Imperiali quota

The Imperiali quota or pseudoquota is an inadmissible electoral quota named after Belgian senator Pierre Imperiali. Some election laws have mandated it as the number of votes needed to be guaranteed to win earn a seat in single transferable vote or largest remainder elections.

The Czech Republic and Belgium are the only countries that currently use the quota, while Italy and Ecuador have used it in the past.. Belgium only uses the quota for local elections.

The pseudoquota is unpopular because of its logically incoherent nature: it is possible for elections using the Imperiali quota to have more candidates pass quota than open seats. In this case, the result must be recalculated using a different method. If this does not happen, Imperiali distributes seats in a way that is a hybrid between majoritarian and proportional representation, rather than providing actual proportional representation.

Formula

The Imperiali quota may be given as:

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

• votes = the number of valid (unspoiled) votes cast in an election.
• seats = the number of seats on the legislature or committee.

However, Imperiali violates the inequality for a valid fixed quota:

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

It 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:

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. 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.