You Are Not (An) Average

You Are Not (An) Average Applying Voting Rules to Panel-Based DecisionMaking in LCA Christoph Koffler, Ph.D. @ LCA XI, Chicago

Phil has a problem‌

Design A

Phil

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Design B

Design C

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… so he does the obvious …

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The consultant then proposes a solution.

weighting ratio estimation

normalization SWING questionnaire MADM

trade-off

Simple Additive Weighting Single Score

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So Phil gathers the relevant people in his company ‌

Group average weight per impact

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‌ who are not too happy with the outcome.

C>A>B

A>C>B

B>A>C

C>B>A

fired A>B>C A>B>C

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B>C>A

But Phil is a smart guy ‌

How to best represent group preferences?

How to select the best alternative?

Best alternative = ‘winning candidate’?

How do votes work?

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… and he thinks he’s onto something …

Nicolas de Condorcet (1743 – 1794) Pairwise comparisons of candidates

Condorcet winner beats all other candidates in the majority of all individual rankings.

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‌ and the more he reads, the better it gets ‌

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.

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‌ and the more he reads, the better it gets ‌

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‌ just to run into the next problem.

Political elections can only have a single winner In LCA, alternatives can be equally preferable

What now?

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So Phil has his heureka moment.

Minimize the opposition against the group decision instead of maximizing the support!

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.

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So Phil has his heureka moment.

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Implementation

Monte-Carlo simulation

Group ranking

p: Anzahl der panel-Mitglieder (k = 1,..,p)

Adapted Voting Rule

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ranking person 1

Weights person 1

ranking person p

[..]

Weights person p

Normalized LCIA results

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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

Claim mean value best represents group opinions if certain assumptions hold!

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Addendum

Prove me wrong!

Prove me right!

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

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