Prescient Governor (PG for the purpose of this post) gives you 50% more research and 50% less production. I thought this trait looked promising if used in the right situation, until I actual recruited a prescient governor and saw how it works.
I apologize for not making these the same height.
If you look closely, you will see that the research bonus and production penalty are not calculated in the same way. The research bonus is an additive bonus that does not stack with other bonuses. It simply adds an additional 50% on top of the other percentage boosts.
The formula for research looks like this:
[Technology input (1+Sum of Bonuses)] Approval
[ 5.89 ( 1 + 1.393 ) ] 0.942
The bonus from PG is 50% (or .5), so we can figure out how much research it is contributing.
[ 5.89 (.5) ] 0.942 = 2.78
We have 13.28 total research, so this means that the total research boost we receive from PG is just shy of 21%.
2.78 / 13.28 = .209
This is a far cry from the 50% most players probably think they are getting. Now, of course, this is planet specific. The research boost will not always equal 21%. This is just an example. But since in any game you will always have some other bonuses to research, it is mathematically impossible for the effective PG bonus to equal 50%. (I say effective PG bonus to distinguish it from the additive bonus, which of course does equal 50%).
Now, let's look at how PG affects manufacturing. Instead of giving a penalty equivalent to the research boost, PG gives a penalty that is outside the main formula, and so much more severe.
The formula goes:
｛ [ Mineral Input (1+Sum of Bonuses) + Core World Capital ] PG Penalty ｝Approval
｛ [ 7.89 ( 1.4 ) + 1 ] -0.5 ｝0.942
As a side note, I have no idea why the Core World Capital production doesn't receive the production bonuses along with everything else. It seems a little odd.
We can easily calculate how much manufacturing PG is costing us by running the formula without the PG modifier, and then subtracting the difference.
｛ [ 7.89 ( 1.4 ) + 1 ] ｝0.942 = 11.35
11.35 - 5.54 = 5.81
It appears like we're actually losing 51% of manufacturing because of the way this game rounds numbers, but I'm not sure.
Now, all that math was to establish that PG costs us more in manufacturing that it gives us in research, but why does it matter? Isn't research more valuable than production anyway? On the surface, it might still seem like a reasonable deal. If you offered me a choice between 1 research point per turn and 2 manufacturing points per turn, I might take the research; but this scenario is not remotely similar to what is going on with PG where the choice is not between two bonuses but between a bonus and a penalty.
No matter how much production I have, with PG it will always be half of what it could be. This means all production projects will take twice as long to complete.
A core world without PG can build production and research districts at twice the rate as an identical core world with PG. This means that the world without PG would soon outpace the PG world not only in manufacturing, but in research as well.
There are still a handful of situations in which you might consider using a PG. You might have a core world that has a lot of research input and very little production input. It might be a world conveniently located so that you can send supply ships there to provide the manufacturing your world lacks. Alternatively, if your planet's social projects are all completed and you have no available tiles for further construction, and you don't mind losing half of your military construction and getting a massive approval penalty for firing a governor, you might replace your governor with a PG governor.
In my mind, this is just far too situational. Even if you met all those criteria, you would still need to find a leader who not only has the PG trait, but also has reasonably good attribute distribution and lacks traits you want to avoid.
PG could easily be fixed by making it affect research and manufacturing in the same way. Either the manufacturing penalty should become part of the main formula with all the manufacturing bonuses, or the research bonus should become an overall boon that multiplies your other bonus.