In an all-way stop, how is the order of arriving at the intersection defined?

Some additional complications.

Here, it’s quite common for there to be interplay between pedestrians and 4-way stops. Drivers who have right-of-way under the 4-way stop rules can not cross because of pedestrians. In consequence, the cars traveling perpendicular get to go first, sometimes several.

Also worth noting: N clearly arrives first, followed by W and, last, S. S is likely to go when N does, even though it isn’t his turn, since W has to yield to N.

I love the last line of the response from Kate Gregory: “Intersections that routinely have 3 or 4 cars lined up in several directions should be converted from all-way stops to something else. Generally, politeness and patience will serve you better than memorizing the rules of the road.” – nice thought, but getting a muni to do that is hard. I have seen many 4 ways that often have line ups on all for stops at certain points during the day.

The response from the Dummies’ Guide is quite helpful, but note “Four-way stops always operate in a clockwise direction.” is dangerously simplistic. That is how I learned it. But I have recently moved to Portland, Oregon. After many frustrating stops at a certain intersection on my daily commute that is ALWAYS lined up (Sorry Katie), i asked my in-laws and checked ODOT rules. In this idiotic state, if there is a line up, each line goes in the order that the original 4 cars went, and the original 4 cars go in the order they arrived. So, instead of going clockwise from N, E, S, W, you could have N, S, W, E.

They ONLY apply the “yield to the right” rule that would result in clockwise alternation if the cars arrive SIMULTANEOUSLY. Since rarely does that happen in real life, you have to sit in line and pay attention to what is going on ahead of you.

Short answer is that the Dummies guide is mostly right, but every state can be different so pay attention. And don’t come to Oregon if you like things done logically because you will want to kill yourself.

The first thing to know about all-way stops is that they are used in low volume intersections. You need to know all the edge case rules about what if people arrive simultaneously but that isn’t what you normally need to deal with. You also need to know that “at the intersection” means having reached the white line painted across the road at the same point as the stop sign, or that imaginary line if nothing is painted. The actual location of the stop sign is relevant. Being in a queue to reach that line is utterly irrelevant and no different from being 100 yards or 2 miles behind the line headed for the intersection. You’re not at the intersection yet.

• If you arrive at the intersection and no other cars are there (the norm) come to a complete stop and then proceed.
• If, as you arrive at the intersection, one or more cars are already there, let them proceed, then proceed yourself.
• Should a car be behind one of those proceeding cars, make eye contact with the driver as it moves forward to the line. You were there first and will be going before that car.
• If you arrive at the line at the same time as another car, the car on the right has the right of way. Make eye contact with the other driver before going through – the other driver may believe you arrived after and should wait.
• Whenever there are other cars at the intersection and you are taking your turn, look at them and pay attention. Pulling into an intersection from a full stop is a low speed maneuver and it’s easy to stop if it seems like there’s a difference of opinion.
• Technically, whether people are turning or going straight is not relevant. In reality, if the intersection does have a line-up, people may make compatible moves out of order. For example if A, B, C, and D arrive in that order with A and C on the north-south road and B and D on the east-west road, when A goes straight there’s a chance C will go straight too even though C should wait until after B has gone. You’re under no obligation to do this sort of thing, so just don’t get worked up if it happens. It doesn’t cost B any time and it saves D time, so everyone should be happy.
• People may wave you through even when you are sure they arrived first. Don’t argue or get into a battle of wills trying to force each other to take the right of way. Move into the intersection a little to show you are accepting the gift, then wave in a “thankyou!” way (not a “go-ahead!” way as the other driver did) and smile.

Intersections that routinely have 3 or 4 cars lined up in several directions should be converted from all-way stops to something else. Generally, politeness and patience will serve you better than memorizing the rules of the road.

I got all of this from here

How to Handle Four-Way Stops: The Dummies Guide
The simplicity of the four-way stop can easily be shown in these few key concepts.

A four-way stop is any intersection with a stop sign in each direction, a flashing red light in each direction, or a broken traffic light should be treated as a four-way stop normally would.

Four-way stops are usually (but not always) labeled as such, having a rectangular sign below the octagonal shape which reads something to the effect of, “4-Way Stop,” “Four-Way Stop,” or “All-Way Stop.”

Each driver arriving at a four-way stop must first come to a stop, then one driver proceeds at a time.

If turning, as you approach a four-way stop engage your turn signal about one hundred feet prior to reaching the stop sign. The four-way stop is one of the most crucial places for using your turn signal compared to almost any other driving situation.

