Expanding approvals rule

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 An expanding approvals rule (EAR) is a rule for multi-winner elections, which allows agents to express weak ordinal preferences (i.e., ranking with indifferences), and guarantees a form of proportional representation called proportionality for solid coalitions.

Further, EAR can be computed in polynomial time and satisfies several weak candidate monotonicity properties.

Aziz and Lee[2] extended EAR to the setting of combinatorial participatory budgeting.

The method of equal shares (MES) can be seen as a special case of EAR, in which, in step 1, the elected candidate is a candidate that can be purchased in the smallest price (in general, it is the candidate supported by the largest number of voters with remaining funds), and in step 2, the price is deducted as equally as possible (those who have insufficient budget pay all their remaining budget, and the others pay equally).

This addressed an open question by Woodall,[4] who asked if there are rules with the same political properties as STV, which are more monotonic.