Imperiali quota

Voting systems
Part of the Politics series
Single district member s.call Plurality voting system s.call Plurality/Majoritarian Simple majoritarianism Limited voting Single non-transferable vote Plurality First-past-the-post Two-round Exhaustive ballot Preferential/ranked/ordinal systems Borda count Bucklin voting Condorcet methods (Copeland's, Dodgson's, Kemeny-Young, Minimax, Nanson's, Ranked pairs, Schulze) Coombs' method Instant-runoff (alternative vote) Contingent vote Oklahoma primary electoral system Cardinal/graded/rated systems Approval voting Proportional approval voting Sequential proportional approval voting Satisfaction approval voting Majority judgment Range voting
Proportional Representation Party-list (Open lists, Closed lists, Local lists) Highest averages (D'Hondt, Sainte-Laguë) Largest remainder (Hare, Droop, Imperiali, Hagenbach-Bischoff) Single transferable vote (CPO-STV, Gregory, Schulze STV, Wright)
Mixed-Member Mixed-member proportional Majority bonus system Additional member system Scorporo, Av+ Parallel voting Majoritarian representation Plurality-at-large Preferential block voting General ticket
Other Proxy voting Delegable voting Delegated voting Random selection Sortition Random ballot Social choice theory Arrow's theorem Gibbard–Satterthwaite theorem Voting system criteria Public choice theory (separate but related) Multiple Ballot Voting Cumulative voting
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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.

Ecuador is among the few countries that uses this allocation system, while Italy used it for its Chamber of Deputies from 1946 to 1993.

If a large number of 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—i.e., favouring larger parties.

Formula

The Imperiali quota may be given as:

\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 2 seats to be filled and 3 candidates: Andrea, Carter and Brad. There are 100 voters as follows:

65 voters

Andrea
Carter

15 voters

Carter

20 voters

Brad

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

\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

Types of majority

Single member	Plurality Majority Supermajority Double majority

Multi-member (election threshold)	Hare quota Droop quota Imperiali quota Hagenbach-Bischoff quota

Voting systems

Part of the Politics and Election series

Single-winner voting system	Approval voting Borda count Bucklin voting Contingent vote Coombs' method Copeland's method Exhaustive ballot First-past-the-post voting Instant-runoff voting Kemeny–Young method Simple majoritarianism Minimax Condorcet Nanson's method Plurality Positional voting system Range voting Ranked pairs Schulze method Two-round system

Proportional representation	Mixed-member Party-list Single transferable vote Schulze STV CPO-STV Highest averages method Sainte-Laguë D'Hondt Largest remainder method Alternative vote Plus Closed list Open list Overhang seat Underhang seat

Semi-proportional representation	Parallel voting Single non-transferable vote Cumulative voting Limited voting Proportional approval voting Sequential proportional approval voting Satisfaction approval voting

Usage	Table of voting systems by country

Voting system criterion	Condorcet criterion Condorcet loser criterion Consistency criterion Independence of clones Independence of irrelevant alternatives Independence of Smith-dominated alternatives Later-no-harm criterion Majority criterion Majority loser criterion Monotonicity criterion Mutual majority criterion Pareto efficiency Participation criterion Plurality criterion Resolvability criterion Reversal symmetry Smith criterion

Voting system quotas	Droop quota Hagenbach-Bischoff quota Hare quota Imperiali quota

Other	Ballot Vote counting system Election threshold First-preference votes Spoilt vote Sortition

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