That depends entirely on what P is, as the nukes example clearly shows.
More nations have nukes than they used to, but far fewer than have guns. Life is lived in a gray area that the "not everyone will follow the law therefore the law is useless" mindset somehow ignores.
And if "P" is "an AI that controls weapons deployed/used in the US," say, then enforcement is likely to be more effective than just "nobody can have AI at all."
So it's probably worth thinking about what specific things we do and don't want AI to be used for, and which of those are more or less practical.
EDIT: oh, and it also assumes that P is something people want for itself, vs "if they're gonna do it I better do it too" or "it's 10% cheaper and the externalities don't directly effect me THAT much" or other similar behaviors that can emerge without regulation. Banning leaded paint and leaded gas vs banning alcohol, say.
An important factor in nuclear proliferation that may or may not be relevant to AI: there are at most half a dozen "lineages" for nuclear weaponry - countries that developed gaseous centrifuges on their own without assistance from an existing nuclear state. By my count they boil down to 1) US, 2) Germany via WWII R&D, 3) UK, 4) Russia, 5) URENCO, 6) South Africa.
None of the most recent entrants to the nuke club did so on their own. China got help from Russia while Pakistan, Iran, and North Korea gained it via Abdul Qadeer Khan's URENCO espionage.
It'll be interesting to see if AI will see the same kind of limitation. If so, then maybe there will be some chance at limiting a catastrophic spread.
More nations have nukes than they used to, but far fewer than have guns. Life is lived in a gray area that the "not everyone will follow the law therefore the law is useless" mindset somehow ignores.
And if "P" is "an AI that controls weapons deployed/used in the US," say, then enforcement is likely to be more effective than just "nobody can have AI at all."
So it's probably worth thinking about what specific things we do and don't want AI to be used for, and which of those are more or less practical.
EDIT: oh, and it also assumes that P is something people want for itself, vs "if they're gonna do it I better do it too" or "it's 10% cheaper and the externalities don't directly effect me THAT much" or other similar behaviors that can emerge without regulation. Banning leaded paint and leaded gas vs banning alcohol, say.