Mathematical mechanism that defines the distribution of seats in the Legislative Branch based on the votes obtained by parties and federations
The Brazilian electoral system for legislative positions — councilors, state deputies and federal deputies — operates under the proportional model, unlike the majority system used for mayors, governors and president. In this model, the central unit of representation is the party or party federation, and not just the individual. The electoral quotient is the fundamental instrument that ensures that the different schools of thought in society are represented in legislative houses in direct proportion to the votes they receive. Understanding this logic is essential to understanding the composition of the National Congress and Municipal Chambers.
Attributions of the electoral and party quotient
The primary function of the electoral quotient is to establish a “cutoff score” or minimum vote threshold that a party or federation needs to reach to be entitled to a seat in parliament. It transforms the total mass of valid votes into a finite number of available mandates.
Two main functions derive from this calculation:
- Definition of chairs by legend: Determines how many seats each party won, regardless of which candidates occupy them.
- List ordering: Once the number of party seats has been defined, they are distributed to the candidates with the most votes from that group, as long as they meet the minimum individual voting requirements.
It is at this stage that the common question arises about how a deputy is elected even though he has fewer votes than another candidate. As the seats belong to the party, a candidate with average votes in a party with a lot of votes (which secured many seats) can be elected, while a candidate with a lot of votes in a party that did not reach the quotient can be left out.
History and evolution of legislation
The proportional system was introduced in Brazil by the Electoral Code of 1932, aiming to overcome the defects of the majority system of the Old Republic, which excluded political minorities. The 1988 Federal Constitution consolidated this model, but infra-constitutional legislation has undergone significant changes in recent decades to correct distortions.
Recent changes have directly impacted the calculation:
- End of Coalitions (2017/2021): Previously, parties could add up their TV time and votes. With the ban, the calculation of the quotient began to be done exclusively with the votes of the party or the formalized federation.
- Individual Performance Clause (2015): To avoid the excessive phenomenon of “vote pullers” carrying insignificant candidates, the rule was established that the candidate must obtain votes equivalent to at least 10% of the electoral quotient to be elected, except in cases of repechage in the remainder.
Practical operation of the calculation
To determine those elected, the Electoral Court follows a logical sequence of mathematical operations after counting the ballot boxes. The process occurs in three fundamental steps.
1. Calculation of the Electoral Quotient (EQ)
The total number of valid votes (excluding blank and invalid votes) is divided by the number of seats in dispute. The result, disregarding the fraction if equal to or less than 0.5, or rounded to one if greater, is the Electoral Quotient.
- Formula: Valid Votes ÷ Number of Vacancies = QE
2. Calculation of the Party Quotient (QP)
It defines how many seats each party initially receives. The party’s total vote is divided by the Electoral Quotient. The resulting integer is the number of direct seats.
- Formula: Party Votes ÷ QE = QP
3. Distribution of Leftovers (Averages)
Rarely does the sum of QPs fill all vacancies. The remaining seats are distributed by calculating the highest average. Parties that obtain at least 80% of the QE and candidates with votes equal to or greater than 20% of this quotient can compete for the remainder.
The phenomenon that explains how a deputy is elected even though he has fewer votes than another candidate lies in the collective strength of the legend. If Party A has enough votes for 10 seats, the 10th place on the list will enter, even if it has fewer absolute votes than the 1st place of Party B, if Party B has not reached the minimum quotient or has only reached votes for one seat.
Importance for democratic representation
The proportional system, governed by the electoral quotient, is vital for maintaining political pluralism. In a purely majority system (“winner-takes-all”), significant minorities in society could be left without any institutional representation if their votes were geographically dispersed.
By focusing on the party’s votes, the system:
- It strengthens party ideology to the detriment of personalism.
- Guarantees a voice for organized minority groups.
- It requires the formation of consensus, as it is difficult for a single party to obtain an absolute majority in the legislative houses.
The electoral quotient is therefore configured as a technical tool for political justice. Although it generates apparently paradoxical situations from the perspective of individual voting, it fulfills the constitutional function of ensuring that the composition of the Legislative Power is a proportional mirror of the different political forces that make up Brazilian society, ensuring that governability is built through dialogue between different ideological spectrums.
