A Preference Programming Approach to Make the Even Swaps Method Even Easier. Jyri Mustajoki Raimo P. Hämäläinen Systems Analysis Laboratory Helsinki University of Technology www.sal.hut.fi. Outline. The Even Swaps method Hammond, Keeney and Raiffa (1998, 1999)
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Raimo P. Hämäläinen
Systems Analysis Laboratory
Helsinki University of Technology
The new alternative can be used instead
These can be eliminated
x practically dominates y
ycan be eliminated
25 Method Even Easier
Commute time removed as irrelevant
(Slightly better in Monthly Cost, but equal or worse in all other attributes)Example
An even swap
Suggestions for the Even Swaps process
Preference Method Even Easier
Updating of the model
Initial statements about the attributes
Practical dominance candidates
Eliminate dominated alternatives
Eliminate irrelevant attributes
More than one
Even swap suggestions
Make an even swap
The most preferred alternative is foundDecision support
Feasible region for the weights
Intervals for the overall values
v Method Even Easieri(xi)
xiInitial assumptions produce bounds
Tighter bounds for the weight ratios obtained from the given even swaps
Better estimates for the values of the alternatives
i.e. if the overall value of x is greater than the one of y with any feasible weights of attributes and ratings of alternatives
Any pairwisely dominated alternative can be considered to be practically dominated
One cannot be sure that the other alternative becomes dominated with a certain swap
85 - 50
A - C
950 - 500
36 different options to carry out an even swap that may lead to dominance
E.g. change in Monthly Cost of Montana from 1900 to 1500:
Compensation in Client Access:
d(MB, Cost, Access) = ((85-78)/(85-50)) / ((1900-1500)/(1900-1500)) = 0.20
d(ML, Cost, Access) = ((85-80)/(85-50)) / ((1900-1500)/(1900-1500)) = 0.14
Compensation in Office Size:
d(MB, Cost, Size) = ((950-500)/(950-500)) / ((1900-1500)/(1900-1500)) = 1.00
d(ML, Cost, Size) = ((950-700)/(950-500)) / ((1900-1500)/(1900-1500)) = 0.56
(Average case values for d used)
Software for different types of problems:
Hämäläinen, R.P., 2003. Decisionarium - Aiding Decisions, Negotiating and Collecting Opinions on the Web, Journal of Multi-Criteria Decision Analysis, 12(2-3), 101-110.
Hammond, J.S., Keeney, R.L., Raiffa, H., 1998. Even swaps: A rational method for making trade-offs, Harvard Business Review, 76(2), 137-149.
Hammond, J.S., Keeney, R.L., Raiffa, H., 1999. Smart choices. A practical guide to making better decisions, Harvard Business School Press, Boston.
Mustajoki, J., Hämäläinen, R.P., 2005. A Preference Programming Approach to Make the Even Swaps Method Even Easier, Decision Analysis, 2(2), 110-123.
Salo, A., Hämäläinen, R.P., 1992. Preference assessment by imprecise ratio statements, Operations Research, 40(6), 1053-1061.
Applications of Even Swaps:
Gregory, R., Wellman, K., 2001. Bringing stakeholder values into environmental policy choices: a community-based estuary case study, Ecological Economics, 39, 37-52.
Kajanus, M., Ahola, J., Kurttila, M., Pesonen, M., 2001. Application of even swaps for strategy selection in a rural enterprise, Management Decision, 39(5), 394-402.