1 (x’-)] = 1
-> Solve for w’1 and w’2
-> Normalize the values for w’1 and w’2

Question 12

Splitting Bias

Answer 12

People tend to overweight an objective that is broken down into subordinate objectives when compared to an objective that is not split up.

Example: Students were asked to give weights for all the individual attributes separately and then weight combinations of attributes at the higher level -> Weight of the sum of the attribute at the higher level is compared with the sum of the weights of the divided attributes below it

Question 13

Splitting Bias with unbiased/biased weights

Answer 13

• Unbiased weights: sum of weights given individual attributes differed less than 20% from the weight given to the group of attributes
• Detail of attribute specification enhances attribute weights
• Overweighting of detailed objectives exists independent of which upper-level objectives is being detailed
• Bias exists for several weighting techniques, but less for techniques that focus attention on concrete trade-offs