[brey]

ah, no, I was wrong - the median only stays the same if only people in the lower half beforehand gave less, and only people in the upper half gave more.

if people cross the old median, this is perfectly possible. although initially counter-intuitive ...

[corin_]

Not just if they cross the median, the median might cross them - for example what if the only people to come back to donate a second time were above the median in their first donation, then even if they all donated the same amount the second time, the median of second-donations would still go up.