The world's best method of conflict resolution, currently (temporarily) unpopular.
Dueling occurred when one man approached another and demanded satisfaction (in a world where double-entendre led to painful death). They were often employed to revenge insults or settle matters of honor, and since this mythical beast "honor" has never been caught they could be used for pretty much anything.
"OK, this settles whether the Enterprise or Death Star would win once and for all!"
In many countries duels were regulated by the Code Duello, because two men hacking at each other with swords and pistols without written rules makes it look rather common. The great thing about a book devoted solely to resolving conflicts through violence is that it doesn't mess around. Check this out:
"When the lie direct is the first offence, the aggressor must either beg pardon in express terms, exchange two shots previous to apology, or three shots followed by explanation" (Commandment IV of the Irish Code Duello)
Who should apologize and when has plagued romances since time began. The Code Duello not only specifies who and when but exactly how much it's worth - an apology is worth an explanation plus one bullet fired at your face.
It's a bad, boring time for conflict resolution.
Our legal system is choked with petty and frivolous complaints. When the plaintiff has to prove their complaint with a broadsword we can expect the frequency of "emotional suffering" suits to fall rapidly, just like anyone who tries it. Mainly because of the hilarious effect of defendants being able to react to that sort of bullshit in the way any normally evolved human would.
We could have Tina Turner take over from Judge Judy, or as it will then be called, The Thunderdome, and ratings will shoot through the roof so hard they'll only narrowly miss the International Space Station. Look at reality TV now. You can't tell us the networks wouldn't show it.
The only downside of the new system is that, with pistols as a traditional weapon, Chow Yun Fat would be utterly unstoppable. But then again, anyone who's seen Hard Boiled already knows that, and anyone who hasn't is entirely too-wearing-a-pink-frilly-dress to survive in the new world order anyway.
The Burr-Hamilton Duel (1804)
A pistol duel between the former Secretary of the Treasury Alexander Hamilton and then Vice President Aaron Burr, making the average Democrat-Republican row look even more like a playground scuffle than usual. The duel was Burr's response to an insulting letter written by Hamilton, and since Hamilton died the 1800's were a considerably worse time to troll.
De Grandpre-de Pique (1808)
Monsieurs de Grandpre and de Pique discovered that their mistresses were actually singular, a Mademoiselle Tirevit cheating with both of them. Rather than kicking her to le curb they decided that honor - and sanity - both needed to be shot at. FROM THE SKY. They ascended to 2,000 feet in hot air balloons and started blasting at each other. De Pique managed to miss an entire hot air balloon with a blunderbuss and therefore deserved everything which came afterwards (de Granpire's buckshot through his balloon and the ground through his everything.)
The Lyon-Wilson Duel (1833)
Canada's final fatal duel. Lyon insulted a local lady, so Wilson killed him and married her. It's unknown if he said "Yippie-kay-ay" afterwards, but we must assume he did so, while fist-pumping.
Everyone knows things would be easier if could all agree on one IBFF (Invisible Best Friend Forever), but they all think it should be theirs. Dueling wouldn't just solve the problem, it'd change religious TV from shiny psychotics begging for money into a UFC-killer. Will Vishnu's extra arms counter Buddha's weight advantage? What happens when Jesus turns the other cheek - and Ra punches that one too? Which God will win: Morgan Freeman, Alanis Morissette, or Charlton Heston, and how much would you pay to see that?
World War II
We're not claiming that everyone in history was an idiot, but millions of lives could have been saved had Winston Churchill just flat out stomped on Hitler. He's huge, he's drunk, and he's incredibly aggressive - while Adolf has the range, muscle, fighting ability and facial hair of a toothbrush. This would unfortunately mean the resurgence of the British Empire until William Taft arrived on the scene - at which point the fate of the free world would be settled by a white Sumo match.
Tell us you wouldn't watch all three, cheering.