Whoever is the confused, pushy, restless, hurried, or idiiot-on-the-cell-phone-person that is still moving and going to do what they want always goes first so I can avoid an accident with them.
There should be signs that say "right car goes first" or something like that but often there isn't. There is one like that down the street from me at a 4 way but I forget what it says exactly but there is another one that has no signs and people do what they want to do.
If no signs, then its the person who has been waiting the longest goes first. If there are cars at the other 3 intersections I wait til all the restless people go first that were there first. Every person has a different judging system when there are no signs or even if there are signs so I wait to see all the people clear away who feel they should go by some divine right that none of the rest of us know about or are actually there first. There often is no pattern of cars clearing based on who actually got there first, nor a circular clearing pattern happening.
You can contact authorities to have signs posted about encouraging a circular clearing.