Imperiali quota

Part of the Politics series
Electoral systems
Single-winner/majoritarian Plurality First-past-the-post Plurality at-large (plurality block voting) General ticket (party block voting) Multi-round voting Two-round Exhaustive ballot Primary election Nonpartisan unified top-four Majority at-large (two-round block voting) Ranked / preferential systems Instant-runoff (alternative vote) Contingent vote Coombs' method Condorcet methods (Copeland's, Dodgson's, Kemeny–Young, Minimax, Nanson's, ranked pairs, Schulze, Alternative Smith) Positional voting (Borda count, Nauru/Dowdall method) Bucklin voting Oklahoma primary electoral system Preferential block voting Cardinal / graded systems Score voting Approval voting Combined approval voting Unified primary Usual judgment Satisfaction approval voting Majority judgment STAR voting
Proportional representation Party-list Electoral list open list closed list local lists Highest averages method D'Hondt Sainte-Laguë Huntington–Hill Largest remainder Hare Droop Imperiali Hagenbach-Bischoff National remnant Ranked party list PR Spare vote Proportional forms of ranked voting Single transferable vote Gregory Wright Schulze STV CPO-STV Proportional forms of cardinal voting Proportional approval voting Sequential proportional approval voting Method of Equal Shares Phragmen's voting rules Biproportional apportionment Fair majority voting Weighted voting Direct representation Interactive representation Liquid democracy
Mixed systems By type of representation Mixed-member majoritarian Mixed-member proportional Non-compensatory mixed systems Parallel voting Majority bonus Compensatory mixed systems Additional member system Mixed single vote (positive vote transfer) Scorporo (negative vote transfer) Mixed ballot transferable vote Alternative Vote Plus Dual-member proportional Rural–urban proportional
Other systems and related theory Semi-proportional representation Single non-transferable vote Limited voting Cumulative voting Binomial voting Other systems Multiple non-transferable vote Double simultaneous vote Proxy voting Delegated voting Indirect STV Liquid democracy Random selection (sortition, random ballot) Social choice theory Arrow's theorem Gibbard–Satterthwaite theorem Public choice theory List of electoral systems List of electoral systems by country Comparison of electoral systems
Politics portal
v t e

The Imperiali quota is a formula used to calculate the minimum number, or quota, of votes required to capture a seat in some forms of single transferable vote or largest remainder method party-list proportional representation voting systems. It is distinct from the Imperiali method, a type of highest average method. It is named after Belgian senator Pierre Imperiali.

The Czech Republic and Ecuador are among the few countries that currently use this allocation system,^{[citation needed]} while Italy used it for its Chamber of Deputies from 1946 to 1993.

If many party lists poll just over the Imperiali quota, it is possible for this method to distribute more seats than there are vacancies to fill (this is not possible with the Hare or Droop quotas). If this occurs, the result needs to be recalculated with a higher quota (usually the Droop quota). If it does not happen, Imperiali usually distributes seats in a similar fashion to the D'Hondt method.

The imperiali quota should not be confused with the highest average method, which is also called Imperiali.

Formula

The Imperiali quota may be given as:

${\displaystyle {\frac {{\mbox{total}}\;{\mbox{votes}}}{{\mbox{total}}\;{\mbox{seats}}+2}}}$

• Total votes = the total valid poll; that is, the number of valid (unspoilt) votes cast in an election.
• Total seats = the total number of seats to be filled in the election.

An example of use in STV

To see how the Imperiali quota works in an STV election imagine an election in which there are two seats to be filled and three candidates: Andrea, Carter and Brad. There are 100 voters as follows:

There are 100 voters and 2 seats. The Imperiali quota is therefore:

${\displaystyle {\frac {100}{2+2}}=25}$

To begin the count the first preferences cast for each candidate are tallied and are as follows:

• Andrea: 65
• Carter: 15
• Brad: 20

Andrea has more than 25 votes. She therefore has reached the quota and is declared elected. She has 40 votes more than the quota so these votes are transferred to Carter, as specified on the ballots. The tallies therefore become:

• Carter: 55
• Brad: 20

Carter has now reached the quota so he is declared elected. The winners are therefore Andrea and Carter.

References

This page was last edited on 7 September 2022, at 14:11