As to the operator name, for my 2¢ I’d suggest the shortest compound variant that makes sense (less typing!) and using internal camel-case so as to follow the style of other compound action names. Thus list
.coOccur() would seem a choice but in truth the inputs/outputs are of more interest.
As to output, unless Tinderbox were to add some new form of view (or in-map visualisation) it might be best to pump out something that can easily be consumed by the likes of an open system such as R (as well proprietary like Office Excel). I may be wrong, but I think both those apps (and similar) would most easily ingest a table with notes ($Name or some UID) on one axis and all the discrete values of the analysed attribute on the other. Working this notion further with example data from up-thread, I’d expect tabular like this:
Name red blue green purple orange white
Note1 1 1 1 0 0 0
Note2 0 1 1 1 0 0
Note3 0 1 1 0 1 0
Note4 0 1 1 0 0 1
Note5 1 1 0 0 1 0
One might add a per-row value count but I suspect that, if exporting to another app for process, the value count might more easily be created after ingest into the other app.
The above data table might appear easily created by exporting an agent with the header line as the $Text and the data rows via ^children^. However, unlike the above example, for more than a few values of $OpenCodes (or whatever multi-value source) iterating through the values might be a complex task for many users so an action or export code to do this would help.
Once the data is exported it might be possible to run the likes of R in context of the export folder so output could be seen from within Tinderbox by viewing the exported page’s preview after the contingency analysis had been run. It does, however, depend on what exactly the user wants too see: a plot of all contingencies (perhaps a a from of heat map)?, a listing of most common, co-occurrences?, etc. A problem for this sort of exploration is that you may often need to try several approaches if you don’t yet know the relationships hiding in the data.
In summary, unless Tinderbox is actually going to visualise the contingency table in some fashion within the app, this task might be better handled as an export code (or an action primarily intended to be called during export). These is offered for discussion and is not a firmly-held viewpoint.