# Can I convert share of preference into X number of purchases, if I have total number of purchases?

For example let's say I have a soda conjoint. If I've asked my respondents how many sodas the purchase in a year and on average respondents purchase 200 sodas a year. After analyzing and simulating a conjoint exercise, I have utilities that say

Brand 1's SOP is 30%
Brand 2's SOP is 45%
Brand 3's SOP is 10%
Other (or None) is 15%.

Can I say that we estimate that for the average respondent:
60 sodas are Brand 1
90 sodas are Brand 2
20 sodas are Brand 3
30 soda are other Brands

Additionally,  if we simulate the introduction of a new Brand and we find that the new SOPs are:
Brand 1's SOP is 25%
Brand 2's SOP is 25%
Brand 3's SOP is 10%
Brand 4's SOP is 30%
Other (or None) is 10%.

Can we say that we predict that:
Brand 4 will take 5% of the SOP from Brand 1
Brand 4 will take 20% of the SOP from Brand 2
Brand 4 will take 0% of the SOP  from Brand 3
Brand 4 will take 5% of the SOP from other Brands (or add purchases to the market???)?

And go further to say we estimate that:

Brand 4 will take 10 sodas per year from Brand 1
Brand 4 will take 40 sodas per year from Brand 2
Brand 4 will take 0 sodas per year from Brand 3
Brand 4 will take 10 sodas per year from Other Brands or add to sales of soda to the market
asked Jun 9, 2016
retagged Jun 13, 2016

Well, under a few really critical assumptions, one could indeed multiply probabilities of choice by expected volume by respondent.  Some of the assumptions are:

1. The probabilities of first choice from a CBC exercise are proportional to purchase volume across multiple brands (and work for predicting volumes of purchases even though we never asked respondents to do a volume allocation in the choice tasks).

2.  The probability of choosing the "None" option indeed reflects the likelihood of picking the "outside good" (either declining to purchase or purchasing from another brand or other substitute category not included in the choice task).

3.  The share of volume switches between the None alternative and the other brands in the simulation will adjust properly when adding new products or taking products away from the competitive scenario...even when we potentially did not ask respondents to evaluate choice tasks with the number of concepts (alternatives) matching the number of concepts in the market simulations.

4.  Respondents can accurately report their annual purchase volume.

These assumptions are critical to obtaining proper predictions of volume.  The scaling of the None% and especially the assumption that one can estimate growth in volume within the category due to adding more brands to the simulation (using choice tasks from the questionnaire that have a constant number of alternatives) are problematic assumptions.  For this reason, choice researchers usually prefer to make the assumption that the category purchase volume remains constant.

Respondents are often not very good at reporting volumes or answering choice tasks by stating volumes per alternative.  This is another reason that choice researchers usually prefer sticking with the "share of preference" assumption and assuming constant volume (no category growth).
answered Jun 9, 2016 by Platinum (148,340 points)
Thank you Bryan that really helped clarify! You guys are great!