Decision Support for the Even Swaps Process with Preference Programming

1. Decision Support for the Even Swaps Process with Preference Programming Jyri Mustajoki Raimo P. Hämäläinen Systems Analysis Laboratory Helsinki University of Technology www.sal.hut.fi

2. Outline • The Even Swaps process • Hammond, Keeney and Raiffa (1998, 1999) • Smart-Swaps web software • The first software for supporting the Even Swaps method • Support for different phases of the decision analysis process • A new combined Even Swaps / Preference Programming approach • Helpful suggestions for the decision maker how to proceed with the process

3. Even Swaps • Multicriteria method to find the best alternative • An even swap: • A value trade-off, where a consequence change in one attribute is compensated with a comparable change in some other attribute • A new alternative with these revised consequences is equally preferred to the initial one  The new alternative can be used instead

4. Elimination process • Carry out even swaps that make • Alternatives dominated (attribute-wise) • There is another alternative, which is equal or better than this in every attribute, and better at least in one attribute • Attributes irrelevant • Each 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 y is slightly better than alternative x in one attribute, but worse in all or many other attributes  x practically dominates y  ycan be eliminated • Aim to reduce the size of the problem in obvious cases • Eliminate unnecessary even swap tasks

6. 25 78 Practically dominated by Montana Dominated by Lombard Commute time removed as irrelevant (Slightly better in Monthly Cost, but equal or worse in all other attributes) Example • Office selection problem (Hammond et al. 1999) An even swap

7. Smart-Swaps softwarewww.smart-swaps.hut.fi • Support for the PrOACT process (Hammond et al., 1999) • Problem • Objectives • Alternatives • Consequences • Trade-offs • Trade-offs carried out with the Even Swaps method

8. Problem / Objectives / Alternatives

9. Consequences

10. Support for the Even Swaps process • Information about what can be achieved with each swap • Notification of dominated alternatives and irrelevant attributes • Attribute-wise rankings indicated by colors • Process history • Backtracking of the actions  Sensitivity analysis

11. Support for the Even Swaps process

12. Making an even swap • Software warns the user if s/he is going to make the swap into ‘wrong direction’

13. Process history

14. A Preference Programming approach to support the process • Even Swaps process carried out as usual • The DM’s preferences simultaneously modeled with Preference Programming • Intervals allow us to deal with incomplete information about the DM’s preferences • Trade-off information given in the even swaps can be used to update the model  Suggestions for the Even Swaps process • Generality of assumptions of Even Swaps preserved

15. Supporting Even Swaps with Preference Programming • Support for • Identifying practical dominances • Finding candidates for the next even swap • Both tasks need comprehensive technical screening • Idea: supporting the process – not automating it

16. Preference Programming Even Swaps Updating of the model Problem initialization Initial statements about the attributes Practical dominance candidates Eliminate dominated alternatives Eliminate irrelevant attributes No More than one remaining alternative Yes Even swap suggestions Make an even swap Trade-off information The most preferred alternative is found Decision support

17. Assumptions in the Preference Programming model • Additive value function • Not a very restrictive assumption • Weight ratios and component value functions are initially within some reasonable bounds • General bounds for these often assumed • E.g. practical dominance implicitly assumes reasonable bounds for the weight ratios

18. Preference Programming – The PAIRS method • Imprecise statements with intervals on • Attribute weight ratios (e.g. 1/5w1/ w2 5)  Feasible region for the weights • Alternatives’ ratings (e.g. 0.6  v1(x1)  0.8)  Intervals for the overall values • Lower bound for the overall value of x: • Upper bound correspondingly

19. 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

20. vi(xi) 1 0 xi Using Preference Programming to support Even Swaps • Bounds for the weight ratios • Bounds for the ratings • Modeled with exponential value functions • Any monotone value functions within the bounds allowed • Additional bounds for the min/max slope

21. Use of trade-off information • With each even swap the user reveals new information about her preferences • This trade-off information can be utilized in the process  Tighter bounds for the weight ratios obtained from the given even swaps  Better estimates for the values of the alternatives

22. Modeling practical dominance with Preference Programming • An alternative which is practically dominated cannot be made non-dominated with any reasonable even swaps • Analogous to pairwise dominance concept in Preference Programming  Any pairwisely dominated alternative can be considered to be practically dominated

23. Candidates for even swaps • Aim to make as few swaps as possible • Often there are several candidates for an even swap • In an even swap, the ranking of the alternatives may change in the compensating attribute  One cannot be sure that the other alternative becomes dominated with a certain swap

24. Applicability index • Assume: yis better than x only in attribute i • Applicability index of an even swap, where a change xiyi is compensated in attribute j, to make y dominated: • Indicates how close to making y dominated we can get with this swap • The bigger d is, the more likely it is to reach dominance

25. Applicability index • Ratio between • The minimum feasible rating change in the compensating attribute to reach dominance and • The maximum possible rating change that could be made in this attribute • Worst case value for d: • Bounds include all the possible impecision • Average case value for d: • Rating differences from linear value functions • Weight ratios as averages of their bounds

26. Example Initial Range: 85 - 50 A - C 950 - 500 1500 -1900 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(MB, Cost, Access) = ((85-78)/(85-50)) / ((1900-1500)/(1900-1500)) = 0.20 d(ML, Cost, Access) = ((85-80)/(85-50)) / ((1900-1500)/(1900-1500)) = 0.14 Compensation in Office Size: d(MB, Cost, Size) = ((950-500)/(950-500)) / ((1900-1500)/(1900-1500)) = 1.00 d(ML, Cost, Size) = ((950-700)/(950-500)) / ((1900-1500)/(1900-1500)) = 0.56 (Average case values for d used)

27. 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

28. Conclusions • Smart-Swaps provides support for the PrOACT process with the Even Swaps method • Modeling of the DM’s preferences in Even Swaps with Preference Programming 1. Identification of practical dominances 2. Candidates for even swaps • Support provided as suggestions by the software

29. References Even Swaps and Preference Programming: 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. Mustajoki, J., Hämäläinen, R.P., 2006. Smart-Swaps – Decision support for the PrOACT process with the even swaps method. Manuscript. (Downloadable at http://www.sal.hut.fi/Publications/pdf-files/mmus06b.pdf) Salo, A., Hämäläinen, R.P., 1992. Preference assessment by imprecise ratio statements, Operations Research, 40(6), 1053-1061. Salo, A., Hämäläinen, R.P., 1995. Preference programming through approximate ratio comparisons, European Journal of Operational Research, 82(3), 458-475.

30. References Applications of Even Swaps: Belton, V., Wright, G., Montibeller, G., 2005. When is swapping better than weighting? An evaluation of the Even Swaps method in comparison with Multi Attribute Value Analysis, Management Science, University of Strathclyde, Research Paper No. 2005/19. 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. Luo, C.-M., Cheng, B.W., 2006. Applying Even-Swap Method to Structurally Enhance the Process of Intuition Decision-Making, Systemic Practice and Action Research, 19(1), 45-59.