Practical dominance and process support in the Even Swaps method

1. Practical dominance and process support in the Even Swaps method Jyri Mustajoki Raimo P. Hämäläinen Systems Analysis Laboratory Helsinki University of Technology www.sal.hut.fi

2. Presentation outline • Introduction to the Even Swaps method • Hammond, Keeney and Raiffa (1998, 1999) • Two new techniques to support the method • New concept based on the PAIRS method • Salo and Hämäläinen (1992) • Aim to provide support for tasks needing mechanical scanning • Smart-Swaps software • The first software for supporting the method

3. Even Swaps method • Multicriteria method to find the best alternative • Based on even swaps • Value trade-off, where the value change in one attribute is compensated in some other attribute • The alternative with these changed values is equally preferred to the initial one  It can be used instead

4. Elimination process • Aim to carry out even swaps that make • Alternatives dominated • Some other alternative is equal or better than this one in every attribute, and better at least in one attribute • Attributes irrelevant • Every alternative has the same value on this attribute  These can be eliminated • Process continues until one alternative (i.e. the best one) remains

5. Practical dominance • If alternative x is better than alternative y in several attributes, but slightly worse in one attribute  x practically dominates y  ycan be eliminated • Aim to reduce the size of the problem in obvious cases • No need to carry out an even swap task

6. 25 78 Example • Office selection problem (Hammond et al. 1999) Practically dominated by Montana Dominated by Lombard

7. Two new techniques • Modeling of the practical dominance • Support for looking for efficient even swaps • New concept based on the PAIRS method • Aim to provide support for tasks needing mechanical scanning • Computer support to help in these tasks • For supporting the process – not for automating it

8. PAIRS Method • Additive value function • Imprecise statements by intervals on • Attribute weight ratios (e.g. 1  w1/ w2 5)  Feasible region of the weights • Ratings of the alternatives (e.g. 0.6  v1(x1)  0.8)  Intervals for overall values • Lower bound for the overall value of x: • Upper bound correspondingly

9. Pairwise dominance • x dominates y in a pairwise sense if 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

10. Modeling practical dominance • General constraints for the weight ratios and value functions • These should cover all the plausible weights and values • If x dominates y in a pairwise sense with these general constraints  y can be seen as practically dominated

11. vi(xi) 0 xi General constraints • On weight ratios • On value functions • E.g. exponential value function constraints • Any value function within the constraints allowed • Additional constraints, e.g. for the slope 1

12. Use of even swaps information • With each even swap the user reveals information about his/her preferences • This information can be utilized in the process  Tighter weight ratio constraints elicited from the given even swaps  Better estimates for practical dominances

13. Support for looking for efficient even swaps • Aim to carry out as few swaps as possible to eliminate alternatives or attributes  Scanning through the consequences table • There may also be other objectives • E.g. easiness of the swaps  Different types of suggestions of even swaps for the decision maker

14. Irrelevant attributes • Look for an attribute in which the most alternatives have the same value  Carry out such even swaps that make the values of all the alternatives the same in this attribute • Compensation in attribute with which new dominances could also be obtained • Possible reduction also in the number of the alternatives

15. Dominated alternatives • Look for such pair of alternatives, where dominance between these could be obtained with fewest swaps • E.g., if x outranks y only in one attribute, carry out an even swap that makes the values of these alternatives the same in this attribute • However, the ranking of the alternatives can change in compensating attribute  We cannot be sure that the other alternative is dominated after the swap

16. Dominated alternatives • An estimate for each swap, how far we relatively are from dominance • The ratio between • The allowed value change in compensating attribute, and • The maximum estimated value change in this • Estimated from general constraints • d(y, x) = 'likelihood' of y dominating x after this even swap

17. Example Initial Range: 85 - 50 A - C 950 - 500 1500 -1900 36 different options to carry out an even swap which may lead to dominance E.g. change in Monthly Costs of Montana from 1900 to 1500: Compensation in Client Access: d(Mon, Bar) = ((85-78)/(85-50)) / ((1900-1500)/(1900-1500)) = 0.20 d(Mon, Lom) = ((85-80)/(85-50)) / ((1900-1500)/(1900-1500)) = 0.14 Compensation in Office Size: d(Mon, Bar) = ((950-500)/(950-500)) / ((1900-1500)/(1900-1500)) = 1.00 d(Mon, Lom) = ((950-700)/(950-500)) / ((1900-1500)/(1900-1500)) = 0.56 (Assumptions: linear estimates for value functions; weight ratios = 1)

18. Use in practice • The proposed techniques assume an additive value function • Not explicitly assumed in the Even Swaps method • Can still be used approximatively  Suggestions should be confirmed by the decision maker

19. Smart-Swaps softwarewww.smart-swaps.hut.fi • Support for the proposed approaches • Identification of practical dominances • Suggestions for even swaps • Additional support • Information about what may happen with each swap • Notification of dominances • Rank colors • Process history

20. Smart-Swaps software

21. www.Decisionarium.hut.fi Software for different types of problems: • Smart-Swaps (www.smart-swaps.hut.fi) • Opinions-Online (www.opinions.hut.fi) • Global participation, voting, surveys & group decisions • Web-HIPRE (www.hipre.hut.fi) • Value tree based decision analysis and support • Joint Gains (www.jointgains.hut.fi) • Multi-party negotiation support • RICH Decisions (www.rich.hut.fi) • Rank inclusion in criteria hierarchies

22. Conclusions • Techniques to support the even swaps process presented • Modeling the practical dominance • Support for looking for efficient even swaps • New concept based on the PAIRS method • Support for tasks needing mechanical scanning • Especially useful in large problems • Computer support needed in practice • Smart-Swaps software introduced

23. References 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, MA. Mustajoki, J., Hämäläinen, R.P., 2003. Practical dominance and process support in the Even Swaps method. Manuscript. Downloadable soon at www.sal.hut.fi/Publications/ 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.

25. Appendix Value function constraints • Exponential value function constraint where a (0, 1) xN = (xi – mini) / (maxi – mini) vi(maxi)=0, vi(maxi)=1 (here a=0.15)

26. Appendix Value function constraints • Slope constraints where s (0, 1) x = (x'i – xi) / (maxi – mini) vi(maxi)=0, vi(maxi)=1 (here s=0.5)

27. Appendix New constraints from the given trade-offs • E.g. change xix'i is compensated with the change xjx'j • Assume an additive value function: wiv(xi) + wjv(xj) = wiv(x'i) + wjv(x'j) • General constraints for value functions  New weight ratio constraint:

28. Appendix The use of practical dominance in practice • Suggestions - not automatization • The user should confirm the dominances • Strict gereral constraints  Smaller feasible region  Alternatives may become incorrectly identified as dominated ones • Loose general costraints  Larger feasible region  Not as many dominances, but all these should be real ones

29. Appendix Estimate how far we are from dominance • Assume, e.g. that • The change xiyi (vi(xi) > vi(yi)) is compensated with the change xjx'j (vj(x'j) > vj(xj)) • x'j should remain under yj to make y dominate x • The allowed value change in j:  The maximum plausible value change in j: • Derived from general constraints in PAIRS

30. Appendix Estimate how far we are from dominance • An estimate how close we are relatively to make y dominate x • The ratio between the allowed compensation and the maximum plausible value change • The bigger the ratio is, the better the dominance would be obtained • Strict constraints can also be used instead of intervals