I think you're missing Martin and Vexing's real point. They're not saying that there are not exploitable policies and strategies in tradition. They're saying that there are much more consistently exploitable policies in Liberty, and backing it up with generally mathematical proofs. Those early bonuses mean that if you played another player who leveraged Liberty early and you went Tradition, you wouldn't MAKE it to the end game you refer to.
Actually I'm not missing their point at all. In fact my last post just said:
"I see liberty as a very fast early bonus tree and early bonuses are very powerful which makes it very powerful."
THEY are missing my points. For whatever reason, I don't know. I think sometimes it is something you get locked into. When you think you are the best and are always right, you tend to teach and ignore the suggestions of the 'lesser' people.
I'm no slouch in math myself. I do have a doctorate after all in the subject. It's a very hard thing to mathematically analyze but I will give it a shot. Let's consider 2 scenarios. In scenario A the player has just completed the liberty branch. In scenario B the player has just completed the tradition branch.
Assumptions:
The branches were completed at the same time
4 cities
The happiness cap has been reached (i.e., 0 global happiness)
3 unique luxuries available to you naturally
2 DoWs (as that's very common on higher diffs). 1 was an 8 warrior rush and the other a more upgraded spearmen, archer, warrior rush.
Cities may build monuments and no other culture buildings. This does not mean they won't get other free culture buildings from tradition.
Ignore intangibles as both civs could've taken advantage of them (trading, CS allying, happiness triggered GAs, beating another civ to a wonder, etc)
Same wonders have been built
Captial is the biggest, second city is smaller but bigger than the 3rd and 4th cities.
Both players are intelligent
Ingore order of policies as both can make intellgent choices to either get more production sooner or get more culture / happiness sooner.
Every city has a library and the capital has the NC
Each worked tile produces an average of of 2 production/turn. I thought about this a lot and since you have few citizens, have access to civil service, granaries, stone works, stables, etc, it seemed a reasonable value to put it at.
I will try to compare bonuses as production one as much as possible as it tends to be most universal between the two.
Under both scenarios the base happiness (before any policy specifc boosts) is 9 + 3 * 4 = 21. The base happiness remaining for citizens themselves is 21 - 4 * 3 = 9.
Scenario A (Liberty)
Thanks to meritocracy you have an extra 3 happiness, 1 for each of your secondary cities. Thus you have a total of 12 for citizens. This implies:
Capital: 5 citizens
2nd city: 3 citizens
3rd city: 2 citizens
4th city: 2 citizens
Policies (and effects):
Liberty opener: providing 4 culture/turn
Collective rule: has saved 106 + 2 * 35 production (the 35 comes from the 50% faster build of the last 2 settlers - you pay 2/3 of the normal cost, saving 1/3)
Republic: It's providing at least 4 production/turn. Let's say the extra 5% amounts to 1 additional production (you won't always be building buildings and it's hard to estimate production but I think 1 is reasonable). So a total of 5 production/turn
Citzenship: saved 70

and a somewhat unmeasurable benefit to tile improvements (meaning its hard to compare / analyze in terms of gains so we will mark is as a benefit and move on)
Representation: free GA (again very hard to compare so we will mark is as a benefit) and reduced culture costs (Approx 10%).
Meritocracy: as discuessed above, is providing 3 happiness. Let's assume the cities are 5 tiles apart. So 5 road sections in other words. that gives you 15 road improvements. Trade routes don't make more than the city sizes themselves AFAIK so you will be getting 3 + 2 + 2 = 7

. For a loss of 8

/turn
Finisher: Used to rush Notre Dame / PT for 400

(NOTE: this just happened, remember, so the Notre Dame happiness couldn't have be utilized yet)
Other Items:
The two wars and the barbarians required you to build 8 units to defend / rome / hunt / etc. We will assume for simplicity all archers. For a total cost of 320
Empre Stats:
15.75 + 4.5 + 3 + 3 = 26.25

/turn
10 + 6 + 4 + 4 = 24 citizen

+ 5 policy

= 29

/turn (see note on citizen production below for an explaination)
-8

/turn + gold from all other sources
4 + 3 + 3 + 3 = 13

/turn
646

saved via policies
Note: What is citizen production? It's production from citizens themselves excluding the city, modifiers, building production, and anything else I haven't thought of as it will be the same for both
Scenario B (Tradition)
A smart tradition player will attempt to grow the capital larger than a non-tradition player. Also as they aren't expanding as fast, the capital will have more time to grow larger too before hitting the cap. So with that said, let's say the capital has grown to size 10. This means you get +5

from monarchy and +1

from landed elite. Thus you have a total of 9 + 5 + 1 = 15 happiness for citizens. This implies:
Captial: 10 citizens
2nd: 3 citizens
3rd: 1 citizen
4th: 1 citizen
Policies (and effects):
Tradition opener: +3

/turn. The faster border popping is quite useful but also hard to evaluate so again we will mark this as a benefit and move on.
Aristocracy: A smart player will build the GL, the Oracle or HG or something like that to take advantage of this... however for comparison purposes lets assume the wonders that would be build are just, NC, HS, and Notre Dame. This totals 185 + 300 + 400 = 885

. With aristocracy you save 116
Legalism: You got 2 free temples and 2 free monuments. This is a savings of 280
Oligarchy: By this point units cost I think 1.5

/turn to upkeep. You had the same wars, but required fewer units to defend. This makes the cities twice as good and usually can be defended with just the garrison archer. Thus you only required 4 archers instead of 8. So you are saving 6

/turn and 160
Landed Elite: Providing just 1 measly happiness
Monarchy: Prodiving 5

and 5

/turn
Finisher: +15% is hard to analyze so we will mark this as a bonus. The +2 food per city we will consider as a way to shift production to be more efficient. Thus +2 food can actually turn into +2 production per city per turn
Other:
Since the trade routes would be a loss at this point, the tradition player opted not to build them. This saved 8

/turn over the liberty variant.
Empre Stats:
27 + 4.5 + 1.5 + 1.5 = 34.5

/turn
20 + 6 + 2 + 2 = 30 citizen

+ 8 policy

= 38

/turn
6 + 5 + gold from all other sources
9 + 5 + 2 + 2 = 18

/turn
556

saved from policies
Now I won't draw any conclusions but you let the reader think about it themselves. I'm 100% certain someone will come along and bash something to pieces and claim the whole thing is invalid and I'm fine with that. I realize that both empires will likely be bigger due to trading and such. But that doesn't change anything. This is a proporital analysis... not an 100% accurate this is how the game will go analysis. I also realize I haven't included upkeep costs, whether you rush buy or produce, whether the liberty player gets a city faster or whether the tradition player gets an extra wonder or completes the tree faster thanks to having more culture. There are so many variables a smart player can take advantage of on both sides that it becomes a wash.
So you have a think and let your creativity run wild