1. S ystems Analysis Laboratory Helsinki University of Technology 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. S ystems Analysis Laboratory Helsinki University of Technology 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. S ystems Analysis Laboratory Helsinki University of Technology 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. S ystems Analysis Laboratory Helsinki University of Technology 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. S ystems Analysis Laboratory Helsinki University of Technology 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  y can be eliminated Aim to reduce the size of the problem in obvious cases Eliminate unnecessary even swap tasks

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

7. S ystems Analysis Laboratory Helsinki University of Technology Smart-Swaps software www.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. S ystems Analysis Laboratory Helsinki University of Technology Problem / Objectives / Alternatives

9. S ystems Analysis Laboratory Helsinki University of Technology Consequences

10. S ystems Analysis Laboratory Helsinki University of Technology 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. S ystems Analysis Laboratory Helsinki University of Technology Support for the Even Swaps process

12. S ystems Analysis Laboratory Helsinki University of Technology Making an even swap Software warns the user if s/he is going to make the swap into ‘wrong direction’

13. S ystems Analysis Laboratory Helsinki University of Technology Process history

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

17. S ystems Analysis Laboratory Helsinki University of Technology 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. S ystems Analysis Laboratory Helsinki University of Technology Preference Programming – The PAIRS method Imprecise statements with intervals on Attribute weight ratios (e.g. 1 / 5  w 1 / w 2  5)  Feasible region for the weights Alternatives’ ratings (e.g. 0.6  v 1 (x 1 )  0.8)  Intervals for the overall values Lower bound for the overall value of x: Upper bound correspondingly

19. S ystems Analysis Laboratory Helsinki University of Technology 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. S ystems Analysis Laboratory Helsinki University of Technology 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 1 0 xixi v i (x i )

21. S ystems Analysis Laboratory Helsinki University of Technology 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. S ystems Analysis Laboratory Helsinki University of Technology 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. S ystems Analysis Laboratory Helsinki University of Technology 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. S ystems Analysis Laboratory Helsinki University of Technology Applicability index Assume: y is better than x only in attribute i Applicability index of an even swap, where a change x i  y i 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. S ystems Analysis Laboratory Helsinki University of Technology 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. S ystems Analysis Laboratory Helsinki University of Technology 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. S ystems Analysis Laboratory Helsinki University of Technology 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. S ystems Analysis Laboratory Helsinki University of Technology 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. S ystems Analysis Laboratory Helsinki University of Technology 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. S ystems Analysis Laboratory Helsinki University of Technology 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.