How good is the average pilot?
Military fast jets have one pilot, but there aren't many that good.
I have instructed future airline pilots. I could only recommend about a quarter of them for single pilot ops.
It's not just about passing checkrides on any given day; a single crew member has to not make significant mistakes (and not notice them him/herself) ever - their entire career.

Something that is not considered in certification of single pilot jet operations is the matter of currency. The jet sales people tend to gloss over this vital aspect of owner-driver flying.
A commercial pilot flying a complex aircraft on an almost daily basis is less likely to get into trouble than a PPL with not much prior IFR time doing the same thing maybe once a month.
As someone observed, a new Mustang is way more user friendly than an old Baron, but if you fly any fairly fast aircraft 50 hours a year and that's the sum total of your flying, unless you have plenty of prior relevant experience, you are likely to struggle. Three approaches in 90 days barely covers it if that's all you do.
And put all your faith in the automatics at your peril. Modern automatics rarely fail, but when they do they always choose the worst possible moment.

A turboprop requires two pilots
 

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2 Pilots
 

I know someone mentioned this before, but I will delve into it a bit more.

Despite the CRM, one pilot checking another, two sets of eyes (which are all vital parts), its the pilot incapaciation which is an issue.

Whilst it hasnt happened to me (touch wood), pilot incapacitation is a very real thing. Its the reason why we cant eat the same meals.

For some hypothetical numbers....how many airliners declared a PAN due to flight crew incapacitation globally last year?

Assuming that these were majority short-medium haul 2 crew ops.....now imagine that they were single pilot ops......a whole lotta big jet crashes.

Eternity, I see you point but I think you might be stretching the truth a little. I wonder how many of the incapacitations to which you refer, involved pilots who had a medical that was endorsed with the proviso 'multi crew only / safety pilot required.' The medical requirements for SP IFR operations are more stringent. While not excluding the possibility of an incapacitation, the stricter medical requirements make it difficult to make an apples with apples comparison here. How many pilots flying an airliner around can't hire a Warrior on the weekend by themselves? We'll never know.

It all comes back to the dollars. It has a cousin which gets discussed more often - single engine vs multi engine... Affordable safety... :\

Gee did I just read SE v Multi eng? Now where talkin' as that's right up my alley:-):E
We've covered the main reasons as to why 2 drivers.

Redundancy, pilot incap, 4 eyes are better than two, work load, system complexity, currency,insurance, cost & plain simple too dangerous with just one driver, all revolves around the two key words with flying, COST & safety, typed like that as it's easy to see where the priority lays.

Wmk2

Correct me if I'm wrong, but I believe the majority of pilot incapacitation issues are caused by temporary things like food poisoning, rather than an underlying health issue?

Dr Dre, you are correct, most are due to usually sudden onset of bad food, gastro or flu type illnesses.

Occasionally on very rare occasions someone has a totally out of the blue heart attack etc and just dies right there in the seat.
I remember a few stories where that happened before takeoff over the years. Guy sitting there pre start says something like, " I'm feeling really tired all of a sudden" and a few seconds later, they are gone.
Thankfully That of course is extremely rare.

Most of the other comments re backup, detecting threats/errors, workload levels, recency etc are all true as well.
Most of the time 2 is better than one but of course some recent disasters shows that is not always the case either, the SFO Asiana being a prime example. Again, thankfully, rare events but they could be rarer still.

Big airplanes usually mean longer flights. Are you going to pee in a bottle and sit down the entire 5 or more hour DVT-inducing flight, or call up the attendant to mind the shop while you go back to the can and have a leak? Practicalities.

What makes a jet need two pilots? The willingness of me and my family... and most probably you and yours.... To buy a ticket and get on board.

What makes a jet need 2 pilots
 

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