Whoever put together this platform did a great job simulating the in-person social interaction experience! I can tell because I hate it for all the same reasons.(To be clear, this isn't at all meant as a complaint. A platform meant to take the place of an in-person party probably shouldn't be optimized to appeal to a person who metaphorically runs screaming from parties unless her partner is there to cling to the whole night, and kinda hates it even then.)
A geometric intuition I came up with while reading:
Take a number line, and put 1, 2, and 4 on it.
-1-2---4-You're moving a pointer along this line, and trying to minimize its total distance to the data points:-1-2---4-....^ Intuitively, throwing it somewhere near the middle of the line makes sense. But drop 2 out, and look what happens as you move it:-1-----4-....^ .|--| ....|--| vs.-1-----4-......^ .|----| ......||
The distance is the same either way! (Specifically, it's the same for any point in between 1 and 4.)
This means we're free to move our pointer only with respect to 2, so the best answer is to get a distance-from-2 of 0 by putting it directly on 2.
To generalize this to medians of larger data sets, imagine adding more pairs of points on the outside of the range - the total distance to those points will be the same, just as it was for 1 and 4.
[edit: formatting came out a bit ugly - monospace sections seem to eat multiple spaces when displayed but not in the editor for some reason?]
Sapience Spell trigger: whenever I crack my knuckles.