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  • $\begingroup$ Interesting argument, analoge of use of proper score functions $\endgroup$ Commented Dec 21, 2018 at 7:12
  • $\begingroup$ Not quite. My answer shows examples where a new high or low value will shift the median. $\endgroup$ Commented Dec 21, 2018 at 10:30
  • $\begingroup$ Not quite what? Nice answer, by the way. $\endgroup$ Commented Dec 21, 2018 at 16:11
  • $\begingroup$ The rational strategy could be to vote extreme. Naturally, there is always a question of how much is known about the others' votes. $\endgroup$ Commented Dec 22, 2018 at 1:34
  • $\begingroup$ @NickCox only if you actually want the extreme to be the proper rating. So I believe what I wrote works in all cases. And it's not in contradiction with your answer. $\endgroup$ Commented Dec 22, 2018 at 2:35