a preference programming approach to make the even swaps method even easier

S ystemsAnalysis LaboratoryHelsinki University of Technology

A Preference Programming

Approach to Make the Even

Swaps Method Even Easier

Jyri MustajokiRaimo P. Hämäläinen

Systems Analysis LaboratoryHelsinki University of Technology

www.sal.hut.fi


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


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


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


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


Example

• Office selection problem (Hammond et al. 1999)

Dominatedby

Lombard

Practicallydominated

byMontana

(Slightly better in Monthly Cost, but equal or worse in all other attributes)

78

25

An even swap

Commute time removed as irrelevant


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


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


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 oneremaining alternative

Yes

The most preferred alternative is found

No

Trade-off information


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


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

n

iiii xvwxv

1

)(min)(


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

jirw

w

j

i ,,

1

0 xi

vi(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


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


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

0])()([min1

n

iiiiii

wyvxvw


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


Applicability index• Assume: y is better than x only in attribute i• Applicability index of an even swap, where

a change xiyi 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

)))()()(/(

)()(min(),,(

iiiiji

jjjj

xvyvww

yvxvjiyxd


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


Example

Initial Range:

85 - 50

A - C

950 - 500

1500 -1900

36 different options to carry out an even swap that may lead to dominanceE.g. change in Monthly Cost of Montana from 1900 to 1500:Compensation in Client Access: d(MB, Cost, Access) = ((85-78)/(85-50)) / ((1900-1500)/(1900-1500)) = 0.20 d(ML, Cost, Access) = ((85-80)/(85-50)) / ((1900-1500)/(1900-1500)) = 0.14Compensation in Office Size: d(MB, Cost, Size) = ((950-500)/(950-500)) / ((1900-1500)/(1900-1500)) = 1.00 d(ML, Cost, Size) = ((950-700)/(950-500)) / ((1900-1500)/(1900-1500)) = 0.56 (Average case values for d used)


Comparison with MAVT

Even Swaps MAVTAssumptions about the value function

Not needed Needed- Additive functions typically used

Elicitation burden

No. of elicitations may become high- Not known in advance- Increases with the no. of alternatives

Weight elicitation- At least n-1 preference statements

Value functions- One for each attribute


Comparison with MAVT

Even Swaps MAVTAnalysis of the results

Dominance relations- No relative scores- Outcomes of the alternatives change during the process

Overall scores for the alternatives- Clear to interpret

Suitability Personal decision making- Proposed approach makes the process easier

Group and policy decisions- Transparency of the process


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


Problem definition


Entering trade-offs


Process history


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


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


ReferencesHämäläinen, 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.

a preference programming approach to make the even swaps method even easier

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