Graduated Majority Judgment: Difference between revisions

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Line 1: Like its predecessor [[Majority Judgment]], '''Graduated Majority Judgment''' or '''GMJ''' is a single-winner, median-based voting system. Here's one way to explain it: :===Ballot Explanation=== :<strong>The ballot will ask you to grade each candidate</strong> on a scale from A (excellent) to F (unacceptable). You may give two candidates the same grade if you wish. Any candidate whom you do not explicitly grade will get an F from you. :===Counting=== ====Conceptual==== :To find the winner, first the "A" votes for each candidate are counted. If no candidate gets over 50% of the voters, the "B" votes are added to the count, then "C" votes, etc. <strong>The first candidate to get over 50% is the winner.</strong> If two candidates would reach 50% at the same grade, each candidate's votes for that grade are added gradually, and the winner is the one who needs the smallest portion of those votes to reach 50%. :This gradual process can be stated as a "graduated score" for each candidate. If a candidate reaches 50% using 8/10 of their "C" votes (along with all their A and B votes), then their graduated score would be 1.7 (a C-). Another candidate who needed only 2/10 of their "C" votes to reach 50% would have a graduated score of 2.3 (a C+), so between those two candidates the second would be the winner. ====Two equivalent full procedures==== It works as follows: # Each voter grades each candidate on a grading scale such as A, B, C, D, F # The top-grade (~~eg,~~ A) votes for each candidate are tallied. # If a single candidate has a majority (that is, a number of votes greater than or equal to 50% of voters), they win. # If no candidate has a majority, the next grade down (~~eg,~~ B) is added to the tally, and go back to step 3. # If more than one candidate has a majority, the last grade tallied is removed from the tallies, and then re-added at the smallest fraction possible so that some candidate has a majority. This is as if the votes at that grade were added 1% at a time until one candidate gets a majority. The above process is conceptually simple, but difficult in practice. The following process gives the same results, and is simpler to run in practice: # Each voter grades each candidate on a grading scale such as A, B, C, D, F # Each grade for each candidate is tallied. # The tallies are used to find the median grade for each candidate. # Tallies are added to find the V(>M), V(@M), and V(><M) (that is, votes above median, votes at median, and votes below median or blank) for each candidate. # A candidate's adjustment is a number between -0.5 and +0.5, calculated using the formula (V(>M) - V(<M)) / (2 * V(@M)) # The candidate with the highest adjustment among those with the highest median, wins. If medians are converted to integers (such as 0-4), then the adjusted median scores can easily be reported alongside the full tallies. [[Category:Graded Bucklin methods]]