The one in a position to give orders takes the role and sends the other away. Common in military situations, and the reason why the king can refuse to leave the city In Its Hour of Need but send away the crown prince. Even when the authority is unquestionable, this one doesn't always work, as the junior may defy the punishment and go on arguing, or resort to force himself.
Force or stealth. One character can trick another into leaving, or knock him out so he can't follow, or shut the door between them, or throw the other onto a moving vehicle he can't jump off, etc, or just do Taking the Bullet or saying I Am Spartacus or making the Sneaky Departure before the other can realize or stop him. This may not involve an actual argument; the first character to realize that conflict is possible often acts quickly to preempt it by ensuring that he must make the sacrifice. However, if he survives, expect a quarrel on this principle after the fact.
One Piece: After fighting and defeating both Oars and Gekko Moria, the Straw Hat Pirates are too worn out to defeat Bartholomew Kuma. All but Zoro have been knocked unconscious. Zoro offers his own life in exchange for the lives of everyone else. Kuma agrees to his request. Suddenly Sanji stands up and offers his life in place of Zoro's. Zoro proceeds to sucker punch Sanji in the side, knocking him unconscious and ending the argument.
A short conflict in a later episode of Death Note has the Anti-Kira Taskforce arguing over who should make the shinigami-eye deal, which cuts a person's lifespan in half, in order to kill Mello and retrieve his Death Note (although, tragically, they don't know they're making this sacrifice for Kira himself). Matsuda offers, and it's obvious Light is happy to assign the task to him, but he didn't plan on his dad wanting it instead, and winning because he's oldest. Light is not happy when this results in his father's death. Even less so when he doesn't even manage to kill Mello and get the Note.
At least one issue of Iron Man where Rhodey knocks Tony out and wears the armor himself. Sort of subverted in that when Tony wakes up, he immediately goes out in a spare suit and arrives just in time to save Rhodey's massively outclassed butt.
X-Men: Jean Grey used force to get Scott Summers to safety on the shuttle before flying it down in face of a solar flare.
In The Mighty Thor, Thor insisted on covering the escape from Hel, only to be cold-cocked by his former enemy Skurge, who then proceeded to declare You Shall Not Pass at the bridge of Gjallerbru in his Crowning Moment of Awesome, and possibly one of the best Tear JerkerCrowning Moment of Awesome moments for Simonson's entire run. He's also trapped in Hel for a year or three until Hela realizes his sacrifice has made him a soul she can't keep, and she sends him on to Valhalla. The final quote, made as on the left hand side of the page he's fighting, and on the right his picture slowly fades:
And when a new arrival asks about the one to whom even Hela bows her head, the answer is always the same - "He stood alone at Gjallerbru." And that is answer enough.
In Justice Society of America, the two Hourmen, father and son, fought over who would be allowed to return to the point in time from which the father had been plucked by the android Hourman, to ensure a Stable Time Loop. This lasts until the android Hourman has a bright idea: he puts both father and son on his time-traveling ship, and fills the point himself.
In the X-Wing Series comic, Zena and Jagged Antilles have to detach a burning section of their refueling station before the fire can spread, which means their deaths. Jagged tries to get Zena to follow the others who were evacuated from this section, but she tells him someone needs to fight the flames while he activates the lancing charge.
Jagged: "Don't be foolish, Zena! Once we detach, they can't save us!"
Zena: "I know that, Jagged. You didn't marry a stupid woman!"
Similar to the movie Spartacus, in Bloodquest (a Warhammer 40K comic) two Blood Angel marines are captured by forces of chaos. They are given a choise. A fight to death, the winner will then be tortured by a slaaneshi marine, who is also their former friend. Other marine tries to say that neither of them will agree to the terms when his friend attacks him, begging for him to subdue and accept death. He has already fallen to the Black Rage and has nothing else in his life except pain anyways.
Hero, with Snow and Broken Sword both trying to wound the other enough so that they can be the one to make the sacrifice.
The Core When they realize whoever releases the Cool Shipthis time will not make it back, they do a little draw-the-shortest-straw contest for the honor (Leaving out the girl, by the way). However, the creator of the ship had rigged the contest to make sure he got the honor, on the grounds that "Virgil is my creation. If he needs blood, is going to be MY blood!"
