Nightfall Series: If a vampire overpowers another and drinks their blood, the loser has to recognize the winner's authority. Prince Vladimir had to resort to this tactic before he could become the leader of all vampires.
Mostly played straight with the Valar and Maiar and Númenórean, Elven and Dwarven kings and other leaders. However, there is also a memorable subversion: Melkor/Morgoth was considered the highest and overall most powerful of the Valar, and Manwë, the Valars' leader after Morgoth went renegade, second to him — but Tulkas, who was not really good at anything except fighting (and feasting) was the only one who could kick Morgoth's ass.
Morgoth was the greatest of the Valar, and Tulkas came to Arda afterward solely in order to help her other Valar against him. The other Valar combined could defeat Morgoth and drive him away, but not capture him; meanwhile Tulkas was Arda's version of Hercules, and could wrestle Morgoth into submission.
At one point in The Silmarillion, one of the last elven princes from the second generation of elves decides he's had it with Morgoth and rides forth to call the devil out. He loses the fight, due to tripping, but Morgoth takes such a beating (leaving scars) in the process that he never leaves his home again, till the Valar come to drag him out in chains.
Elven-kings were the most powerful of all the Elves; after all, Elves were immortal, and the kings were the strongest and wisest— particularly the Eldest ones. Also, Morgoth was very much weakened due to his obsession with material things. Elves were not created equal.
In Lord of the Rings, those in highest authority are also the greatest warriors. Aragorn is the best human warrior alive, but still he's nothing like Elendil who was almost 8 feet tall, and able (with Gil-Galad's help) to wrestle with Sauron to the death at the end of the War of Last Alliance; likewise, Isildur was over 7 feet tall, and so terrifying that the orcs fled from him even after shooting him dead. Boromir was also the hardiest warrior in Gondor, being Prince of Minas Tirith, and Faramir was a close second. Even Denethor was a fell warrior, greater than his own knights — as was King Théoden, in the Battles of Helm's Deep and the Pelennor Fields. (Tolkien wrote elsewhere that leaders should fight in their own battles; meanwhile Denethor was a subversion of this, as he advocating that "wise" leaders use others to do their fighting for them).
The toughest orc is always in charge, and maintains his place by this ability. This is asskicking equals authority, but it also means you always know which orc you need to watch out for.
The moredhel (dark elves) of The Riftwar Cycle are tribal, war-like and live in a harsh, cold and barren land. A moredhel isn't considered an adult until they're a hundred years old, and they usually need to live another hundred before they're eligible for the position of clan chieftain — all while surviving in the cold amidst constant bloodshed and starvation, mind you. Thus, if you ever run into a moredhel chieftain, you better believe they're damn hard to kill.
Justified in The Firebringer Trilogy, as the prince/princess of the unicorn herd is also their warleader in times of war (and they have considered themselves at war for over four hundred years).
Subverted in the Horatio Hornblower series, in which it is noted that Petty Officers could be Drill Sergeant Nasties, but that would be beneath Hornblower's dignity as an officer as well as above his physical capacity. Hornblower got into much more tough physical confrontations as a midshipman and lieutenant than he did as a commander.
Peter's one-on-one sword fight with King Miraz lasts much longer than his fight with Lord Sopesian immediately afterward.
Earlier in the book, Edmund defeats Trumpkin the dwarf, a seasoned fighter, in a swordfight. While Edmund's intention may simply be to persuade Trumpkin that he (and, by extension, his older brother) are valuable allies to have during a war, the ultimate effect of Edmund's victory, and Susan's similar victory in an archery contest, is to convince Trumpkin that they are in fact the kings and queens of legend.
Authority Equals Asskicking even is in effect when the main characters are children. Trumpkin's confusion stems in part from the fact that Peter, Edmund, Lucy, and Susan returned as they were in England, as schoolchildren, and had lost much of their skill and ability. It returns to them slowly due to the "Narnian air."
In The Magician's Nephew, Jadis treats with contempt the notion that Uncle Andrew could be anything but a king: commoners are never magicians. This could be Asskicking Equals Authority, in view of her ruthless use of magic for power, but she treats it as this trope.
Albus Dumbledore, Headmaster of Hogwarts and leader of the Order of the Phoenix, is the only one who could kick Voldemort's ass in a duel.
