The Romans tried that

The winner becomes president, the one with the most votes next becomes vice?

I would imagine each president would just veto the other

More presidents? Sounds worse than having one.

What if we paid for the leadership you want; if you want to know your food is safe, you only buy foods that are stamped by a private regulatory agency that you trust, like kosher; if you want security, you pay for a service like ADT or Ring

Then the USA inhabitants have gaslit times. 👯

What do you mean "both"? Remember Abraham Lincoln was the first Republican (Republicans of then and now are completely different etc etc add ins you gotta mention to not distract from your real point)

Point is, at the time he was a 3rd party. So "why not both" assumes each is equally valid.

Now coalitions on the other hand like I hear about some European countries doing could be interesting.

Scott Adams was predicting it in 2020

I suspect somehow or other competing presidential claims will be resolved, possibly involving some compromise like this: https://www.youtube.com/live/-6wq0D5xbfo?si=TjN62-0-5jDZPuJl

"You will eat bugs and they will be delicious"

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