This is the “Odd and Even Day” rule. Our son was assigned the odd days and our daughter the even days.
Every time there was an argument between them and neither would budge, i.e. wanting to watch a different TV program, to sit by the window in a train, to hold the bag, to walk the dog, etc. we would say, “right, what day is it?”. If it was an odd day, Malcolm would be the one who would be able to choose. If it was an even day, then Carly would be given the right to decide. This would stop them fighting immediately because there was a fairness in this system that could not be argued with.
I hear you say, “but this is not fair because there are more odd days than even days in a month”, well true but this was counteracted by the fact that the system also worked in bad situation. When one had to do something that neither wanted to do it, then the odd and even rule would be used again.