Averted elsewhere in the Harry Potter series, however. Minister of Magic Cornelius Fudge was never shown to be an outstandingly powerful wizard. His successor Rufus Scrimgeour was undoubtedly better, having been the former head of the Aurors, the Ministry's special forces; however, his chronic limp may be a handicap in a fight — and anyway he was killed with relatively little struggle when the Ministry was taken over. Played relatively straight after the war, when Kingsley Shacklebolt is elected Minister, a powerful Auror who actually fought alongside the protagonists a few times and was assigned as personal protection for the British Prime Minister, lest he be magically dominated via the Imperius curse. Dumbledore himself was repeatedly offered the job of Minister, and he always turned it down; it was suggested that Voldemort may have wanted to take up the post earlier in his career, but he never did — though he controlled the acting Minister for most of a year.
However, played straight with the Hogwarts professors during the Battle for Hogwarts, when the school's teachers proved themselves more than a little adept at the use of magic in the defense of their students against Voldemort and the Death Eaters. Those who can do, teach, eh?
The Death Eaters themselves are an example. Voldemort can hold his own against Dumbledore in a duel, and can fight any other THREE wizards simultaneously and without effort. His highest-ranking Death Eaters also tend to be his most dangerous servants; in fact, most duels between named Death Eaters and any good guy tend to go in favor of the Death Eaters.
Justified in the sense that intelligent people (such as Dumbledore and Voldemort) know how to better utilize magic and thus fight using it - though that's not the only quality needed to make a good fighter, as exemplified by the valedictorian yet hysteric Hermione.
Played straight in the Urban Fantasy environment of the Nasuverse, at least when a character is involved in an organization. The heads of particular divisions in the Magi Association tend to be holding their position due to their overwhelming brilliance. Naturally, this means that the Lords of the Association are scarily powerful. On the other hand, you also have oddities like how the last person on Earth who can use the Unified Language is teaching in a random high school.
Heavily justified. The main principle of the Mobile Infantry is "Everybody drops, everybody fights": all officers are promoted from enlisted ranks, and even generals are expected to be the first soldiers on the ground (although they have bodyguards to help keep the enemy riffraff away). Plus the higher-ups get command suits with both the speed of scout suits and weaponry and gear on par with if not superior to that of standard marauder suits. And to get the highest rank of Sky Marshal, one has to go through the ranks of both the Mobile Infantry and the Navy.
Subverted in The Film of the Book, when they find a general hiding in the freezer while exploring an abandoned fort. He's shown to be completely useless; he's probably suffering from shellshock after seeing his men get their brains sucked out.
While Klingon Promotions are not supported, an officer is proven to be incompetent if he lets the morale and/or his personal level of asskicking sink so low that his underlings would even think of attacking him and surviving the attempt.
The Wizards (at least in the earlier books) are an example of this. Progression is by the time-honored "Dead men's pointy boots" system, and the wizards don't usually wait for them to get emptied naturally.
Archchancellor Ridcully is possibly one of the most powerful combatants on the Disc, and the Patrician is a trained and skilled assassin.
In full force. Alerans have access to "furies," kind of like D&D elementals, which confer power over fire, water, air, earth, wood, and metal. Societal hierarchy is based on the power of one's furies, with Knights typically showing exceptional strength in one area, High Lords possessing amazing abilities in all areas (i.e. capable of causing conflagrations, flying, and possessing super strength and swordfighting skills), and the First Lord, well... he approaches Physical God status.
Also you have Canim leaders Varg and Nasaug, two of the deadlist hand-to-hand combatants on the continent, and the Vord Queen, who is far more powerful than any of her spawn. Of course, since the Alerans are practically a Proud Warrior Race, the Canim are definitely a Proud Warrior Race, and the Vord are a Horde of Alien Locusts with a Hive Mind centered in their queen, all of this makes a certain amount of sense.
This trope is played with a lot in this series. Alera is in a 20-year succession crisis because the current First Lord has no acknowledged heir and he's getting old, but as we see during the series, he still has amazing power with furies in his own right. Societal hierarchy is not actually based on the power of one's furies, but is strongly influenced by it; for just one example, a bastard will generally have his parent's power with furies but only the status he is born into. The protagonist is considered a freak at first because he is unique in not having access to any furies, (though he gets some slight power at the end of the third book,in the fourth he reaches knight level, and by the fifth he is on par with the first lord) and yet he eventually gets a great deal of authority because he's capable of Awesomeness by Analysis.
