So I actually talked with a dictionary expert that was a developer for WordNet. He told me that he spent tons of time trying to determine which definition is the right one. He came to the conclusion that dictionary authors quite often disagree on the ordering of definitions and that it is a lost cause to try to rank definitions.
I disagreed with him though. I think that definition form, word usage within the definition, and definition popularity can all contribute to selecting a "right one". That's why I applied statistical techniques to rank the definitions and reorder them to hopefully put the "right one" first.
Sadly, it seems that I didn't do such a great job for you with the word "quarrel".
Feedback noted as this will help when I start collecting data from users and make a push to improve my statistical analysis.
Thank you again and please let me know if you would like to discuss this further with me. Hope all is well. :)