Imperiali quota

The Imperiali quota or pseudoquota is an inadmissible electoral quota used to calculate the number of votes needed to earn a seat in single transferable vote or largest remainder elections. It is named after Belgian senator Pierre Imperiali.

The Czech Republic is the only country that currently uses this allocation system, while Italy and Ecuador used it in the past.

It is possible for elections using the Imperiali quota to have more candidates win quota than there are vacancies to fill. If this occurs, the result needs to be recalculated with a higher quota (usually the Droop quota). If this does not happen, Imperiali distributes seats in a way that is a hybrid between majoritarian and proportional representation.

Formula
The Imperiali quota may be given as:


 * $$\frac{\mbox{votes}}{\mbox{seats}+2}$$

However, Imperiali violates the inequality for a valid quota:
 * votes = the number of valid (unspoiled) votes cast in an election.
 * seats = the number of seats on the legislature or committee.

$$\frac{\mbox{votes}}{\mbox{seats}+1} \leq \mbox{electoral quota} \leq \frac{\mbox{votes}}{\mbox{seats}-1}$$

This can lead to impossible allocations that assign parties more seats than actually exist.

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:


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

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. 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.