Consider a problem where we ask a number of people to select and rank their top three choices out of a number of options. The set of options is the same for everyone, and they all have to rank their top three choices.
How can I go about the estimating the ranking of the options given data collected? How can I model the problem?
For example, say that we get the following data (only showing the first four options, and the rankings whenever someone included them in the ranking):
Option A: 1 Option B: 1,3,1,2,1 Option C: 3,3 Option D: 2,2,2
Where the way to read the above is:
- First row: Only one person chose
Aas their top choice
- Second row: Three people chose
Bas their top choice, one person chose it as their second best choice and one more person chose it as its third choice.
A trivial, but unhelpful answer would be to average the ranking for each option. That would be:
Option A: 1 Option B: (1+3+1+2+1)/5 = 1.6 Option C: (3+3)/2 = 3 Option D: (2+2+2)/3 = 2
The above averaging is unhelpful because it would not consider the number of people that chose a given option, and given the way the experiment is designed, the more often a given option is chosen in the top 3 list, the higher the ranking should be.
How can I go about modeling this problem?