Let's say I have a large series of three-item bundles, like so:
item1 item2 item3 1 F C H 2 H F D 3 D C R 4 S B X 5 M Q F 6 J X U 7 O T G 8 W U F 9 Y B S 10 V G A n ... ... ...
Where I know the following:
The items each have a unidimensional "location" characteristic, and are all arrayed somewhere between 0 and 1.
The bundles were each chosen such that the constituent items come from disparate parts of this 0-1 range. Not necessarily maximally distinct (although that might be a useful optimand), but such that the bundle-chooser would not select three items all from the same part of the 0-1 range if another item is available to the chooser. (So, a bundle-chooser would typically prefer (0.2, 0.25, 0.8) > (0.2, 0.25, 0.5), and (0.1, 0.3, 0.8) > (0.2, 0.2, 0.8)).
I would like to infer, given this 0-1 constraint, and the entire collection of bundles, the most likely "locations" for each item (A-Z, in this case).
Does this type of model have a name? How should I go about fitting this model? Is there an R package I could use to help me find a solution?