I have not gotten around to the simulation math and actual testing of these improvements yet, but so far I am sceptical.
Using a ring radius analysis approach, I would say that the decision to build the courthouse would be based on how many rings (4 or 5 tiles of radius) that the city lies out from your capital of FP city. As you go out further from these two center points the corruption and waste in the cities goes up exponentially.
Cities in ring 1 (next to the center) may not receive enough of a reduction in the corruption and waste to cover the cost of maintenance for the courthouse and/or recover the sheild cost to build the improvement in the first place becasue the percentages are applied to a lower corruption and waste factor.
In ring 2, there seems to be some benefit, in ring 3 the impact begins to be neglible even though the waste and corruption can be large.
If you have a city built way off on another continent and that city is crippled by corruption and waste, you often have to just but in the improvements using excess cash generated by your core cities. The question in this case becomes, does the cost of buying the courthouse justify any benefits to production or shields or gold. Should you buy in the courthouse, so more shields will be produced to complete other improvements or should you just buy in the other improvements and ignore the worthless courthouse because its potential benefit cannot even cover the cost of its own maintenance?
Some of the nonsense in corruption may be based on a lack of global perspective by the corruption team at Firaxis. The Civ3 game is only 540 turns in length and usually courthouses begin to come into play with 400 turns remaining. A corruption crippled city takes 60 turns to build a temple (30 for religious civs) and then 80 turns to build in a courthouse. At the point these two improvements are built, the corrupt city can only be in the size range of perhaps 4 to 6 citizens depending on some luxury and water constraints and then the city's shield and gold output is still only at 50% of what it could be. It takes 140 of the remaining 400 turns to build the first two improvements at an agonizingly slow pace.
In the new V1.21 release, I can see some impact of the courthouse in the 1, 2, and 3 rings around the core areas but the fringe cities seem to remain crippled beyond all hope.
There is also no appreciable time benefit gain from a courthouse. Things do not get better or worse over time just accounting for time alone.
If you are already near to democracy and the targeted city is more than 3 rings away from one of the two core cities, then it will probably be on military and improvement lifesupport for its entire life cycle and virtually immune to propoganda so that will make the courthouse effectively cost more to maintain than it would ever hope to generate in reduced corruption and waste costs.
Just my take on it so far ..
.... cracker
