# Difference between revisions of "Graduated Majority Judgment"

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Like its predecessor [[Majority Judgment]], '''Continuous Majority Judgment''' or '''CMJ''' is a single-winner, median-based voting system. It works as follows: | Like its predecessor [[Majority Judgment]], '''Continuous Majority Judgment''' or '''CMJ''' is a single-winner, median-based voting system. It works as follows: | ||

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+ | # 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 voter grades each candidate on a grading scale such as A, B, C, D, F | ||

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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)) | ||

# 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. |

## Revision as of 11:14, 6 January 2013

Like its predecessor Majority Judgment, **Continuous Majority Judgment** or **CMJ** is a single-winner, median-based voting system. 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.