christoph koffler lca xi presentation

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!

Thank you very much! c.koffler@pe-international.com

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