Wasn't the girl the pilot? Stupid to risk her life.
In Spartacus, the titular character's revolt of gladiatorial slaves is put down. The two primary protagonists are made by the Big Bad to fight each other, with the winner to be crucified. The result is a real fight, just as intended.
In Star Trek: Nemesis, Data doesn't bother to argue. He just wordlessly slaps the microtransporter on Picard to beam him back to the Enterprise before doing the Heroic Sacrifice in his place.
In Tangled, Flynn and Rapunzel argue briefly about whether she should have her freedom at the price of his life (Flynn's view), or he should live at the price of her letting Gothel keep her prisoner for life (Rapunzel's view). Rapunzel goes to save his life, taking advantage of his being too weakened by the mortal wound to stop her. He is not however too weak to cut her hair, making it impossible.
In Dan Abnett's Gaunt's Ghosts novel His Last Command, Gaunt and Wilder know that someone will have to make a last stand to give the rest of the regiment a chance to escape. Gaunt lays it out and offers to do it. Wilder refuses, points out that Gaunt does not have a command position, and orders him to take the regiment to safety.
In William King's Warhammer 40,000 novel Space Wolf, Sergeant Hengist sends Ragnar and some other young Marines to Bring News Back (of Chaos Space Marines) while Hengist and others hold them off. Ragnar wants to protest, and Hengist tells him that being a Space Marine is not easy, and sends him off. When one of the other Marines is injured during their escape, Ragnar sends the others on while he tends the injured — over their objections, succeeding when he threatens them, and they leave only with the comment that next time, it will be their turn to tend the wounded.
Red Seas Under Red Skies: Locke and Jean have both been poisoned, and there's only enough antidote for one. Each one wants the other to take the antidote. Jean threatens to physically force Locke to take it, but Magnificent Bastard Locke reveals that he's already slipped the antidote into Jean's drink.
In C. S. Lewis's The Voyage of the Dawn Treader, when invisible beings threaten to massacre them unless Lucy goes into a magician's tower to cast a spell, Lucy agrees to do it, and the boys argue with her that they want to defend her. Only when the fearless Reepicheep refuses to try dissuading her, observing that she is being brave and doing a heroic act, are they convinced to let her go.
At the end of L. M. Montgomery's Anne of Green Gables, Anne gives up a scholarship so she can stay at Green Gables where Marilla needs her. She gives it up before she tells Marilla, so that Marilla can't argue with her.
In Rainbow Valley, Ellen refuses to release her sister Rosemary from The Promise when she wants to marry. Later, Ellen wants to marry, and she can't even bring herself to ask Rosemary to release her—but she does tell her suitor why she refused. So the man asks for her. Rosemary agrees at once; the catch is that she didn't tell her suitor why she turned him down, and she's sure that he wouldn't want her if she went back to him, and so refuses to even try. So Ellen refuses to marry her suitor, even knowing that they are both going to be miserable. (It's a good thing that Rosemary's suitor's youngest daughter intervenes.)
Part of the legend of Ciaphas Cain is that he always seems to get into these situations (as the second volunteer). As far as he's concerned, he's only volunteering to find a way to escape, but...
In Rick Riordan's The Titan's Curse, Percy has a hard time persuading Artemis to let him hold up the sky instead of her. He wins for the "valid argument" reason: She can fight Atlas, who will kill him if they don't change places. In fact, her reluctance is rather Honor Before Reason.
In Jim Butcher's Dresden Files novel Dead Beat, Rawlins tells Harry that if he can get free, he should just go without him. Harry tells him
You're siphoning my noble hero vibe. Cease and desist, or I'll sue.
In Grave Peril, Michael tells Harry that he can ensure that Harry and Susan escape; since he's a Knight of the Cross, he's supposed to protect the innocent. Harry tells him that he's supposed to have his sword, too, and since it's Harry's fault that he doesn't, Harry will not escape that way.
