I failed to check my results back. sunsmountain is probably right that it's a rounding error, but the deviation is a bit to big to be left with that.
If inserted into the original formula, sunsmountain estimation of 16800 gives a public order bonus of 17.229 for four peasant units.
Mine gives 17.436
Simetrical's population cut off of 14756 gives 20.003
Since what we want to know is at which population 4 peasant units give less than 20 public order bonus, Simetrical's figure is the best one.

We can conclude that the formula we have found above says that above a population of approximately 14500, games become cheaper than garrison to fix public order.