Can I use conjoint (and Sawtooth) to find the weight given to the difference of two attributes?

Question

Hi!

I'm going to show people pairs of wealth distributions to the richest, middle, and poorest thirds of society, and people will choose which is more fair.

I want to know how much weight people give to the amount allocated to each group, but I ALSO want to know if people care about, e.g., the DIFFERENCE between the rich & poor.

Is it possible to figure out a weight put on the difference (or ratio) between two variables in a conjoint?

Answer 1

I'm a little unclear about your design.  Will the three proportions rich, middle, poor be levels of two separate attributes (because the proportion of wealth in the third group will always be implied by the wealth in the other two right?).  

Typically you cannot make cross-attribute level comparisons in conjoint analysis because utilities for different attributes have different user-specified origins (depending on where your coding places the zero).  I suppose in your case if you coded richest third and poorest third as two continuous variables with natural zeros for their origins then maybe you could compare the difference between rich and poor.  

But please clarify your design a little if you will.

Comments

Thanks so much for getting back so quickly, Keith.

Your final note there re: coding richest & poorest thirds with their natural zeros was helpful. This design/software is most useful only if I can make these sorts of comparisons. Here's a toy example:

*****
WHICH OF THE FOLLOWING SEEMS MORE FAIR TO YOU:
COUNTRY A:
Richest: $1,000,000 annual income
Middle: $90,000 annual income
Poorest: $33,000 annual income

OR

COUNTRY B:
Richest: $1,500,000 annual income
Middle: $135,000 annual income
Poorest: $30,000 annual income
*****

For each factor (richest, middle, poorest) we'd have 4 levels of avg annual income, with the highest level being 2x the lowest level. This implies that the lowest level for the middle, e.g., must be more than 2x the lowest level of the poor.

*WHAT I'M INTERESTED IN:*
(a) A utility score for richest, middle, and poorest (that seems easy to do in Sawtooth) to determine weight put on that attribute;
(b) A weight put on the DIFFERENCE between rich & poor.

Is (b) possible, given the above?

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Well, you'll have utilities you can estimate for the various combinations of R/M/P.  For each of those you know the difference (in $, not in %, as the latter is a constant 2) between rich and poor.  Then you could simply regress the utility of the different combinations on the differences they imply.  If this weight is relatively constant then your regression will have a high R-squared.  But you might also look for a non-linear relationship
 between the ratio of rich:poor and the utility of a the combinations (e.g. maybe a log function fits better).

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Fantastic. Thanks, Keith!