Imperiali quota

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.

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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 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—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 two seats to be filled and three 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

Electoral systems
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Single-winner	Approval voting Combined approval voting Unified Primary Borda count Bucklin voting Contingent vote Supplementary vote Condorcet methods Copeland's method Dodgson's method Kemeny–Young method Minimax Condorcet Nanson's method Ranked pairs Schulze method Exhaustive ballot First-past-the-post voting Instant-runoff (ranked choice) voting Coombs' method Majority judgment Simple majoritarianism Plurality Positional voting system Score voting STAR voting Two-round system
Proportional	CPO-STV Dual member Hare-Clark Highest averages method Webster/Sainte-Laguë D'Hondt Largest remainder method Mixed-member Party-list Schulze STV Single transferable vote
Semi-proportional	Parallel voting Single non-transferable vote Cumulative voting Limited voting Proportional approval voting Sequential proportional approval voting Satisfaction approval voting Alternative vote plus
Criteria	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
Quotas	Droop quota Hagenbach-Bischoff quota Hare quota Imperiali quota
Other	Ballot Election threshold First-preference votes Spoilt vote Sortition
Comparison	Comparison of voting systems Voting systems by country
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Types of majority
Single member	Plurality Majority Supermajority Double majority
Multi-member (election threshold)	Hare quota Droop quota Imperiali quota Hagenbach-Bischoff quota