Depending on the Civ, mixing authority with either Tradition or Progress can be really strong, as the bonuses from authority become applicable over a much longer span of time, while most tradition and progress bonuses are strong regardless of when you pick them. Additionally, I don't think the tier 2 policy branches are particularly strong for domination, as statecraft and artistry don't do much, and fealty doesn't work that well IMO. I usually find I'm ready to build castles and armories a decent bit before I get my second fealty policy, and the bonus yields from pastures is situational, while the two wing policies are just objectively weak. The only good policy is the double border growth during WLTKD, but that's at minimum your fourth (tenth total) policy. There are many tradition and progress policies that are just as strong that you can get much earlier.
One of my favorite civs to play is Prussia, a warmonger civ that really benefits from the Tradition capital and GP bonuses (more specialists=more great generals and military units, larger capitol=more specialists can be worked), but also can really benefit from some of authority. This also works great with the Timurids (another one of my favorite civs), and can work pretty well with France, Assyria (though you may want to take 1 more authority policy before starting tradition), Byzantium (if you go for a GP focused religion), and essentially any other civ that wants to war but play somewhat tall or at least have a great capital. For them, here's a strategy I've used a few times that is quite strong:
Policies: I first take 2 authority policies (opener and tribute), then 2-4 tradition policies depending on whether or not I'm warring somebody (I start with the Artist one to try to get religion and stack with tribute from Authority), then 2 authority policies (imperium first if I'm about to conquer anyone, dominance first then imperium if I'm only just beginning to war), then finish tradition and finish authority.
Why this can work:
- 1) The Authority opener is incredibly strong in the right situation (i.e. decent number of barbs, close city states for barb quests, raging barbs even) and makes it easier to get super experienced units. Conversely, the Tradition opener can be incredibly weak in a lot of situations, as that 2 extra pop rarely can work good tiles until like 20 turns later and the extra happiness is usually irrelevant. Additionally, the extra culture from the Authority opener and from Tribute (if you're in a position to get good tributes) makes up for the relatively weak culture given by Tradition and can help you power through both branches.
- 2) there is good synergy between some of the policies (particularly tribute and sovereignty for border growth)
- 3) going straight authority means that some of the bonuses come too early, especially the garrison bonus and supply-free units on 10 pop cities, while going full Tradition into Authority means that many of the Authority bonuses come too late.
- 4) some domination civs (specifically the ones I mentioned, i.e. Prussia, Timurids, France, Byzantium, and Assyria) disproportionately benefit from both Tradition and Authority and thus aren't hurt as much by working through the trees more slowly, or want to boom and play tall for a bit before they start conquering.
Additionally, mixing Authority and Progress can be quite strong for many of the same reasons as mixing Authority and Tradition (policies coming unnecessarily early if you go straight down a branch, good synergy between policies, Authority opener being super strong in the right situations, etc...). If you mix Authority and Progress, that usually means you are playing a civ that wants to play really wide and either conquer a bit or is particularly worried about defending. However, I don't think mixing Authority and Progress is as good as mixing Authority and Tradition, except for Carthage who greatly benefit from a few policies from each branch (specifically Tribute and Fraternity).
I'd probably go for a similar mix, i.e. going 3 Authority (going down the left side), then 3 Progress (either go down the right side or the left side, depending on the civ, don't bother with the happiness policy yet), then finishing Authority, and then finally finishing Progress.
Good civs for mixing Authority and Progress are:
- Carthage: buying quinquiremes with gold from city founding, getting even bigger tributes with the tribute policy, getting instant science and food from Fraternity due to free city connections, wanting to play super wide due to how easy it is to build decent, easily defensible cities (i.e. remote coastal) as Carthage
- Babylon: good early military units, investment bonus synergizes really well with wide play and Progress
- Byzantium: if you go for a religion with great non-WLTKD wide bonuses (like triple buildings or something), though Fealty is quite good for them (especially the opener and the WLTKD policy) so I might try to either work in the Fealty opener relatively early, or just go straight Authority or Progress then straight Fealty. Honestly, going Progress, Fealty, and full WLTKD religion does just kind of sound like a better way to play wide in almost any situation, unless you're really under pressure or have really weak neighbors.
- China: they are a great straight Progress civ, but if you're in a threatened position or have weak neighbors Authority can be really useful
- America: another great straight Progress civ that could use some warring bonuses in the right situations
- Russia: get authority stuff purely for hunting barbs and insane border growth yields, then go full progress and wide boom.
As for the third policy branch, honestly all three of them can be really good for conquest/a domination victory depending on the context:
- If you're behind on tech or want to get further ahead on tech to compensate for poor production, then Rationalism is a great choice. If doing the latter, then Rationalism is especially good for civs that mixed Tradition and Authority.
- If you're just going normal conquest stuff on a water/hybrid map (i.e. islands, continents, relatively non-pangaea-y communitas), then of course imperialism is great. Great for civs that went Authority into Fealty or civs that mixed Authority and Progress.
- If you aren't playing super aggressively and have played quite thick, then industry is great. It can help you really jumpstart your economy and stay relevant on tech to build up a huge late game army. Industry works really well with civs that blended Authority and Progress
If you go Rationalism or Industry, then I would probably go Order for your ideology, and if you go Imperialism then I'd probably go Autocracy. You can also go for Freedom if you went Industry, pretty much solely so that you can generate a ton more gold via trade routes (and get CS influence too) to purchase a crap ton of units that start with full XP.
