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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

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
Outline Method Even Easier

  • 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


Even swaps
Even Swaps Method Even Easier

  • 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


Elimination process
Elimination process Method Even Easier

  • 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


Practical dominance
Practical dominance Method Even Easier

  • 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


Example

25 Method Even Easier

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


Supporting even swaps with preference programming
Supporting Even Swaps with Preference Programming Method Even Easier

  • 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


Supporting even swaps with preference programming1
Supporting Even Swaps with Preference Programming Method Even Easier

  • 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


Decision support

Preference Method Even Easier

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


Assumptions in the preference programming model
Assumptions in the Preference Programming model Method Even Easier

  • 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


Preference programming the pairs method
Preference Programming – The PAIRS method Method Even Easier

  • 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


Initial assumptions produce bounds

v Method Even Easieri(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


Use of trade off information
Use of trade-off information Method Even Easier

  • 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


Practical dominance1
Practical dominance Method Even Easier

  • An alternative which is practically dominated cannot be made non-dominated with any reasonable even swaps

  • Analogous to pairwise dominance concept in Preference Programming


Pairwise dominance
Pairwise dominance Method Even Easier

  • 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


Candidates for even swaps
Candidates for even swaps Method Even Easier

  • 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


Applicability index
Applicability index Method Even Easier

  • 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


Applicability index1
Applicability index Method Even Easier

  • 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


Example1
Example Method Even Easier

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)


Comparison with mavt
Comparison with MAVT Method Even Easier


Comparison with mavt1
Comparison with MAVT Method Even Easier


Smart swaps software www smart swaps hut fi
Smart-Swaps software Method Even Easierwww.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


Problem definition
Problem definition Method Even Easier


Entering trade offs
Entering trade-offs Method Even Easier


Process history
Process history Method Even Easier


Www decisionarium hut fi
www.Decisionarium.hut.fi Method Even Easier

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


Conclusions
Conclusions Method Even Easier

  • 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


References
References Method Even Easier

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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