The binomial system is a voting system that was used in the parliamentary elections of Chile between 1989 and 2013. From a voting system point of view, it is a multiple-winner method of proportional representation with open lists, where winning candidates are chosen through the D'Hondt method. Its particularity comes from the fact that only two candidates are elected in each district, resulting in an over-representation of the second majority list. Its use was prescribed in the respective constitutional organic law during the Pinochet regime.
The binomial system was invented in Poland in the 1980s under the Wojciech Jaruzelski regime, in order to foster political stability in the democratization process, maintaining the preeminence of the Polish United Workers' Party against the rise of the opposition movement Solidarność, being recognized as a system that promoted consensus and negotiation between opposing sides of government.
The binomial system was considered by most analysts as the main constitutional lock that prevented completion of the transition to democracy.
The system works in the following manner: Parties and independent candidates group themselves into lists or coalitions, basically electoral blocs. Each list proposes up to two candidates per electoral region, province, or other geographical unit. Votes are first tallied by list instead of by candidate, and unless the list which obtained the first majority has double the voting as the second majority, each of the two lists gets one of their candidates, the one who got the most voting, into office. In other words, the binomial system basically means that the first and the second majority get equal representation unless the first majority doubles the second. For example, in the following cases the candidate that would get elected under a binomial system are marked with an [e]: