Graduated Majority Judgment: Difference between revisions
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Like its predecessor [[Majority Judgment]], ''' |
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: |
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===Ballot Explanation=== |
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<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. |
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===Counting=== |
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====Conceptual==== |
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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%. |
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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. |
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====Two equivalent full procedures==== |
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It works as follows: |
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# Each voter grades each candidate on a grading scale such as A, B, C, D, F |
# Each voter grades each candidate on a grading scale such as A, B, C, D, F |
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# The top-grade ( |
# The top-grade (A) votes for each candidate are tallied. |
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# If a single candidate has a majority (that is, a number of votes greater than or equal to 50% of voters), they win. |
# If a single candidate has a majority (that is, a number of votes greater than or equal to 50% of voters), they win. |
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# If no candidate has a majority, the next grade down ( |
# If no candidate has a majority, the next grade down (B) is added to the tally, and go back to step 3. |
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# 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. |
# 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. |
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The above process is conceptually simple, but difficult in practice. The following process gives the same results, and is simpler to run in practice: |
The above process is conceptually simple, but difficult in practice. The following process gives the same results, and is simpler to run in practice: |
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# Each voter grades each candidate on a grading scale such as A, B, C, D, F |
# Each voter grades each candidate on a grading scale such as A, B, C, D, F |
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# Each grade for each candidate is tallied. |
# Each grade for each candidate is tallied. |
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# The tallies are used to find the median grade for each candidate. |
# The tallies are used to find the median grade for each candidate. |
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# Tallies are added to find the V(>M), V(@M), and V( |
# 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. |
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# A candidate's adjustment is a number between -0.5 and +0.5, calculated using the formula (V(>M) - V(<M)) / (2 * V(@M)) |
# A candidate's adjustment is a number between -0.5 and +0.5, calculated using the formula (V(>M) - V(<M)) / (2 * V(@M)) |
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# The candidate with the highest adjustment among those with the highest median, wins. |
# The candidate with the highest adjustment among those with the highest median, wins. |
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If medians are converted to integers (such as 0-4), then the adjusted median scores can easily be reported alongside the full tallies. |
If medians are converted to integers (such as 0-4), then the adjusted median scores can easily be reported alongside the full tallies. |
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[[Category:Graded Bucklin methods]] |
Latest revision as of 15:20, 7 August 2019
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
The ballot will ask you to grade each candidate 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. The first candidate to get over 50% is the winner. 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 (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 (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.