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The rule for four-way stops is simple: Right-of-way is established in order of arrival at the intersection. First to arrive at the stop sign can go first, followed by the second, etc.

Not everybody follows the rule, and technically they're breaking traffic laws by doing so.

And you're right. I prefer roundabouts too, they're objectively safer. Massachusetts has a fair few roundabouts, but other parts of the country seem to abhor them.

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There are other rules. Always yield to pedestrians. Two cars can sometimes go at the same time if they're not on a collision course. If pedestrians are blocking the person whose turn it is, you can go instead. Order is based on arrival time, unless there's a lot of cars then it's yield to the right if you're unsure.

These rules combine in such a way that it's genuinely unclear who should go in some situations - the above rules might contradict, or you might need information you don't have cause you got there after something broke "the order". But if you think it's your turn and start to go, people will let you, and ultimately no one gets stuck forever.

not in Illinois: here, after whoever arrived first goes, the right of way goes to whoever is to their right (or, next, going counter clockwise), regardless when they arrived (as long as they arrived before the first car went)

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