PRIME Preference Ratios in Multiattribute Evaluation

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PRIME Preference Ratios in Multiattribute
Evaluation
A. Salo, R.P. Hämäläinen (2001). Preference
Ratios in Multiattribute Evaluation (PRIME)
Elicitation and Decision Procedures under
Incomplete Information, IEEE Transactions on
Systems, Man, and Cybernetics 31/6, 533-545
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Hierarchical value tree
Subcontractor
Collaboration
Proposal content
Schedule(a1)
Overall cost (a3)
Quality of work (a2)
Reputation (a4)
Possibility of changes (a5)
Large firm (x1)
Small entrepreneur (x2)
Medium-sized firm (x3)
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Theory gives a flat value tree only
Subcontractor
Schedule(a1)
Overall cost (a3)
Quality of work (a2)
Reputation (a4)
Possibility of changes (a5)
Large firm (x1)
Small entrepreneur (x2)
Medium-sized firm (x3)
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Linking weights to attribute ranges

• Correspondence between weights and value
  differences
• All weight statements can be expressed in terms
  of scores
• Weights of higher-level attributes
• Normalization constraint of weights
• Weight ratio statements possibly detached from
  attribute ranges (AHP, PAIRS)
• These statements can be tied to value differences
  between most and least preferred achievement
  levels
• Approach
• Elicit preferences in terms of ratio comparisons
  about value differences
• Express all preference statements in terms of
  non-normalized scores
• Derive all value intervals and dominance results
  from resulting LP problems

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Ratio comparisons

• Ratios must pertain to value differences
• Ratios of positive value differences
• Not actionable as choices between naturally
  occurring options
• Axiomatizations by Dyer and Sarin (1979) and
  Vansnick (1984)
• Analogues to the direct rating of alternatives on
  range 0,100

A., Salo, R.P. Hämäläinen (1997) On the
Measurement of Preferences in the Analytic
Hierarchy Process, J of Multi-Criteria Decision
Analysis 6/6, 309-319.
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Score elicitation

• Ratio estimates of positive value differences
  within an attribute
• Alternative procedures
• Comparisons between pairs of adjacent levels
• Comparisons with regard to least preferred
  achievement level

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Weight elicitation

• Ratios of value differences with regard to two
  attributes
• Choice of alternatives
• Interval SMARTS the least and most preferred
  achievement levels on each attribute
• Rank the differences, assign 10 to the smallest
  one, procee to larger ones, normalize
• Reference alternatives any two alternatives
• Choice of attributes
• Reference attributes largest value difference
• Attribute sequencing (rank) order attributes
  and compare adjacent ones

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Many other preference statements possible, too

• A major benefit of modelling through
  non-normalised scores
• Comparisons with regard to any higher-level
  attribute
• Alternative x1 is better than x2 with regard to
  Proposal content (three first twig-level
  attributes associated with Proposal content)
• Schedule is least twice as more important as
  Collaboration (attributes are not even on the
  same level of the value tree)
• Holistic statements
• Alternative x1 is the best one overall

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Hierarchical value tree
Subcontractor
Collaboration
Proposal content
Schedule(a1)
Overall cost (a3)
Quality of work (a2)
Reputation (a4)
Possibility of changes (a5)
Large firm (x1)
Small entrepreneur (x2)
Medium-sized firm (x3)
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Dominance structures

• Absolute dominance and pairwise dominance
  concepts apply
• Solved subject to
• All elicited preference statements
• Normalisation and non-negativity constraints

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Decision criteria (1/2)

• The same decision criteria can be applied, too
• Max-max
• Max-min
• Minimax regret

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Decision criteria (2/2)

• Central values
• Central weights
• The using weights, assuming that scores are known

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Elicitation processes (1)
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Computational convergence

• Questions
• How effective are imprecise ratios?
• Which decision rules are best?
• Randomly generated problems
• 5,10,15 attributes 5,10,15 alternatives
• True parameters generated from random
  distributions
• Attribute weighting by interval SMART
• Error ratios 1.2, 1.5, 2
• 5000 problem instances

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Results

• Central values minimise the expected loss of
  value
• Few imprecise ratios improve performance in
  relation to ordinal information
• As the number and precision of imprecise ratios
  increases
• The number of non-dominated alternatives
  declines
• The expected loss of value decreases

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Genetically modified organisms

• Technology assessment study for the Finnish
  Parliament
• Commissioned by the Futures Committee
• Delivered to the Speaker of the Parliament in
  September 1998
• Debated in the plenary session in an extensive
  two-hour discussion
• Precautionary Principle in Risk Management
• Commissioned by Research Centre of the EU
  (JRC/ESTO)
• presented to the Forward Studies Unit of
  Directorate-General Research
• Problem characteristics
• Timely and controversial
• Large uncertainties with many concerns

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Value tree
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Ranges of weights
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Intermediate results
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Ranges of attribute weights
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Decision rules
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Ranges of weights
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Ranges of attribute weights
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Intermediate results
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Decision rules
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Case study Valuation of a high-technology company

• Problem context
• Estimate the market capitalization value of a
  high-technology company
• Carried out in collaboration with a Scandinavian
  investment bank
• The company (SoneraTrust)
• Provides information security for mobile
  transactions using PKI technology
• Turnover of about 1.84 MEUR at the time of
  estimation
• Considerable future growth expected
• Approach
• Use forecasts about the growth of mobile
  communications (Gartner)
• Determine and the relative size of different
  market segments
• Withtin these, estimate the proportion of
  services that call for PKI technology
• Combine the above to produce a valuation estimate
  

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Classification of wireless services
Gustafsson, J., A. Salo and T. Gustafsson
(2001). PRIME Decisions An Interactive Tool for
Value Tree Analysis. In M. Köksalan, S. Zionts
(eds.), Multiple Criteria Decision Making in the
New Millennium, Lecture Notes in Economics and
Mathematical Systems 507, Springer-Verlag,
Berlin, 2001, 165-176.
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Estimates weights and scores
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Results

• About 700 MEUR
• In the neutral growth scenario the total PKI
  market share was about 8.5
• NPV calculations were based on a 12 discount
  rate
• Other growth scenarios suggested market shares of
  about 3.5 and 13.4
• Comparison
• Merrill Lynch came up with an estimate of about 6
  billion EUR
• Earlier Nordea estimate about 17 billion EUR
• Lessons
• Systematic analyses may be helpful in eliminating
  cognitive biases
• Analysis was done at an usual moment, SmartTrust
  soon faced problems