The Senior Council. The governing body of wizards is comprised of the seven strongest wizards on the planet; the youngest and weakest, Ebenezar McCoy brought down a decomissioned Soviet satellite on an island full of vampires for revenge at the end of Death Masks, and the Merlin and the Gatekeeper stalled an entire army of Red Court vampires and Eldritch Abominations with a single ward during the events of Dead Beat (Harry's comment: "You don't get to be the Merlin by collecting bottle caps"). The Wardens are also ranked by badassitude, but since they're a somewhat military organization that needs everyone they can get their hands on, it's more justified.
Other example include the Sidhe queens, the Red King, and other similarly powered rulers. Mostly justified in that these are beings who have been alive for thousands of years or more and have had time to build and consolidate power, although people promoted to some of these positions (such as the Summer Lady) essentially immediately become a Person of Mass Destruction.
On the vanilla mortal side of things, we have GentlemanJohnnyMarcone, who can hold his own against a Fallen Angel with a Kalashnikov.
On the heavy end of the scale are the Lords of Outer Night from Changes—vampires so old and powerful that they actually are the pantheon of the Mayincatec civilizations of South America. The very next book, Ghost Story, shows this trope on the light end of the scale, with a smalltime sorceror (someone who has some magical ability but is beneath the notice of the White Council as friend or enemy) pushing around a group of teenage orphans a la Oliver Twist.
In James Thurber's The 13 Clocks, the duke trusts in his captain of the guard, who has only been defeated once. But a minion points out that the prince who is trying to marry his niece was that one defeat.
The series is full of royals who not only actually fight things, but tend to be totally awesome at fighting them. Of particular note are PrinceGwydion, King Smoit, King Morgant and King Pryderi, all feared and respected war leaders as well as being mighty warriors in their own right.
High King Math is a double subversion. He is very idealistic and peace-loving, and far too old to fight. However, in the final book he proves himself to be the most badass man alive by getting out of his deathbed to make a heroic final stand against the Death-Lord's army of undead minions.
Subverted with ArawnDeath-Lord who, despite being a powerful sorcerer, barely fights (though he does kill someone) before being decapitated.
Frequently the most powerful nobleman leading an army is also its more powerful swordsman. During the First Blackfyre Rebellion, the royal pretender Daemon Blackfyre was considered undefeatable with a sword. During Robert's Rebellion, each side was lead by their strongest fighter: Robert Baratheon and Rhaegar Targaryen. After Robert killed Rhaegar in single combat and won the war, he became king. Also, the most powerful noble families breed most of the continent's best warriors: Loras Tyrell, a great jouster and Jaime Lannister, the greatest swordsman are all members of Great Houses. This is justified, as heirs and leaders of Great Houses they'd receive the most and best training, nutrition, and even genetics, as the need to appear strong is important as vassal houses are known to overthrow them if they appear weak. True choose to slack off. For example, when Jon Snow becomes a member of the Night's Watch and thinks he's better than the other recruits because he can beat them all in single combat. It's pointed out, In-Universe, that he's been trained for years by his master-at-arms, whereas the lower class recruits can't even afford a sword, let alone receive proper training in it.
Warriors from the Great Houses are quoted to have been trained to ride and fight from when they could talk and walk. More often than not, their teachers would be experts at combat themselves. As individual fighters, the Heavy Troops (knights) are thought of as the strongest, bar none, and could very well be the most capable individual fighters in the entire world, even more so than Dothraki, pit fighters, and Unsullied. One must remember that Arthur Dayne, Gregor Clegane, Barristan Selmy, Loras Tyrell, Jaime Lannister, and Daemon Blackfyre were all knights.
Justified in the case of the Dothraki, who only follow the powerful. Khal Drogo in particular was never defeated in battle and led an incredibly large group of warriors.
Subverted quite a few times when it comes to certain noble characters, despite certainly looking and acting the part. This is noted by some characters.
The most textbook cases are when a young knight, supposedly much better trained and equipped, ends up being defeated by an older, more lowborn man. The reasons tend to range from the lowborn man being much stronger or the young knight underestimating him to the knight misunderstanding the finer technicalities of battle (e.g. terrain, fatigue, mobility vs. protection) and acting inappropriately, while the lowborn man has much more experience.
Justified in The Book of the Named, Clan leaders can be challenged for their position by any Clan member, and thus must be good at fighting to stay the Clan leader.
Beowulf, from the epic poem of the same name, is an inversion. He's far more kickass than the local king, and becomes king after his amazing feats of badass in defense of Hrothgar's land. He still dies against a dragon.
