I think it will help if you can get them to celebrate the President/King day. It really reduces corruption by a lot.
No, it does not. If you want to decrease corruption do build courthouses. WLTKD reduces corruption on shields which is called waste. But it does not reduce corruption on commerce. Thus the effect on net commerce is negative. Net commerce is beakers + gpt. So if you produce 400 beakers per turn at -60 gpt, than your net commerce is 340. Net commerce is the main determinant for research in the long run.
Once you have courthouse and police station the effect of WLTKD on waste is low.
And if you are Commie, the most important buildings to improve happiness may actually be Courthouses and Police Stations,
That is highly unlikely. If you go commie you likely have an empire large enough to not depend on luxus slider. Courthouses are a must have as a commie, but police stations only have low return on investment. 2 gpt maintenance for a reduction of corruption by about 2 hardly is worth the investment of 160 shields.
For a republic courthouses can be important for the luxus slider in the semicore.
What would such a town build, with so few shields?
At a production of 1 wealth is the natural choice. Due to rounding you get 1 gpt for only 1 shield. That is exceptionally good.
While you are still short on workers building workers is quite natural, too. Every other option seems like a bad idea. Artillery is possible, but likely this takes way too long to be reasonable. Wealth is usually more feasible.
Settlers could make sense in some circumstances, but i estimate those circumstances to be unlikely.
If there still is plenty land to be used by further sciencefarms, than cash rushing settlers in science farm may make sense. A new farm saves 2 gpt in unit support, gives at least 1 gpt in uncorrupt commerce and would give 1 gpt due to wealth and the city tile produces a net food 2 or 3 if you are agricultural.
Cost for a settler could be 10 gold for 10 turns of not producing wealth, 80 gold for cashrushing, 1 more gold for not producing wealth in the final turn and 40 food for the 2 population the town looses on completion of the settler.
I value 2 food = 3 beakers because scientists produce 3 beakers per turn at the price of 2 food per turn.
Investment = 10+80+1+60 gold = 151 gold.
Return on investment = 2+1+1+3 gtp = 7 gpt.
This is not an excellent investment, but not a particularily bad one either. With 7gtp/151 gold= 4,64% per turn it is better than 2,5% per turn as a benchmark for long term investments.
The relevant issue is that land will be scarce and the limited land can be used with settlers from regulars towns not relying on cash rushing.
Building a few settlers to support further conquests and to take advantage of opening gaps due to warfare makes sense. Obviously it is better to put shields into settlers than to put them into wealth first and cashrush settlers second. Regularily built settler from science farms cost 30 gold(wealth) + 60 gold(food) + 2 gtp(unit support).
One should properly plan ahead to mitigate losses from cash rushing and losses due to unit support. I consider it a good idea to disband units in freshly taken towns to get shields up to 30 and built foreign settler without delay. This reduces the risk of flipping and foreign settler cost no units support.
For doing the Space Race, do I correctly assume Universities help along with Libraries? I've been building them, but haven't really analyzed their usefulness; I've just assumed it.
On average tiles generate a base somerce of about 1.5 as commie or 2.5 in a Republic. The later is usually the relevant case. The city tile itself can be asssumed to produce 5 base commerce. So city tile +12 citizens produce 35 base commerce out of which 20% might be corruption. This leaves 28 base commerce.
Libraries, universities and the modern labs give 50% on this base uncurrupt commerce. So that is 14 beakers each.
If shields are scarce than their value is higher than 1 gold. If commerce is scarce than 1 gold is more valueable 1 shield. For the sake of simplicity i assume 1 gold = 1 shield.
Libraries cost 1 gtp and 80 shields or 40 shields with discount. So it is (14 gtp - 1 gtp)/80 gold = 16.25% p.t. or even (14 gtp - 1 gtp)/40 gold = 32.5% per turn.
Universities cost 2 gtp and 200 shields or 100 shields with discount. So it is (14 gtp - 2 gtp)/200 gold = 6% p.t. or even (14 gtp - 2 gtp)/100 gold = 12% per turn.
Laboratories cost 2 gtp and 200 shields or 100 shields with discount. So it is (14 gtp - 2 gtp)/200 gold = 6% p.t. or even (14 gtp - 2 gtp)/100 gold = 12% per turn.
If you are not a republic those building take much longer to pay off. The assumptions of only 20% corruption and 100% scence sliders are also a bias in favour of those building.