I thought of this idea before but I believed there was a problem with it which I can’t immediately see now—probably having to do with something that happens when multiple people are moving at once. If I can figure out what the problem was I’ll let you know.
EDIT: Yeah, I can’t see what the problem with it is. I think I convinced myself for some reason that this invariance would break if multiple people were moving at once but it doesn’t, so I think this works.
Yeah, to make this explicit we can just apply the same argument over and over again to show that moving any set of points any distance towards the median preserves the median.
I thought of this idea before but I believed there was a problem with it which I can’t immediately see now—probably having to do with something that happens when multiple people are moving at once. If I can figure out what the problem was I’ll let you know.
EDIT: Yeah, I can’t see what the problem with it is. I think I convinced myself for some reason that this invariance would break if multiple people were moving at once but it doesn’t, so I think this works.
Yeah, to make this explicit we can just apply the same argument over and over again to show that moving any set of points any distance towards the median preserves the median.