Preference elicitation Dorota Kurowicka Preference elicitation - PowerPoint PPT Presentation

Preference elicitation Dorota Kurowicka

Preference elicitation • Discrete choice over alternatives A over B, A over C, B over C in order to infer positions of items A, B, C on some relevant scale (typically utility scale) • Used in econometrics, marketing etc…

Vending machine • What products should the vending machine offer? • Laura Middeldorp (BSc project) • Study people’s preference over snacks • Discover market share of different products

Questions • Do you prefer an apple or a snickers? • Do you prefer a bag of crisps or a snickers? • …….. • ……..

Expert 1

Expert 2

Pairwise comparison data 7 choose 2 = 21 questions asked to 79 people Almond Crisps paste cookie Rice cookie Snickers Sponge cake Muesli bar Apple Crisps 0 56 57 52 45 54 34 Almond paste cookie 23 0 38 31 20 33 15 N = Rice cookie 22 41 0 39 24 39 14 Snickers 27 48 40 0 27 41 24 Sponge cake 34 59 55 52 0 49 24 Muesli bar 25 46 40 38 30 0 20 Apple 45 64 65 55 55 59 0

Bradley-Terry model • 𝜌 " >0 is called the preference potential of product i 𝜌 " is constant independent of other products • The probability that product i is preferred to product j is 𝜌 " 𝑞 "$ = 𝜌 " + 𝜌 $ • ∑ 𝜌 " =1

Bradley-Terry model • Parameters 𝝆 = (𝜌 ) , … , 𝜌 , ) can be estimated from data matrix N= (𝑜 "$ ) via Maximizing Likelihood , 3 45 𝜌 " 𝑀 𝝆 𝑂 = 1 𝜌 " + 𝜌 $ ",$2) • By a numerical solution of likelihood equations Using a MM (Minorizing Maximizing recursive algorithm) •

Bradley-Terry model • Estimated preference potentials of products Almond paste Crisps cookie Rice cookie Snickers Sponge cake Muesli bar Apple 𝜌 " 0.20 0.07 0.08 0.10 0.16 0.09 0.30 • Ranking of snacks

Bradley-Terry model Almond paste Crisps cookie Rice cookie Snickers Sponge cake Muesli bar Apple 𝜌 " 0.20 0.07 0.08 0.10 0.16 0.09 0.30 6.8 The probability that is preferred to is 6.896.: = 0.6 • The probability that is preferred to is 0.81 • The probability that is preferred to is 0.53 •

Circular triads Do you prefer an apple or a snickers? • • Do you prefer a bag of crisps or a snickers? • Do you prefer an apple or a bag of crisps? A < S < C < A circular triads

Remedy - Circular triads • Expert quality • Reduced elicitation designs • Extension of Bradley-Terry model All photos provided by Laura Middeldorp used with permission.

Thank you for your attention!