Title: Decision Support for the Even Swaps Process with Preference Programming
1Decision 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
2Outline
- 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
3Even 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
4Elimination 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
5Practical 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
6Example
- Office selection problem (Hammond et al. 1999)
An even swap
7Smart-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
8Problem / Objectives / Alternatives
9Consequences
10Support 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
11Support for the Even Swaps process
12Making an even swap
- Software warns the user if s/he is going to make
the swap into wrong direction
13Process history
14A Preference Programming approach to support the
process
- Even Swaps process carried out as usual
- The DMs preferences simultaneously modeled with
Preference Programming - Intervals allow us to deal with incomplete
information about the DMs 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
15Supporting 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
16Decision support
17Assumptions 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
18Preference 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
19Pairwise 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
20Using 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
21Use 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
22Modeling 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
23Candidates 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
24Applicability index
- Assume y is 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
25Applicability 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
26Example
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)
27www.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
28Conclusions
- Smart-Swaps provides support for the PrOACT
process with the Even Swaps method - Modeling of the DMs preferences in Even Swaps
with Preference Programming - 1. Identification of practical dominances
- 2. Candidates for even swaps
- Support provided as suggestions by the software
29References
- 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/Publication
s/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.
30References
- 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.