In Small Favor, Michael and Harry argue about who gets to be the last one on the helicopter. Harry, having promised his daughter and having seen a Valkyrie eye him, wins. Michael ends up shot and very nearly dead while dangling from the helicopter.
It is worth noting that if Harry had gone first, both would have died. According to Uriel in 'The Warrior'.
In Ben Counter's Warhammer 40,000Horus Heresy novel Battle for the Abyss, when Cestus asks for the bombs, Brynngar punches him instead, on the grounds that it's a one-way trip. Cestus does make it to the escape pod, to find that the traitor captain is also there. He kills him and dies himself, for a full Kill 'em All.
In Outbound Flight, the last surviving Jedi and the brother of the man who caused all this try to put Outbound Flight into a stable orbit over a planet, only to find that the drive is too damaged. It shuts down, and they see that Outbound Flight will crash. They and the Dreadnaught where the fifty-seven survivors went to were on opposite sides, and the only way that the other survivors could live through the crash would be if the side the two of them were on hit first.
Thrass: "There's still time for you to leave, you know. You may at least be able to get to the core before we hit, perhaps even all the way to D-Four."
Lorana: "You can't handle the landing alone. But I could do that while you go."
Thrass: And who would keep the remaining systems from self-destructing while you cleared a path through the pylons for me? No, Jedi Jinzler. It appears we will both be giving our lives for your people."
In The Chessman of Mars, when Tara and Turan do not wish to leave Ghek in danger, Ghek persuades Turan that he must force her, or they will kill her.
In Myth Adventures when strangers have snuck through a door in their house, Aahz and Skeeve argue about who gets through it to retrieve them; then Aahz points at the corner and knocks out Skeeve to win the argument.
In the first Harry Potter book, Ron sacrifices himself to the White Queen so that Harry can checkmate the White King and proceed. This is a case falling under all three rules upahead, as Harry is the only one who can stop Snape Quirrel/Voldemort, Ron is the only one in position to make the sacrifice, and Harry and Hermione had surrendered rank to him since he's the only one who's good at chess.
A lesser version in The Half Blood Prince, when Dumbledore and Harry are breaking into Voldemort's cave. A hidden door requires a sacrifice of blood, as deduced by Dumbledore; Harry offers to provide it in his place, but Dumbledore insists that Harry's blood is more valuable and takes the initiative to cut his own arm open with a knife (and promptly heal it back up again with magic).
Later, when they're leaving, it's Harry's turn to pull this, using the valid argument that he's already bleeding anyway.
In James Swallow's Warhammer 40,000 novel Red Fury, Dante tries to get the Chapter Masters off-planet when the mutants attack. One is offended at the thought they would run away from mutants, Dante says that they did not bring about the problem; Blood Angels did, and another says they will nevertheless help fight it, because the first was right, it could be construed as an insult. Dante says he is honored.
In Ptolemy's Gate, Bartimaeus and Nathaniel lie to Kitty, telling her that they will be able to escape alive when she can't, to persuade her to leave. Then Nathaniel, at the very end, dismisses Bartimaeus against his will, so he alone has to die.
Boromir thinks this is his motivation for wanting to take the Ring away from Frodo (self-deception, since the Ring is clouding his mind).
Frodo concludes he must go off alone, without telling the others, to forestall their willingness to come with him.
Sam deduces this and threatens to prevent his leaving if he doesn't take him — but Sam's actions are only borderline this, because he wants to share the burden, not take it from Frodo entirely.
In book two of The Hunger Games, Katniss and Peeta are each determined that the other will be the survivor of the Games. Both of them have arguments in their favor: Katniss realizes that Peeta's public speaking skills will be valuable in the coming revolution, whereas she herself is more useful as a martyr. On the other hand, Peeta tells Katniss that while she could live quite happily without him, he couldn't live without her; although they can't speak of the revolution openly, this seems to imply that he wouldn't bother joining it if she were dead.
The trope is used several times in Animorphs, with Ax and Rachel being the two most likely to play the role of arguing about who gets to go on the suicide mission. It has happened enough that in the final book, when Jake sends Rachel on a mission that really will kill her off for real, he knows that he needs to defy the trope by making sure that only Rachel knows about her Heroic Sacrifice ahead of time.
