Rummy while ideas like this are precisely what are needed, I would not agree with a division based slider system. This comes from three main reasons;
1. What of the people who enjoy composing armies from base units?
Obviously if your a macro player, who's not actually that bothered about the composition, just that it is 'effective' in the general sense. i.e. your general [3xINF 1xART] divisions. Then a slider system is perfect, because it allows them to throw some of everything into a division to give it effect.
However it doesn't give much satisfaction to a player having a division on the front who only needs to up the AT slider, or AA slider when it comes under attack from the respective opponants equipment.
It doesn't reward strategic planning or putting the right units into place. It only benefits the macro-player with the RTS 'spam this' mentality. Whereby victory is a result of spamming the counter to whatever your opponent is spamming, and swapping through the 'rock-paper-scissos' unit list faster than your opponent can.
As a long time RTS player, I don't play HoI for RTS similarity on a massive scale.
2. Runs the risk of the 'ultimate ratio' combination
By limiting the number of brigades of different types within a division, it is impossible to create a division that can excel in all areas. Because of this, tactical play is greatly awarded by looking at what is on the field and finding the weakness presented.
With a ratio format, I can tell you with certainty that you could mathematically construct an 'ultimate ratio' between all the groups. Once you've worked that out (even by trial and error) your not going to go back to 'inferior' ratios.
For MP, the game turns into who has the MP and IC and the better front line. For SP you win all battles with 'equal' nations.
3. It's actually quite complicated; steep learning curve
Anybody can understand “Pick any 4 from this list”, and after that they can start to experiment with combinations. This gives replay value in itself, as there are n! Different combinations of troops where n is the number of different troop types in the list.
While a slider has the capacity for near infinite numbers of different combinations, it's not intuitive. There is too many different combinations, where do you start? 80:20? 5:5:5:75? 1:2:3:4:5:6:7?
This also ties into the back end of how the game would work. The introduction of a slider in that sense for each division means not only keeping track of the divisions constituents, but also how it should be precisely filling those constituent requirements.
While in itself that's not too taxing a problem, but when scaled up to keep track of litterally millions of game day updates it could end up requiring far too much processor time.
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Opinion: The merit of sliders is in operational actions
Assigning air and naval missions are tedious. The units are constantly in motion across a large map, there is no 'front' that you can jump to and the unit could be anywhere requiring a search for it first.
Then there is the fact that the missions you assign are very short term. A campaign for a land division lasts for months as it crawls across the map. Your stance, attacking/defending only needs to be updated fairly infrequently. This is because that is the strategic aspect of the game.
Aircraft and Naval units represent tactical assets.
Because of that their uses change continually. With many of them it becomes impractical to control. If you were to, it would take up your entire game experience assigning missions, pulling them back, rebasing and in general micromanaging your army.
The strategy in tactical assets is the missions they take on.
So by setting priorities for the forms of missions they take on you gain the strategic aspect of tactical assets. For example, air superiority is needed when an airbase gets attacked. It would be pointless to create a strategy where the plans stay on the ground to get bombed while the pilots rest between bombing missions. Therefore while your priority is bombing missions, your airfields still take on key missions when needed.
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The larger your manpower pool, the more money you get as they are working in the economy.
From this you can set laws regarding drafts which will alter the percentage of men taken from the available manpower pool and after a period of 100 days will turn them into raw recruits.
This. Mostly. Rather I would prefer to see leadership be your MP multiplier by your level of education, plus any centres of academic excellence (read cities/urban terrain resource). Now perhaps this is the way it currently works, perhaps not. But to me often leadership has appeared rather arbitrary across the nations in Ho3.
Money doesn't necessarily increase with number of people in the nation, as those same people cost the government. Rather the more 'communist' you are, the less money you get (more social spending or not taxing workers), the more libertarian, the more money should be generated off trade, and fascism should improve resource gathering rather money due to 'autarktic principles' that often come with fascism. Tax rate should be a politics option. Communism gains an IC bonus politics at lower unity levels etc. to offset not having a monetary boon. After all Communism wasn't about generating wealth, more about insuring it was evenly spread.
[tl;dr] In my opinion money generation should be a function of politics, not population.