This is an unspoken assumption in Dune. When Baron Harkonnen learns that the guards escorting Paul and Lady Jessica have been killed, he asks who their rescuer may have been and his Mentat replies, "It was a clean, silent killing, my Lord. Hawat, perhaps, or that Halleck one. Possibly Idaho. Or any top lieutenant." Apparently, the Atredies couldn't possibly employ competent assassins without giving them high ranks, and no ordinary soldier would be able to manage a clean, silent kill. Besides, isn't Hawat, like, a hundred?
The Thrawn Trilogy: Grand Admiral Thrawn doesn't fight anything. He's The Strategist. He watches everything, plans, and gives orders; he's got to be highly intelligent, but there's no sign of him being physically adept, and no one knows how old he is or if his species is more or less powerful than humans are. Track down the Thrawn Trilogy Sourcebook, a supplement for West End Games' now-defunct Star Wars d6 RPG, and you see that his physical stats are pretty damn good, better than any of the other bridge officers', better than his counterparts in the Rebellion, better than almost any of the others who don't actually, physically, fight. Other parts of the Star Wars Expanded Universe prove him to be really good with a blaster, and he can move in armor. He impersonates Jodo Kast, a Palette Swap of Boba Fett, and actually makes Kast seem cool. In Outbound Flight, we see him board a slaver ship to lead his men into battle. While he has the crew of his ship backing him up, it's pretty obvious that he's cowing his opponents through sheer chutzpah. And once we meet his species (the Chiss), we find out that they're all extremely badass, though more in his "planning ahead" vein than in physical prowess. Thrawn is still portrayed as exceptionally talented even among the very-talented Chiss, though. On the other hand, his stats are probably bumped up to ensure that he survives contact with the average Player Character.
In Currahee!: A Screaming Eagle at Normandy, a memoir from a WWII paratrooper, he recounts how someone sabotaged the parachute chord of a strict drill sergeant during parachute training, which was fortunately noticed before he jumped out of the plane. In response, the sargeant challenged anyone who had a problem with him to fight him. Two large recruits then fought him, but he beat them both. After that he didn't have any more parachute problems.
The universe is filled with this, which makes sense, because Post-Shift Atlanta is pretty much ruled by survival of the fittest.
The Shapeshifters are the most prominent example of this, since positions of power in the Pack are won by fights to the dead, so all Clan leaders have to survive a bunch of challenges to stay in power. Since they are the strongest and best fighters, they also take the lead in any violent confrontations.
Curran is the Beast Lord, the Alpha of Alphas, because he is strong, fast, and lethal enough to utterly destroy them. He won his position by single-handedly taking down a rampaging were-bear that weighed in over 2000 pounds and had killed several dozen people. At age 15. He's not only their leader, he's also their biggest weapon, so he takes point at nearly every confrontation involving the Pack.
While not technically a shapeshifter, Kate becomes the Consort of the Beast Lord, which means she has the same position of power as Curran. She earned her position by surviving 22 challenges while wounded, tired and emotionally compromised because of Curran's coma. All shapeshifters are stronger, larger and heavier than Kate when in warrior-form, and yet she killed them all with a six-inch knive.
A lot of the higher-level warlords in the web-novel Domina are also extremely physically dangerous, due to the fact that there's an easy Bio-Augmentation device lying around, so anyone with the money (such as people in charge of a culture) can make use of it. It also goes the other way into Asskicking Equals Authority; people who manage to get augmented on their own can carve out their own culture easily.
Glory Road, Her Wisdom Star is the Empress of many worlds, but to retrieve the Egg of the Phoenix she goes on a quest herself, using one of her grandsons and finds Oscar Gordon to help her.
In The Mortal Instruments is the big villain Johanthan Morgenstern. He created a army of shadowhunters, who are "fall to the dark side". But because it is not merely a shadowhunter but partly also a demon, he is much stronger than the dark shadowhunters, and also much stronger than ordinary shadowhunters.
If werewolves there seems to be a common ritual that the werewolf who leads the pack, only one can become "alpha male" if he defeated and kill the previous leader in a fight.
In The Infernal Devices but it is inverted. Axel Mortmain is an ordinary human with some magical powers, but he's the leader of some demons and an army of steampunk robots.
In Necroscope a "vampire feasts" is basically governed by a vampire-lord or vampire-lady. And he (or she) is significantly more powerful than the subordinates; perhaps apart from the rather unintelligent warrior-creatures.