A point was reached where the maximum biomass was being produced, where adding another animal would result in a small reduction in total biomass production. That is, each animal on the common would end up a tiny bit skinnier, with the sums of the weight loss just exceeding the weight of the new animal.
It was obviously in the village's best interests at that point not to add an animal.
It was just as obviously in any villager's interest to add an animal--for him/her, the slight weight loss from each personal animal would be more than offset by the new animal.
Persuading all the more enlightened villagers not to add animals only left the field open for the less communally-minded. In the long run, coercion never works. What's the answer?