Four-way stops always operate in a clockwise direction. That is to say, the car furthest to the right always has the right of way, and then cars take their turns in a clockwise direction.

If multiple cars approach a four-way stop at about the same time, the driver who comes to a complete stop first proceeds first.

If two or more cars arrive at a four-way stop simultaneously, the driver furthest to the right always proceeds first, and each next driver in the clockwise direction follows.

If four cars arrive at a four-way stop simultaneously, drivers going straight should proceed first. If all four are turning right, they may all proceed simultaneously. These aside, there is no distinguishable way to see who should go first, so the intersection is at a standstill until one driver gets up the nerve and begins to inch forward, alerting the other drivers of his or her intentions, and proceeds through the intersection (thus starting the clockwise rotation from that driver).

If two cars opposite each other are proceeding straight, both turning right, or one proceeding straight with the other turning right, they may go at the same time. The turn then goes to the adjacent cars at the stop, who may follow the same rule if applicable.

Complications (or Simplifications, Depending on How You Look at It)

Of course, complexities inevitably arise. Follow these tips to avoid adding further miscommunication to the situation.

Pedestrians always have the right of way. Please do not run anyone over simply because you think it’s your turn to go; it may very well be your turn to go, but if a pedestrian is in a crosswalk that interferes with your desired path, do not go.

You must always stop at a four-way stop, whether you’re in downtown Chicago with lines of cars at the intersection or in rural Bismarck with not a car in the foreseeable horizon. Of course, I’m perfectly fine with the rolling stop in such instances, but don’t assume that just because you don’t immediately see someone you shouldn’t at least slow down to a few miles per hour at the intersection.

If you’re desired path does not interfere with any of the other drivers–for instance, if you are turning and none of the other drivers at the four-way stop need to use the road you’ll be turning right onto–you may turn right while another car is going straight or turning onto a different road.

Some drivers will ignore all the rules of the four-way stop and ignorantly assume that they have the right of way, since they are clearly the center of everyone’s universe. Even if it is your legal turn to proceed forward, always do so with caution, being wary of idiot drivers who may be too hasty to wait another ten seconds for you to clear the intersection.
Some drivers will not use their turn signal when approaching a four-way stop. This may cause you to suspect, for instance, that it is safe to proceed straight because the car opposite you seems to be going straight. However, the oblivious person driving towards you actually plans on turning left, thus crossing your path when you attempt to drive straight. Be wary of such stupid drivers, as they can occasionally look like actual people.
Disgustingly polite drivers mean death to a four-way Stop. If you encounter one such annoying person who incessantly waves you on, just go or you will simply add to the problem. Honking and waving your arms in the air in disgust is an appropriate reaction to ensure that he knows you’re not impressed with his or her attempted “chivalry.” If his or her apparent significant other is in the car, this is most likely the reasoning for this, so be sure to shake your head, furrow your eyebrows, and mouth, “Oh, really?”
Similarly, there are the completely oblivious drivers. They make their complete stop and completely forget the order of all things around them. Though it is rightfully their turn, they stare blankly at you or refuse to make eye contact with anyone at the intersection, knowing very well they’re an idiot. Attempt to wave them on with a kind gesture, politely showing them that it is their turn, but if they refuse to go, the person directly to their left should proceed instead, continuing the clockwise circle.

Cell phones. In recent years, they may be one of the biggest complications to a four-way stop. If you are approaching a four-way stop and feel you may not be able to perform at your peak while continuing the conversation with whoever could be so important, please, put it down. I don’t even care if you hang up, but take it away from your ear. This accomplishes more than you would think. First of all, it allows your focus to be on you’re driving, as it already should have been. Second, it allows you to not focus on the person on the other end of space, but to focus on the drivers who are actually present at the intersection with you. Thirdly, it gives the other drivers a sense of security; a feeling that maybe you do actually know what you’re doing, or at least that you’re trying and paying. If they see a cell phone, you’re just going to anger them, potentially causing road rage, a real condition which thousands of Americans suffer from on a daily basis.

If any emergency vehicle is approaching from any direction, pull over; they get the right of way everywhere, including a four-way stop. Duh.

THIS ISN’T A FOUR-WAY STOP. Frequently, people will observe cross lanes of traffic instead of following the road they’re on. This leads to people approaching a two-way stop, assuming it’s a four-way stop, and stopping when their have no stop sign an, in fact, have the right of way. This causes much confusion and potentially chaos as the drivers of the cross street can’t figure out what to do until the genius who actually has the right of way goes, usually after realizing he was never supposed to stop in the first place.

Keep in mind that these aren’t my words!