christoph koffler lca xi presentation
TRANSCRIPT
You Are Not (An) Average Applying Voting Rules to Panel-Based Decision-Making in LCA
Christoph Koffler, Ph.D. @ LCA XI, Chicago
Phil has a problem…
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? Design A
Design B
Design C
Phil
… so he does the obvious …
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? ? ? ? ?
The consultant then proposes a solution.
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normalization
weighting
questionnaire SWING
ratio estimation
Simple Additive Weighting
Single Score
trade-off
MADM
?
So Phil gathers the relevant people in his company …
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Group average
weight per impact
… who are not too happy with the outcome.
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A > B > C
A > C > B
A > B > C
B > A > C
B > C > A
C > A > B
C > B > A
fired
But Phil is a smart guy …
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How to best represent group preferences?
How to select the best alternative?
Best alternative = ‘winning candidate’?
How do votes work?
… and he thinks he’s onto something …
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Nicolas de Condorcet (1743 – 1794)
Pairwise comparisons of candidates
Condorcet winner beats all other candidates in the majority of all individual rankings.
… and the more he reads, the better it gets …
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Single scores are cardinal; rank information is ordinal
Cardinal-Weighted Pairwise Comparison (Green-Armytage 2004):
Sum up the differences between single scores across all individual rankings that support the
majority opinion, and use it as the sorting criterion for the order in which the pairwise statements are
taken into account to construct the group decision.
… and the more he reads, the better it gets …
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… just to run into the next problem.
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Political elections can only have a single winner
In LCA, alternatives can be equally preferable
What now?
So Phil has his heureka moment.
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Sum up the differences between single scores across all individual rankings that oppose the
majority opinion, and use it as the sorting criterion for the order in which the pairwise statements are
taken into account to construct the group decision.
Minimize the opposition against the group decision instead of maximizing the support!
So Phil has his heureka moment.
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Implementation
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Normalized LCIA results
ranking person 1
ranking person p
Adapted Voting Rule
Group ranking
Monte-Carlo simulation
Weights person 1
Weights person p [..]
p: A
nzah
l der
pan
el-M
itglie
der (
k =
1,..,
p)
Monte-Carlo simulation to test robustness
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Monte-Carlo simulation to test robustness
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Published in 2008
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Addendum
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Claim mean value best represents group opinions if certain assumptions hold!
Addendum
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Prove me wrong!
Prove me right!