In Dorothy L Sayers's Nine Tailors, Lord Peter Wimsey and the police learn that the two men who had respectively put a man in the belfrey and buried him after he died were shielding each other because they thought the other had murdered him.
In the Chinese tale of the "righteous stepmother of Qin", her son and stepson were found near a murdered body. Both men confessed to the crime in an attempt to shield the other. (When the stepmother recommended the execution of her son, not her stepson, and explained that he was the junior, and she had the duty to look after her stepson, the king pardoned them both for her devotion to duty.)
In the Isaac Asimov collection I Robot, the story "Runaround" features Powell and Donovan arguing over who should risk their life to rescue a malfunctioning robot. Powell proposes a math contest: whoever can solve a difficult math problem gets to go. Of course, he has already solved it in his head before he proposes it, and immediately solves it and runs off before Donovan can stop him.
In Adrian Tchaikovsky's Dragonfly Falling, Salma tries to tell Totho he can't sell himself to the Wasp to save him, but Totho informs him that he has already done so, and if Salma doesn't take the escape he did it for, Totho has done it in vain.
In Jasper Fforde's Lost in a Good Book, Thursday goes to kill herself to appease Aornis. Her father stops her and derails Aornis's plans despite her objections that it will kill him; among other things, he points out he's aged, and he will go without a decline this way.
In Something Rotten, Spike tries to take Thursday's place in the underworld; they argue, and when he can't be moved, Thursday tells the crowd he's alive. Then Cindy shows up and argues Thursday into letting her do it.
In Mary Jo Putney's Thunder and Roses, the hero and a miner are escaping a flooding mine. When it seems likely that there will only be time for one of them to be pulled up to safety, the hero orders the miner to go up first - only for the miner to cold-cock him and send him up. The miner survives to explain his reasoning: as a devout Methodist, he was confident that he'd go to heaven, but he wasn't nearly so sure about the hero. According to the author's note, this was based on a true story.
In L. Jagi Lamplighter's Prospero Lost, Mab orders Miranda to flee while he contains the barghests. She started to obey, and then goes back and refuses to leave again.
In Poul Anderson's "Sunjammer", though it never comes to the point, the men argue about who will be left behind to pilot the ship over a cargo ship with explosive fuel. West argues that he's the older, by far; the two younger men, that they are unmarried. In the end, when they have found another possibility, all three stay even though what they are trying may not work.
In Poul Anderson's "Lodestar", the three characters are arguing about who retreats to their ship from the attack first, in the opening.
In Michael Flynn's Spiral Arm novel On the Razor's Edge, in Flashback, he beckons for Issa to come, but she refuses. She will maintain the illusion as he escapes.
In Julie Kagawa's The Iron King, Ash and Meghan dispute — Ash tells her it has come to the point where she must choose between saving him and Ethan, and she tries to refuse.
In Smallville, when Lex Luthor is in a coma with critical information in his head, Chloe offers to heal him, but Clark refuses as the effort might kill her, and instead uses technology that might fry his brain. She ended up doing it anyway.
Chloe returns the favour in Arctic when she offers to use kryptonite on Kara, who has been acting violent, even though she doesn't think it is a good idea because Clark would do it anyway.
In Odyssey, Clark tells Chloe not to heal him as the effort might render her dead, and permanently. She does it anyway but somehow it doesn't work. Never explained.
In Legion, the legionnaires think the only way to stop Brainiac is to kill his human host, Chloe Sullivan. They knock her unconscious, but when Lightning Lad holds the knife, he couldn't do it, so Cosmic Boy snatches the knife and tries to stab her, if not for Clark to rush in.
In Doomsday, Oliver shoots Clark with a kryptonite arrow so that Black Canary, Bart and him could face Doomsday by themselves. Might count as a What the Hell, Hero? instead.
In Patriot, Oliver decides to be the one to see what happens if they go with the Super Registration Act instead of Clark. It makes sense because his identity has been exposed anyway.
On at least two occasions in 24, Jack Bauer intended to die in an explosion to save the day - or at least a portion of it - only to have someone else go ahead and do it.
