A majoritarian voting system is an electoral method which gives the right to appoint all the representatives to the majority of the electors, denying representation to all minorities. Historically the first electoral method to be used, it was later progressively modified or eliminated, due to its non-democratic effects.
Majoritarian representation Wikipedia
The majoritarian right was upheld by a large and important group of scholars. Aristotle launched a theory which was later assumed by many Roman thinkers who said that quod maior pars curiae efficit, pro eo habetur ac si omnes egerint (the decision taken by the majority of the senators is valid as it would be approved by all). Jean-Jacques Rousseau, consequently to his concept of general will, said that la voix du plus grand nombre oblige toujours tous les autres (the voice of the greater number ever forces all people). Adhémar Esmein said that if the entire country was a single constituency, the electoral majority would have the right to appoint all the deputies, as it appoints the head of the executive power; even in its extreme consequencies, this system does not cause an injustice to the minority, because the majority obtains no more than its right.
Quite undisputed until the first half of the 19th century, the classic majoritarian system, sometimes referred as block voting, began to be more and more criticized when great ideological differences arose. Corrections were worldwide progressively introduced in two senses:a first possibility was to reduce the size of the constituencies, so to divide the election in many local contests, and consequently increase the possibility for the minority to win in some areas. At-large elections were substituted by many multi-member constituencies and, finally, by single-winner electoral districts;
a second possibility was to introduce corrections even still voting at-large or, at least, in multi-member constituencies:
the limited voting system allowed the electors to vote a number of candidates which was lower than the contesting seats;
the cumulative voting system allowed the electors to concentrate their full share of votes on fewer candidates;
the single non-transferable vote was the extreme of the limited vote, the elector having a single choice in a multi-member race;
the preferential block voting system allowed the electors to rank the candidates, imposing a quota to be elected;
the party-list voting system, which established proportional representation, fully abandoning the majoritarian criterion.
Nowadays, at-large majoritarian representation is no longer used for national elections, while it is sometimes still used for local elections organised on non-partisan bases.
Residual usage in several multi-member constituencies is reduced to the election of the Electoral college of the President of the United States. Block voting is also used to elect a part of the assemblies in the regional elections in Italy and France: in these cases, the majoritarian quota is one of two parts of an additional member system.