Thanks for the effort.
Unfortunately, your examples are flawed, as the basic assumptions are already flawed.
In Civ4, the slider is used to split the surplus of commerce (not being used for units, city maintenance, civic upkeep and inflation) between treasury (gold) and science (beakers) - just to stay with the two basic ones, I will just ignore culture for the moment.
Which is exactly what I've done. You work very hard to not understand when people talk to you.
Already wrong.
You will have 15 commerce, which by the slider you can split in steps of 10% between treasury and science.
I told you already, correcting my math will simply illicit an "I don't care", from me. The math, itself, is well outside my actual point, which you have missed. So, as promised...
I don't care.
This is broken down to the individual cities relating to their contribution to the nation's overall commerce.
I know. I put that in my example, if you would have read it. Psst... here's a hint. The words "Gold" and "Commerce" are interchangeable.
I will admit that there are problems due to Firaxis' unfortunate affection to go with small integers (which later was partially reworked to allow for decimals, too) and the resulting rounding.
Nevertheless, the principle stays the same:
You have created 20 commerce, of which 5 are taken away for maintenance, thus leaving 15 to be split between treasury and science.
Since in your example no further costs are to be covered, you may set the slider to 100% science, thus creating 15 beakers each turn.
Assuming equal maintenance per city (2.5 in your example), city A would generate 7.5 beakers per turn. Since that building is generationg additional 100% of the beakers, the total of city A would be 15 beakers.
The total for your empire (which would be displayed next to the slider) then would be (7.5 + 7.5) for city A and 7.5 for city B, totalling up to 22.5 for your empire.
Here we face the undenied weaknesses of Firaxis' kind of thinking, because this will lead to 22 beakers for science with the rest being added to your treasury.
All you have done here is repeat what I have already said. My point isn't "Look at my math" my point is "Look how needlessly complex and confusing this system is." All you are doing here is illustrating my own point for me. The basic point is, and will continue to be "The Non-Slider System is Easier to use then the Slider system." You've basically confirmed that in this section here.
Luckily, the slider functionality will do all these calculations for us (with the mentioned problems of roundings, since beakers are of non-fractional dimension) and will display all the resulting values.
I can even run local deficits, and nevertheless I can adjust the slider for my empire according to my likings.
According to a general idea of your likings, this much is true. It is plain that your likings, and my likings, are entirely different. They've already made your game, now it's time for mine.
Honestly, I cannot really see where the problem is.
The problem is, as I've already stated before, a lack of control, and focus. Perhaps I would like to collect more gold? Perhaps I'm playing a strategy that involves shifting around which tile is getting worked when quite alot, and I'd be very interested to know quickly exactly how much of every resource I can have available, and where it's coming from. The "Where it's coming from" is extremely key. And not just in a general wash kind of way. Let me be blatantly clear.
I want to know exactly what each and every tile in my civilization is doing at all moments and exactly how I can adjust them to best suit my needs on a turn by turn basis. The slider system is a confusing one that allows only for a general washing of information, at best. You get an idea that a city is doing X or Y, but I want concrete information.
Honestly, I think the slider system is easier, since all I am interested in (as far as getting technologies is concerned) are the total number over all of my empire.
I just don't care whether city A or city B or city Z are producing more or less (under the assumption that I've set up each city in a way in which it produces the max of what it shall produce [food, production, science]).
And this is where you and I differ entirely. I do care whether city A, B, or Z are producing more or less. On an intricate and detailed level I deeply care. I very much want to play a game where I can view all my cities, turn by turn, on marathon mode, and maximize their output to my needs; making some cities science beacons of amazement, and others produce culture wildly successfully, and other pushing out nothing but military units.
You seem perfectly happy with general information and basic gameplay. I am more interested in specific information and deeper gameplay.
Since technologies are a nation-wide effect, all I am interested in are the total number for all of my empire => slider.
Then enjoy playing Civilization 4!
While I appreciate the idea of enjoying a system that already exists, you've gone so far as to illustrate my own point for me. The slider system is confusing, and you basically need to play with a calculator beside you if you want to adjust anything, or put up with moving things around and seeing what happens, which is arduous.
By your own description, the system you claim to enjoy is difficult. Why don't you want to play in a system that is less difficult?