CMJ (continuous majority judgment) is an MJ-like system using the numeric tiebreaker*:
Median¹ + ((Votes_above_median - Votes_below_median) / (2 * Votes_at_median)) The CMJ formula is actually a simplified version of the trimmed-mean-like formula: Median + ((Votes_above_median - Votes_below_median) / (Votes_at_median + |Votes_above_median - Votes_below_median|)) This full version is not equivalent algebraically, and it gives slightly different scores; but it is fully equivalent in all cases in terms of the order of candidates and specifically the winner. A similar formula can be given for MJ itself: Median + ((Votes_above_median - Votes_below_median) / |Votes_above_median - Votes_below_median|) * ((Votes_at_median - |Votes_above_median - Votes_below_median| + 2) / (4 * ((Votes_at_median - |Votes_above_median - Votes_below_median| + 1)) This is equivalent to a subset of the MJ tiebreaker. That is, if it breaks a tie it always does so in accordance with MJ, and it breaks most of the ties that MJ does; but if the MJ tiebreaker has to cross more than one rating boundary to break the tie, then this formula will not break the tie. I suspect that the above formula could be simplified further. Jameson Quinn ¹ "Median" is the median grade, converted to an integer
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