Jack treated Paul Raines like shit, to say the least, before and after he saved Jack's life. Neither was trying to prove anything, but Jack's saviour definitely seemed like the bigger man after that sequence of events, while Jack came dangerously close to becoming unlikeable, displaying a mindset similar to that of the terrorists he was combating.
Star Trek: when aliens offer Kirk the choice of sacrificing McCoy or Spock, McCoy takes out Kirk with drugs. Spock is glad; being in command, he can make it himself. Then McCoy takes him out to make the sacrifice.
Several more canon Trek examples, such as "Once More Unto The Breach" and "These Are the Voyages", and Nemesis.
Also an unsuccessful attempt in "Obsession".
The Trek novel The Return.
Voyager's Tom and B'Elanna do this once.
Tom: On your feet, Lieutenant. That's an order.
B'Elanna: You can't order me, we're the same rank.
In another episode Angel and Spike shared one of these when they were told of some cup that a vampire with a soul had to drink in order to save the world, the cup is known as "The Cup of Perpetual Torment". They were arguing over which one of them was the prophesied vampire and, because it's Spike and Angel, ended up having one of the most brutal fights ever seen on the show to drink from it and prove themselves the true champion. Effectively, punching each other while shouting "I'm more of a hero than you!" Spike wins, but the cup turned out to contain Mountain Dew and be made in China.
In LOST, Charlie and Desmond couldn't decide who should undertake the thought-to-be-suicidal mission of swimming down to the Looking Glass station and deactivating its jamming device. Charlie resolved the situation by knocking Desmond out with an oar. He then proceeded to swim down to the station and carry out his Heroic Sacrifice (albeit not quite in the way he expected).
Surely River Song's sacrifice in the Library counts here. She knew the Doctor would have sacrificed himself to save Donna and the others, and cold-cocked him so he couldn't do it.(Just why did she have those handcuffs, anyway? Business or pleasure?)
Used in the ITV adaptation of Hornblower. Rather than using the novel's elaborate set-up to ensure an/the eponymous duel is An Even Chance, the TV version has Hornblower's second cold-cock him with a sea-lantern because he (the second) was shamed by 17 year old Hornblower's courage, and didn't believe that either of them stood a chance in a duel against Mr Midshipman Simpson.
Both played straight and for comedy in Chinese Paladin 3: at one point, the heroes have to enter the forbidden Demon Prison Pagoda, which is forbidden to members of the Church Militant. Undeterred, the chief acolyte promptly asks his superiors to expel him from the order. They refuse, and The Hero—who can do the job just fine himself—tells him to stop trying to steal his thunder.
Stargate SG-1 and Stargate Atlantis: CONSTANTLY. There's always a life-or-death situation, someone always needs to be sacrificed, and our heroes always argue over who gets to risk their lives this time. The CO usually "wins" but it's not unheard of for someone else to beat him to the punch.
Mitchell: Well now you know that the hard part about being part of this team is not risking your own life. It's watching your friends take chances with theirs.
In Merlin, Merlin and Arthur argue over who will drink the not actually deadly poison. Arthur actually resorts to "Look over there!" just to get to drink it.
The Legend Of William Tell: Will and Aruna have to get a MacGuffin to Kalem, but the shelter's surrounded by Mooks. Will, still suffering the aftereffects of hypothermia, declares his intention to draw the bad guys away so Aruna can get through. Aruna shoves the MacGuffin into his arms and runs off before he can stop her.
In Some Kind of Hero by Leslie Fish, a starship's engineer offers to flip a coin for the last spacesuit on the ship. The ship's navigator knocks out the engineer and stuffs him into the suit.
Tales of the Abyss: the last third of the game has Luke and Asch arguing repeated about who is going to make a Heroic Sacrifice, actually two of them over the course of this part of the game, with each one wanting to make the sacrifice himself. They both survive the first - neutralizing the miasma - but Asch dies in the second on Eldrant, though depending on how you interpret the ending he might be alive in some capacity after it's all over.
