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Graduated majority judgment
Graduated majority judgment (GMJ), sometimes called the usual judgment or continuous Bucklin voting, is a single-winner rated voting rule that selects the candidate with the highest median score. It was first suggested as an improvement on majority judgment by Andrew Jennings in 2010.
GMJ begins by counting all ballots for their first choice. If no candidate has a majority then later (second, third, etc.) preferences are gradually added in, continuing until one candidate reaches 50% approval. The first candidate to reach a majority of the vote is the winner.
Votes should be cast using a cardinal (rated) ballot, which ask voters to give each candidate a separate grade, such as :
When counting the votes, we calculate the share of each grade for each of the votes cast. This is the candidate's "merit profile":
For each candidate, we determine the median or majority grade as the grade where a majority of voters would oppose giving the candidate a higher grade, but a majority would also oppose giving a lower grade. This rule means that the absolute majority of the electors judge that a candidates merits at least its median grade, while half the electors judge that he deserves at most its median grade.
If only one candidate has the highest median grade, they are elected (as in all highest median voting rules). Otherwise, the election uses a tie-breaking procedure.
Graduated majority judgment uses a simple line-drawing method to break ties. This rule is easier to explain than others such as majority judgment, and also guarantees continuity.
Graphically, we can represent this by drawing a plot showing the share of voters who assign an approval less than the given score, then draw lines connecting the points on this graph. The place where this plot intersects 50% is each candidate's final score.
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Graduated majority judgment
Graduated majority judgment (GMJ), sometimes called the usual judgment or continuous Bucklin voting, is a single-winner rated voting rule that selects the candidate with the highest median score. It was first suggested as an improvement on majority judgment by Andrew Jennings in 2010.
GMJ begins by counting all ballots for their first choice. If no candidate has a majority then later (second, third, etc.) preferences are gradually added in, continuing until one candidate reaches 50% approval. The first candidate to reach a majority of the vote is the winner.
Votes should be cast using a cardinal (rated) ballot, which ask voters to give each candidate a separate grade, such as :
When counting the votes, we calculate the share of each grade for each of the votes cast. This is the candidate's "merit profile":
For each candidate, we determine the median or majority grade as the grade where a majority of voters would oppose giving the candidate a higher grade, but a majority would also oppose giving a lower grade. This rule means that the absolute majority of the electors judge that a candidates merits at least its median grade, while half the electors judge that he deserves at most its median grade.
If only one candidate has the highest median grade, they are elected (as in all highest median voting rules). Otherwise, the election uses a tie-breaking procedure.
Graduated majority judgment uses a simple line-drawing method to break ties. This rule is easier to explain than others such as majority judgment, and also guarantees continuity.
Graphically, we can represent this by drawing a plot showing the share of voters who assign an approval less than the given score, then draw lines connecting the points on this graph. The place where this plot intersects 50% is each candidate's final score.