How rich is the Traveller ecology? How many fundamentally different settings are there?...
I think it depends a lot on two base assumptions:
1) is trade like modern earth i.e. every system generates trade proportional to wealth (population * TL) with a large part of trade being the shipping of raw materials to the high TL systems.
or
is it more like age of sail earth in that the higher TL a system is the more self-sufficient it is in most items within its own system and trade is mostly in exotic goods and luxuries: the equivalent of spice, sugar, coffee etc.
One reason this is important is if the high pop. high TL worlds are very self-sufficient then they have less motive to care about the backwater worlds.
The second reason is the first case would create a denser more interconnected setting while in the second case all the important stuff is on the prime worlds and the routes in between them creating a more skeletal setting with lots of unimportant worlds in between the important ones
and
2) small fleet or big fleet i.e. can the high pop. high TL worlds produce fleets big enough to conquer other worlds.
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Those two assumptions between them create four base combinations of incentive to expand (low trade vs high trade) and ability to expand (small fleet vs large fleet) which imo effects everything else that comes after.
The four options being
1) low trade + small fleet ( low incentive + low ability)
2) high trade + small fleet (high incentive + low ability)
3) low trade + large fleet (low incentive + high ability)
4) high trade + large fleet (high incentive + high ability)
LBB 1-3 doesn't imply any specific option imo but I'd say "Mercenary" does imply high trade / incentive and "High Guard" implies large fleet so with those two added I'd say the OTU is pretty much solidly option (4).
However if you treat books 4 and 5 as optional then you have all four options. Mercenary I think implies high incentive but could work with both small and large fleet. (It almost implies small fleet in a way) and High Guard although it implies large fleet could work with both high and low trade settings.
so I'd say
LBB 1-3 -> options 1-4
+Mercenary -> option 2 or 4
+High Guard -> option 3 or 4
so I think it was really Mercenary and High guard which pushed the setting in a specific direction
however even with the assumptions set to option (4): high trade + large fleet, there are still numerous sub-options:
1) each / most alpha systems are independent.
I think this is quite plausible given that offensive jump-capable fleets are potentially a lot less powerful than defensive in-system fleets and planetary defenses. Especially given the importance of fuel I could see systems building up massive defenses around each refueling point making any attack on an alpha system very difficult.
2) voluntary federation e.g. Star Trek, e.g. member planets only have in-system fleets and communally fund a relatively small federation fleet with marines as red shirts rather than infantry units (so it's not a threat to the members).
3) empire:
- overtly coercive - Darth Vader
- covertly coercive - spies everywhere
- loose - lots of local autonomy
etc
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going back to the base four options
option 1 (low trade + small fleet) creates the classic Dumarest setting
option 2 (high trade + small fleet) is semi-Dumarest but if there was high trade but no large fleets you might want a reason why (e.g. some kind of trade federation that controls jump tech)
option 3 (low trade + large fleet) implies there's no commercial reason for an alpha system to conquer other systems even though they could have the fleets to do so (although historically there have been plenty of other reasons for expansion: ideology, religion, glory, loot, megalomania etc).
option 4 (high trade + large fleet) implies both a strong incentive to expand and the potential ability to do so.
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And that's all before you
1) introduce history i.e. take any of the above settings but at a stage of their development where it's just beginning or breaking up
or
2) have optional world generation DMs to create particular kinds of alternate sub-sectors.
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so basically a lot but (imo) the options can be tightly constrained early on by a couple of important assumptions.