Transcript We have the tools – how to attract the people?

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
S ystems
Analysis Laboratory
Helsinki University of Technology
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
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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
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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
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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
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Example
• Office selection problem (Hammond et al. 1999)
25
78
An even swap
Practically
Dominated
dominated
by
Commute time
by
Lombard
removed as irrelevant
Montana
(Slightly better in Monthly Cost, but equal or worse in all other attributes)
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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
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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
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Decision support
Even Swaps
Problem initialization
Eliminate dominated
alternatives
Preference
Programming
Initial statements about the attributes
Practical dominance candidates
Updating of
Eliminate irrelevant
attributes
No
the model
More than one
remaining alternative
Yes
Make an even swap
Even swap suggestions
Trade-off information
The most preferred
alternative is found
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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
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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:
n
v ( x )  min  w i v i ( xi )
i 1
• Upper bound correspondingly
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Initial assumptions produce bounds
• For the weight ratios
wi
 r , i , j
wj
• For the ratings
• Modeled with exponential
value functions
• Any monotone value functions
within the bounds allowed
• Additional bounds
for the min/max slope
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vi(xi)
1
0
xi
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
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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
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Pairwise dominance
• x dominates y in a pairwise sense if
n
min  w i [v i ( xi )  v i ( y i )]  0
w
i 1
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
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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
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Applicability 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:
v j ( x j )  v j (y j )
d ( x  y, i , j )  min(
)
(w i / w j )(v i ( y i )  v i ( xi ))
• 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
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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
S ystems
Analysis Laboratory
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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)
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Analysis Laboratory
Helsinki University of Technology
Comparison with MAVT
Even Swaps
MAVT
Assumptions Not needed
about the
value
function
Needed
Elicitation
burden
Weight elicitation
No. of elicitations
may become high
- Not known in
advance
- Increases with the
no. of alternatives
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- Additive functions
typically used
- At least n-1
preference
statements
Value functions
- One for each
attribute
Comparison with MAVT
Analysis of
the results
Even Swaps
MAVT
Dominance
relations
Overall scores for
the alternatives
- Clear to interpret
- No relative scores
- Outcomes of the
alternatives change
during the process
Suitability
Personal decision Group and policy
making
decisions
- Proposed approach - Transparency of the
makes the process
easier
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Analysis Laboratory
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process
Smart-Swaps software
www.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
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Helsinki University of Technology
Problem definition
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Entering trade-offs
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Process history
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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
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Analysis Laboratory
Helsinki University of Technology
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
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Helsinki University of Technology
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), 394402.
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Analysis Laboratory
Helsinki University of Technology