People wants to talk about authority, let's talk about authority
Thanks for the resurrection!
I already wrote something about authority in the Zulu thread, but I'll continue here.
From my point of view the biggest problem with authority is the lack of science. There are basically two possible routes in the authority tree, one is taking the left policies first, the other one is rushing to discipline, then returning to the left policies and finally taking honor. Neither can match progress.
If you decide to take the scientific path, you'll start to get science when you get your second policy and choose dominance. The amount of culture varies depending on the combat strenght of the opponent, but on standard speed you'd get 6 science for killing an archer and 7 science for killing a brute, hand-axe or warrior. If you want to match the science output of the progress opener, which can be obtained earlier, you'd have to kill 3-4 units in the time it takes the progress player to grow his/her capital. This is hardly possible even in the best case scenario and even then the progress player gets his initial science earlier, which means that you should somehow catch up his advantage. The third tech grants you more science in the form of imperium. 25 science for each city you settle is, however, quite meaningless and once again, this can be compared to progress. Fraternity can be obtained as the third tech of progress and it grants 2 science for each city connection. The first one actually grants 4 science, as it gives the city connection to the capital too. It takes progress just 13 turns of city connection to overtake the science output of imperium. This is all science these trees get and progress gets so much more of it. At this point you realize that you have chosen your policies based on science but progress still has the edge. You have also neglected culture by not rushing dominance and it will take you ages to fill the tree. You don't even have a policy that would increase your food or production output.
If you, on the other hand, decide to take tribute and discipline first, you won't get any extra science before your fourth policy. This means falling scientifically far behind progress. One could argue that tradition has the same problem, but with tradition you can reach the fourth policy a lot faster, you get a lot more science there and you also get faster growth in the capital, which helps a bit with science. Rushing discipline means that you can perhaps keep up with progress culturally, but progress has a massive science advantage when you are at the stage where you can actually conquer cities, meaning that with progress you could have started the war earlier and would have faced less advanced units. In the end you can see that you have two options with authority: being culturally and scientifically behind progress or being somewhat equal to progress culturally and being massively behind scientifically. Neither sounds good.
Another issue with authority is that you can't conquer cities in ancient era and doing it in classical era requires catapults, which means that you must have iron. If you don't have siege units, it can take you more than 30 turns to take the city on ancient or classical era, even if your opponent doesn't have any military other than a garrison. Ordering a military unit to attack a city with walls or a garrison is a suicide even if the city had a very low population and wasn't built on a hill. Dromons might help, but even then it only helps if both you and your opponent have a coastal city. As a result, early war isn't really a viable possibility (unless you are Montezuma and only want a peace deal). With progress you can reach medieval era a lot faster than with authority, and that is when (I think) it gets easier to take cities.