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A Preference Programming Approach to Make the Even Swaps Method Even Easier

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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A Preference Programming Approach to Make the Even Swaps Method Even Easier

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  1. 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

  2. Outline • The Even Swaps method • Hammond, Keeney and Raiffa (1998, 1999) • A new combined Even Swaps / Preference Programming approach • PAIRS method (Salo and Hämäläinen, 1992) • Additive MAVT model of the problem • Intervals to model incomplete information • Support for different phases of the Even Swaps process • Smart-Swaps Web software • The first software for supporting the method

  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. Supporting Even Swaps with Preference Programming • 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

  8. 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

  9. 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

  10. 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

  11. 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

  12. vi(xi) 1 0 xi Initial assumptions produce bounds • For the weight ratios • For the ratings • Modeled with exponential value functions • Any monotone value functions within the bounds allowed • Additional bounds for the min/max slope

  13. 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

  14. Practical dominance • An alternative which is practically dominated cannot be made non-dominated with any reasonable even swaps • Analogous to pairwise dominance concept in Preference Programming

  15. 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  Any pairwisely dominated alternative can be considered to be practically dominated

  16. 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

  17. 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

  18. 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

  19. 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)

  20. Comparison with MAVT

  21. Comparison with MAVT

  22. Smart-Swaps softwarewww.smart-swaps.hut.fi • Identification of practical dominances • Suggestions for the next even swap to be made • Additional support • Information about what can be achieved with each swap • Notification of dominances • Rankings indicated by colors • Process history allows backtracking

  23. Problem definition

  24. Entering trade-offs

  25. Process history

  26. 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

  27. Conclusions • Modeling of the DM’s preferences in Even Swaps with Preference Programming allows to • Identify practical dominances • Find candidates for even swaps • Makes the Even Swaps process even easier • Support provided as suggestions by the Smart-Swaps software

  28. References 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.

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