Livinhope you obviously have a problem here that is causing you concern - quite understandably....
I would ask whoever is in charge of the site for a copy of you allotment rules / handbook and, if asked why, explain your concern.
The other alternative would be to go and talk to the people who own the plot on the otherside of your problem neighbour.... then you'd have a choice:
a) walk round using the paths and make it a serious worthwhile conversation - ask them about your concerns
b) walk in a perfectly straight line without looking down as you cross the pests plot
Either might have an interesting result.
Personally I would find out what the handbook / rules say about respecting other peoples hard work and sticking to the paths. I would ask for advice and I would drop some very direct hints... such as:
"Oi! What the h*ll do you think you are doing tramping across the middle of my plot? Would you accept it if I did the same to yours? Please, if you don't mind, have some thought for my efforts and stick to the path in future!"