Chi-Square test with relative values?

Question

I am working with a weird data set and it is driving me crazy.

Survey respondents (a,b, c,...) were asked to each distribute 15 points among 3 different preferences. Accordingly, every preference can have 0 to 15 points, but the points must be 15 in total. Now I want to test whether the two groups A and B have different a preferences or not.

Can I simply aggregate the totals of all points for all categories and then test for difference with a Pearson Chi-Square test (see example below)?

Or does the data entail relative values as every preference can only have 0-15 points which prohibits the use of Pearson Chi Square? I am super confused....

Example:

Raw data:

Respondent	Preference 1	Preference 2	Preference 3	Total
a	5	5	5	15
b	8	2	5	15
c	7	4	4	15
...	...	...	...	...

Table for Chi-Square:

Group	Preference 1	Preference 2	Preference 3	Total
A (a+b+c)	20	11	14	45
B (d+e+f)	18	10	17	45

Answer 1

The chi-squared test for homogeneity in a contingency table would not be appropriate here. You do not have a table of independent counts! It seems to me that each respondent, which distributes somehow 15 points over three categories, represent one data point, which can be treated in a model as independent. No standard model or hypothesis test seems appropriate.

I would first decide one test statistic (and the chi-squared test statistic could be one possibility ...) and then maybe a permutation test.