Graduated majority judgment

Condorcet methods Positional voting Cardinal voting Quota-remainder methods Approval-based committees Fractional social choice Semi-proportional representation By ballot type Pathological response Strategic voting Paradoxes of majority rule Positive results Graduated majority judgment (GMJ), sometimes called the usual judgment[1] or continuous Bucklin voting,[2] is a single-winner rated voting rule that selects the candidate with the highest median score.

[1] It was first suggested as an improvement on majority judgment by Andrew Jennings in 2010.

preferences are gradually added in, continuing until one candidate reaches 50% approval.

[4] 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.

Graduated majority judgment uses a simple line-drawing method to break ties.

[1] 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.

The tiebreaking rule can be explained using an analogy where every candidate is in a race.

The winner is the first candidate to cross the finish line at 50% of the vote.

In the unusual case of a tie where the formula above does not determine a single winner (if several candidates have exactly the same score), ties can be broken by binning together the 3 grades closest to the median, then repeating the tie-breaking procedure.

This process can be repeated multiple times (binning more and more grades) until a winner is found.

As an electoral system, the graduated majority judgment shares most of its advantages with other highest-median voting rules such as majority judgment, including its resistance to tactical voting.

The tie-breaking formula of the graduated majority judgment presents specific advantages over the other highest-median voting rules.

As small differences of votes are less likely to change the outcome of the election, candidates are less likely to contest results.