Electoral quotient: for congressman positions, most voted candidates are not always the elected ones

Imagem mostrando a urna eletrônica.

In addition to obtaining votes for themselves, candidates for federal or state deputy positions also depend on the votes given to the party or coalition they belong to in order to get elected. Unlike majority positions, for which election is solely based on absolute votes cast, for parliamentarians victory depends on the calculation of the electoral and party 'quotients'.
Electoral quotient
To participate in the distribution of seats in the federal House of Deputies or the state Legislative Assemblies, the party or coalition must reach the so-called 'electoral quotient' - the number of valid votes cast in the election (all counted votes except blank and null ones) divided by the total number of seats to fill in each house.
Party quotient
Once the electoral quotient is obtained, the 'party quotient' is then calculated for each party or coalition, and will determine the number of seats that each of them will be awarded. The party quotient is calculated by dividing the number of votes each party/coalition has received by the electoral quotient. Thus, the more votes a party/coalition gets, the greater the number of seats that party/coalition gets to fill. The seats must be filled by the most-voted candidates of each party or coalition until reaching the number determined by the party quotient.
The use of electoral and party quotients may lead to very specific scenarios. For example, a given candidate A, may not be elected to a seat if his or her party does not reach the electoral quotient, even if receives more votes than a given candidate B. Candidate B, in turn, may be elected even with low or insignificant vote counts if his or her party/coalition reaches the electoral quotient.
Examples
Let us assume that the number of valid votes in an election for federal deputy in a given state reaches 1 million, and the number of seats to fill is 10. The electoral quotient is therefore 100,000, or the result of the division of the former by the latter. This means that for every 100,000 votes, a party or coalition guarantees the right to hold a seat in the Chamber of Deputies.
Thus, a coalition that has received 400,000 votes is entitled to four seats, which will be filled by the four most-voted candidates of that coalition. The fourth most voted candidate in this coalition is now elected, even if it has received but a single vote.
On the other hand, if the other party/coalition was able to obtain 99,000 votes and its most voted candidate has achieved 90,000 of such votes, that candidate will not be elected because the party did not reach the electoral quotient (which happened to be of 100,000 votes).
It goes in the same way for city councilor elections. In the municipal elections of 2012, Juvina Camargo Duarte won a seat in the City Council of Lajeado do Bugre, state of Rio Grande do Sul, having received exactly one vote. She was first elected as a deputy councilor, but took office in place of Councilor Everaldo da Silva, who resigned the post.
In June 2012, Sirlei Brisida, who also got only one vote, was sworn in as Councilor in the city of Medianeira (state of Paraná). In 2008 she was also elected a deputy councilor, but took office in place of Edir Josmar Moreira, impeached due to party loyalty violation.