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 N =

Crisps Almond paste cookie Rice cookie Snickers Sponge cake Muesli bar Apple Crisps 56 57 52 45 54 34 Almond paste cookie 23 38 31 20 33 15 Rice cookie 22 41 39 24 39 14 Snickers 27 48 40 27 41 24 Sponge cake 34 59 55 52 49 24 Muesli bar 25 46 40 38 30 20 Apple 45 64 65 55 55 59

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

𝑞"$ = 𝜌" 𝜌" + 𝜌$

• ∑ 𝜌"=1

Bradley-Terry model

• Parameters 𝝆 = (𝜌), …, 𝜌,) can be estimated from

data matrix N= (𝑜"$) via Maximizing Likelihood 𝑀 𝝆 𝑂 = 1

",$2) ,

𝜌" 𝜌" + 𝜌$

345

• By a numerical solution of likelihood equations
• Using a MM (Minorizing Maximizing recursive algorithm)

Bradley-Terry model

• Estimated preference potentials of products
• Ranking of snacks

Crisps Almond paste cookie Rice cookie Snickers Sponge cake Muesli bar Apple

𝜌" 0.20 0.07 0.08 0.10 0.16 0.09 0.30

Bradley-Terry model

• The probability that is preferred to is

6.8 6.896.: = 0.6

• The probability that is preferred to is 0.81
• The probability that is preferred to is 0.53

Crisps Almond paste cookie Rice cookie Snickers Sponge cake Muesli bar Apple

𝜌" 0.20 0.07 0.08 0.10 0.16 0.09 0.30

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!