this is my first time posting here, so please bear with me if you can.
I am currently doing an experiment where I ask a group of individuals (let's say 10) to "group" a set of 50 objects. How they group these objects is entirely up to them, and the number of groups (minimum 2, maximum of 50 groups possible) they can create is also up to them as well. (e.g. even-numbered objects as group 1 and odd numbered as group 2; red items as group 1, blue as group 2, yellow as group 3, and so forth).
So these individuals have grouped the objects together as follows: Objects sorted into groups by different people
My question: is there a quantitatively feasible method of analyzing how "similarly" each individual grouped these objects? The challenge here is that someone may have grouped a set of items into "Group 1," but another individual(s) may have grouped a similar set of items as "Group 3," making a visual comparison difficult.
So far, I have looked at some articles pertaining to network science and graph theory but these focus on how similarly different graphs are arranged; I am looking at how a set of objects are similarly grouped.
Any advice would be very much appreciated. Thank you!
The first (so, probably, a most natural :-) ) idea which came to my mind is to put a metric between two partitions $A$ and $B$ of 50 objects into groups as the minimal number of moves which is needed to obtain $B$ form $A$. Each move consists of removing an object from one group and adding it to an other.