Here is a quote from the "Do you think you understand corruption" thread.
The FP gets a whole new set of cities where the number-of-cities factor starts at zero. So placing a FP never increases corruption at mid-range cities, even though there are now more cities closer to a center of your empire (capital or FP) than there were before).
The ranking idea goes something like this (there are detailed formulas in that post). Each city is rated for distance to the capital. The first closest (other than the capital itself) will have a rank of 1, and have very low corruption. The second closest will be slightly higher (maybe only a couple of percent) and so on. Once you reach the Optimal city number, in this example 16, corruption starts to rise dramatically. It is also at this point that more cities starts to affect the earlier 16 cities. Note that these are the 16 closest to the capital. Depending on your layout, they could all be tightly packed, within say 6 tiles, or spread out, up to 15 tiles or whatever. It is the actual number of cities that matters for this factor. The actual distance influences a different part of the courruption formula. So even in an ICS, it is still the first 16 (or whatever the OCN is) that are included in the ranking.
What the FP does is start a seperate list of up to 16 cities that are within the OCN limits. Thus a city that was say ranked 20th in distance from the capital, but is the 2nd closest to the FP, would now be considered under the OCN limit, and would have the same corruption rate as the second closest city to the actual capital. This does not affect the ranking or corruption rating of any of the original 16 cities, nor does it change the calculations for the next worst city (#21) unless that city is also closer to the FP than it is the capital. Under ideal circumstances, the FP will be far enough from the capital that there is no overlap, and you will now end up with 32 cities that are considered to be under the OCN limit. However, when you have overlap, is when it gets confusing. (If it isnt already
)
Lets say the FP is build at a medium distance from the capital, near some of the original 16 cities. Now city XYZ, which used to be 14th in distance from the capital, is close to the FP, lets say 3rd in order. It now has corruption of say 8% instead of 35%, so it sees an improvement in its corruption rate. However, it is still considered to hold the 14th spot on the capital list, so those above it (#15, 16, 17 etc) do not 'move up' in the ranking, they are not affected. Therefore, when there is overlap, it is possible that the number of cities considered to be within the OCN limit will not necessarily double, as some cities that are in the overlap will be considered to occupy slots on both lists. They get the advantage of whichever they are closest to, but other cities may not benefit from that.
I hope this explains it a little better, and I am sure I am not doing Alexman's research true justice. I definitely recommend his article:
http://forums.civfanatics.com/showthread.php?s=&threadid=19922&highlight=Understand+Corruption
