I guess it also can depend on circumstances and/or level, I only play on Emperor, but without having done the exact math, I feel that even if I want to go for a quick Collective Rule, I'll get there sooner if I start by taken Tradition opener for the extra CPT which is much more than I get from Liberty opener very early in game. But I guess one could fairly quickly do the math on that.
Edit >
Just to follow up on that, I did a quick math. Not taking possible culture ruins into account, and assuming that you build Scout-Scout-Monument and complete Monument after 20 turns to get some early policies, the math looks like this:
Straight Liberty
You need 25+30+60 Culture to get to Collective Rule. You'll pick Liberty opener > Republic > Collective Rule
- You'll earn first policy on turn 22 (having finished the monument on turn 21).
- You'll earn second policy after another 8 turns (2 CPT).
- You'll earn third policy after an additional 15 turns (2 CPT, assuming you haven't settled a second city by then - would you have?)
This means a total of 45 turns to get to Collective Rule, maybe slightly shorter if you manage to pop a second city before this for another +1 CPT.
Tradition opener, then Liberty
You need 25+30+60+105 Culture to get to Collecture Rule. You'll pick Tradition opener -> Liberty opener -> Republic -> Collective Rule
- You'll earn first policy on turn 22 (having finished the monument on turn 21)
- You'll earn second policy after another 5 turns (6 CPT).
- You'll earn third policy after another 9 turns (7 CPT).
- You'll earn fourth policy after another 15 turns (7 CPT, assuming you haven't settled a second city by then - which there's a slightly larger chance that you would have)
This means a total of 50 turns to get to Collective Rule, so you do actually get there faster by skipping Tradition. However, this requires that you build the Monument fairly quickly, pushing back Monument in the production cue will make the two break roughly even. On the other hand, finding a culture ruin will have greater impact for people going strict Liberty, because the 20 Culture from the ruin will cut 10 turns off at 2 CPT while only 3 turns off at 7 CPT.
So if we take beelining Collective Rule as the objective for a Liberty start (which is probably not a bad assumption) it actually pays out to skip Tradition. Go figure - I think I'll work on a mod that makes these trees incompatible just to try it, I always had the (seemingly wrong) feeling that taking early Tradition would promote early policy progression.