Imperiali quota

Part of the Politics and Economics series
Electoral systems
Comparison of electoral systems Social choice theory Mechanism design List (By country)
Single-winner methods Single vote-runoff methods Plurality (FPP) Two-round (US: Jungle primary) Related: Partisan primary Instant runoff (IRV) / Alternative vote (US: Ranked-choice/RCV) Condorcet methods Condorcet-IRV Minimax Kemeny–Young Nanson Schulze Ranked pairs Maximal lottery Positional voting Plurality(el. IRV) Borda count (el. Baldwin) Antiplurality (el. Coombs) Cardinal voting Score voting Approval voting Majority judgment STAR voting Quadratic voting
Proportional representation Party-list List type Open list Closed list Localized list Panachage Mixed single vote Apportionment Highest averages Largest remainders National remnant Biproportional Quota-remainder methods Hare STV Schulze STV CPO-STV Quota Borda Cumulative Approval-based committees Thiele's method Phragmen's method Expanding approvals rule Method of equal shares Fractional social choice Direct representation Interactive representation Liquid democracy Fractional approval voting Maximal lottery
Mixed systems By results of combination Mixed-member majoritarian Mixed-member proportional By mechanism of combination Non-compensatory Parallel voting Coexistence Conditional Majority bonus Compensatory Additional member system (MMP, AV+) Scorporo Dual-member proportional Rural–urban proportional Majority jackpot By ballot type Single vote Two vote Mixed ballot
Voting system criteria Spoiler-resistance Condorcet criterion Smith independence Spoiler independence Clone independence Strategy-resistance No lesser evil voting Binary independence Maskin monotonicity Later-no-harm Later-no-help Rational response Participation criterion Positive response Reinforcement criterion Reversal symmetry
Social and collective choice Impossibility theorems Arrow's theorem Majority impossibility Moulin's impossibility theorem McKelvey–Schofield chaos theorem Gibbard's theorem Fishburn's example Positive results Median voter theorem Condorcet's jury theorem May's theorem Campbell-Kelly theorem Harsanyi's utilitarian theorem Tournament sets Smith set Landau set Copeland set Split-cycle set Bipartisan set
Politics portal Economics portal
v t e

The Imperiali quota or pseudoquota is an inadmissible electoral quota named after Belgian senator Pierre Imperiali.^[1] Some election laws have mandated it as the number of votes needed to earn a seat in single transferable vote or largest remainder elections.

The Czech Republic is the only country that currently uses the quota,^{[citation needed]} while Italy and Ecuador have used it in the past.^{[citation needed]} The pseudoquota is unpopular because of its logically incoherent nature: it is possible for elections using the Imperiali quota to have more candidates winners than seats.^[1] In this case, the result must be recalculated using a different method.^{[citation needed]} 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.

The Imperiali quota may be given as:

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

• 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:

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

As a result, it can lead to impossible allocations that assign parties more seats than actually exist.

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. 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.