Dynasty Warriors: Gundam has a minor example at the end of Char's/Amuro's Original plotline when Char takes away Amuro's chance to play the hero and goes down with the underground cave. (He gets better)
After the final battle of Dragon Age: Origins, it's possible to stop and argue with Alistair about who gets to finish off the Archdemon. Under most circumstances, the player character can either let Alistair have his way or insist on doing it him- or herself. If the player-controlled Warden is in a romance with Alistair, however, he takes the decision out of her hands entirely.
Played with in Metal Gear Solid 4. Either Snake or Raiden have to get to GW's server room, through a hallway saturated with microwave radiation. The other will stay behind and hold off an endless army of Mooks. Both forks in the road point to "heroic death", but naturally there's a More Hero Than Thou conversation between the two about who will do what.
Breath of Fire II: Nina goes through a personal quest to acquire an artifact that will allow her to become The Great Bird. Unfortunately the process is permanent and she's basically sacrificing her humanity and sentience for the good of the group, and the world. Her sister Mina has other ideas and steals the artifact so SHE can sacrifice herself instead.
In Mega Man X 5, in order to stop the Colony Drop, one of the heroes has to maneuver a shuttle into crashing into it. Zero volunteered himself, as he stated that, whether or not he (Zero) survives the crash, the world is still in danger, and X is needed more than he is.
At the end of L.A. Noire Cole and Jack argue over who will boost the other out of the sewer before the water rushes through. Cole maintains that he has a better chance to make the jump without any help, as Jack had been shot in the arm. ("You're wounded, Jack. Let me help you.") He then lets himself die.
After Arthas is killed in World of Warcraft, Tirion and Bolvar have a minor disagreement over who should be the next Lich King. The latter wins out.
At the end of Baten Kaitos Origins, Sagi is grabbed by a machina as the party flees Tarazed's core. Milly realizes the control unit doesn't have enough power to override the machina and prepares to power it herself, which would kill her. Before she can do it, however, Guillo rushes past her and powers it up, sacrificing itself.
One person from the team has to stay in Paradise while the others go to Great Glacier in "Pokemon Mystery Dungeon": Gates to Infinity. None of them want to stay behind, but they want each other to be happy. Even after picking strips of paper to decide who should stay and Dunsparce gets the marked one, the characters still argue over it and volunteer to stay until Emolga tells them to accept the results. At the last minute, though, Emolga switches with Dunsparce, to everyone's surprise.
When Gil and Tarvek are on the ground remaining motionless so that motion-detecting robots can't find them, The Dragon points out that if one of them tries to fight off the robots, the other one can sneak away and help Agatha. They both immediately jump up, yelling "Don't screw this up!"
Tarvek: You know, perhaps we should have discussed this... Gil: Too late now!
Homestuck: Dave and Rose have a disagreement over who will be the one to take the Tumor to the Green Sun, which will kill them. It winds up subverted: both Dave and Rose end up going, and they both turn out just fine, due to being on their Derse Quest Beds when the Tumor detonates.
Danny Phantom takes this to ridiculous extremes with a scene which involves dozens of people knocking each other out in succession over who gets to go on a suicide mission.
In the Warner Brothers short Dumb Patrol, World War One pilot "Captain Smedley" (Porky Pig) is chosen to shoot down "Baron Sam von Shamm" (Yosemite Sam). Bugs Bunny knocks him out.
"Ya know, I just had to take his place. He's got a wife and six piglets."
This is subverted in the first animated X-Men series' version of the Phoenix Saga. Jean Grey is apparently dead, but the Phoenix Force reveals that it can save her by transferring life energy from others to her. Jean's love interests Cyclops and Wolverine get into a brief argument about who will sacrifice himself for her sake. Both insist on doing it themselves. The Phoenix then explains that the life energy doesn't have to come from one person; it can take energy from a group of people (shortening their lifespans) to revive Jean. All of the X-Men hold hands and allow the Phoenix to do just that.
Scottish clans used to race to be the first one into battle.
Celtic warriors have been stereotypically accused of this indiscipline as early as the Romans. It is a very grievious flaw for simple mathematics; the first man into battle is always outnumbered, as is the next one and so on which is why it is necessary to keep good order in a hand-to-hand fight.