I broke my own home brew rules. I've gone back to the basics and tried again. This time a little bit more detailed. As I've always got game in the brain here is some of my tinkerings.
Transportation and Logistics TL. The size of a state is affected by its transportation and logistics technology. In GURPS TL2 the Roman Empire was able to span the entire breadth of Europe. Unfortunately the certain limitations meant that that very little of taxes found their way to the administrative central because of the diminishing return of transportation costs. This explains in a way why Rome can be divided by east to west.
Every citizen has 1/3 of their taxes, which is 1/3 of their Cost of Living (if they are at the wealth level of struggling or higher), is supposed to go to the central government. This is because their initial taxes goes to their local government and typically 1/3 is demanded by overlords as tribute/taxes.
Every taxable unit, which is a family, would normally pay $33.33 ($66.67 going to local administration). I will simply this to $6.67 per individual. So a population of 88M spread out over 17 per sq km or around 5M sq km. This would normally provide $7,600M in taxes per month. Unfortunately if you find a way to calculate the relationship of the distance, this value will greatly diminish.
To find this out I had to use Justinians reign and finances. Thanks to Tribonian, his infamous Questor, his reign was one of the most effectively taxed and detailed eras.
What I got was a basic system where I used the area of the state to determine the level of inefficiency. I established a technological base line of logistics and transportation. This was: a state had an effective organizational efficiency of 100km x [1 + (TL x0.5)]. So Rome at TL 2 had an organizational efficiency of 200km radius (6 days by road). at 88M inhabitance or an area of 1300km radius the inefficiency was around 15% dwindling the resources by $1,170M.
At 1300, that would take a 40 days for the legion to march there or 2 days by the fastest ships. Its pretty troublesome. So the there is 2 forces at work: Size and Logistics that go against each other.
Justinian thought it was a "good" idea to reunite the empire because his ego and who can say no to having more people to tax. Unfortunately as the distances became greater the costs of keeping lines of contact open with security, ships, animals, ports, and bureaucracies got more difficult. You can say there are "free market" forces at work here: Demand for taxes vs. the cost of maintain control over that source.
Social Mobility TL.The second interesting affect TL has on groups of people is in Social Mobility. A state with more entrepreneurial or well compensated people is a happier state (yeah right), unfortunately happier people are more demanding. They would rather not get involved in anything stupid someone else has planned, like going into war, if they had a choice.
In Building Low-Tech Landscapes II: Overlords, you have a system in GURPS to create communities. This is where mercantilism comes in. Rome was pretty mercantile, but that was lost after the fall. The survivors of Rome, those who initially colonized the more defensible marshes of Venice and City States continued to become more meritocratic and surpassed Rome. The rest of the world rebuilt at around the 11C and exceeded Rome in the 13C onward.
Yeomen and Merchants were as well to do. Merchants were as wealthy as nobles, but unlike them, you can tax them a pretty penny. Sergeants were actually social class. Consider them Yeomen who were professional servants (which is what sergeants meant). Typically a Lord will have a couple of squadrons of sergeant man-at-arms. A well to do knight would normally have a sergeant to do the scouting, shield-bearing and valet duties.
In a group where practically everyone was a struggling peasant share croppers and serfs, the taxable income was $100 per family. Serfs and Slaves can't be made to fight and are considered dependents. Peasants, like the plebians can be made to fight by the state or the lord they are pledged to. So in a way, serfs are more controllable but your exchanging that head ache for the skilled warriors you would have to hire. Peasants are demanding, they can fight and are obligated to fight but you would have to be a d*ck to get your way with them.
A population of 60% serfs, 25% peasants, and 15% yeomen produces 15% more. Unfortunately 40% of the population can be obligated to fight. At 80% peasant, 18% yeomen, and 2% non-taxable noble/gentry you have 15% more productivity but 98% population to levy. At 80% peasant, 15% yeoman, and 5% merchant you have 30% more productivity. At 60% peasant, 20% yeoman, 15% merchant you have 60% more productivity.
So basically a minor lord of Status 4 (filthy rich) can have his $840k income from a several villages and a castle of total population of 3040 at the 11C, a town with a population of 2700 at 12C, or town with a population of 2200 at 13C.
Social Mobility modifier allows for greater income generation. So at Rome's mercantile height of +15% productivity (since merchants didn't have a very great status), compared to Italian city state republics of +200% productivity.
Given the Empire example above, at an annual revenue of $1,170M income would be around $1,345M with a relatively large freeholder class.
Medieval Tech for me. TL 3 for me is 10C-15C. The very steep population decline since the fall of the Roman Empire from 4C all the way to the slow resurgence at around 11C is indicative of the return to regular levels of civilization. After that Medieval World lecture, I'm pretty much convinced of that Rome was not-so-kinda TL4. Most of the lost tech came back at around 12C, and food production was something the Roman didn't have any better than the Medieval World which counts more than just the difference in Literacy and Bureaucracy.
Primogenitur, or the ability to Monopolize and Accumulate power and wealth over generations really got much better in the medieval era. It allowed for more stable transitions between rulers. Although, the meritocracy of military coup was great, it always left a huge mess. It also stopped siblings from killing each other to reunite the properties.
I think warfare was what really had a slow resurgence back to roman levels of discipline, and organization. The problem with the Roman techniques is that it was highly dependent on skilled individuals. After you exhausted it, no-one inside the small niche was able to pick up after the previous generations.
Looking at population levels, it appears that at the height of Rome population was at its own height. After all the wars and fights, population levels didn't get back to full strength of 88million until the 15C (the Renaissance). Population is heavily correlated to Technology, because of the rules governing economics and specialization.
So it is no wonder that highly motivated citizen armies didn't come back to fashion till the renaissance.
The mark of TL 3 warfare is citizen armies and the ability to sustain a standing force regardless of weapons and technology is TL4. Rome was TL3 in warfare but TL2 in transportation and social mobility. There were few ways to keep that army sustainable: barbarian levies and plunder were the limited methods. TL4 armies was the obsolescence of a cavalry elite.
Feudal Obligations to fight, and levies are pretty much TL2 in my opinion. You can find them all over the ancient era.
States could not normally sustain a citizen army because of cost of money and life. Its so much cheaper to make promises instead (levies). It costs money to keep a standing force kicking ass. There is only one thing that will allow a state at this point to keep a larger standing force: social mobility or tollerance.
One of the first people to get that right were the Ottomans with their Janissaries. Their tolerance towards the Jews and Christians allowed them to have more merchants around, which provided a lot of income. It also didn't hurt that their "open" recruitment policy gave them a large man-power pool to draw from.
More and more evidence that stirrups were not a big deal in mounted combat have been coming a lot lately. First hand, I've seen mountain pony riders in my country prefer to hug the horse with their legs over the stirrup in uneven terrain. This was the conclusion more than 20+ years ago and it has been thoroughly debunked by now. Second, china has had access to it since the 2C and Kataphrakts have been doing shock maneuvers before it found its way west.
TL3 ends at Civil Bureacracy. Stewards and Logothetes count as TL 3 bureaucracy for me. China got there first with their standardization, paper, wood block printing and really high literacy rate. Literacy rate more than 15% is bordering TL4.
Age of Sail is very TL4, venetian galleys or fast galleys are the height of TL3 ship making. Longships are TL3 ships when it mostly was populated by TL2 ships.
Well thats what I wanted to unload, sorry for the mess. I just have to get it out of my system now and then.