Binomial voting

Proportional representation Condorcet method D'Hondt method

The binomial system (Spanish: Sistema binominal) is a voting system that was used in the legislative elections of Chile between 1989 and 2013.[1] 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.[2]

The binomial system was considered by most analysts as the main constitutional lock that prevented completion of the transition to democracy.[3]


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]:

Case 1 Case 2 Case 3 Case 4
List 1 40% 50% 60% 39%
Candidate 1A 30% [e] 30% [e] 50% [e] 20% [e]
Candidate 1B 10% 20% 10% [e] 19%
List 2 40% 30% 30% 33%
Candidate 2A 22% [e] 18% [e] 18% 18% [e]
Candidate 2B 18% 12% 12% 15%
list 3 20% 20% 10% 28%
Candidate 3A 11% 11% 6% 26%
Candidate 3B 9% 9% 4% 2%

The most common case is Case 2, in which one list gets a total voting that is higher than the other but both get exactly the same number of candidates elected, candidates 1A and 2A respectively. In the unlikely case that both lists get exactly the same number of votes each gets a candidate into office. Only in the case that List 1 doubles the voting of List 2 will List 1 be able to get two seats, even if, like in Case 3, the second elected candidate of the majority list received the fewest votes of all the candidates of the two majorities. The system makes it difficult for minority parties to elect candidates: in Case 4, candidate 3A receives the most votes, but under the binomial system, candidates 1A and 2A will be elected.

As can be seen, the binomial system acts to equalize the representation of the second majority to the point of making it roughly equal, or only slightly smaller, than that of the first majority. Furthermore, it acts to exclude any minority from the process, in practice generating a locked two-party, or two-bloc, system in which it is exceedingly difficult for one of the blocs to get an upper hand on the other. The table below posits the electoral results of the 2005 lower chamber parliamentary elections with three different voting systems.

, a centre-left coalition
Alianza, right wing conservatives Juntos Podemos Más, left wing progressives, ecologists, and others Fuerza Regional
, regionalist movement
Binomial 65 dip. 54.2% 54 dip. 45.0% 0 dip. 0.0% 1 dip. 0.83%
Direct Election 69 dip. 57.5% 50 dip. 41.6% 0 dip. 0.0% 1 dip. 0.83%
Proportional System 62 dip. 51.6% 46 dip. 38.3% 9 dip. 7.5% 1 dip. 0.83%


The binomial system, proponents argue, acts to stabilize the political situation by making it almost impossible for a single political bloc or coalition to make important choices in a one-sided manner.[4] This in turn leads to great political stability and prevents the emergence of the long-term personality-centred populist regimes that have been common throughout the history of Latin America. It has also been argued that it fosters consensus-building, debate and negotiation. Finally the point of representation is often cited in defence of the binomial system, as it provides a representation to the big minority that first-past-the-post systems don't.


Critics of this system argue that it makes for a flawed democracy, as it does not necessarily elect the candidate who received the most votes. Furthermore, it effectively excludes the smaller political forces that are not a part of either of the two big electoral alliances.


  1. ^ "Electoral reform in Chile: Tie breaker". The Economist. 14 February 2015. Retrieved 17 March 2015.
  2. ^ Maira, Luis (2001). «El amarre institucional del General Pinochet y las restricciones de la transición chilena». En Labastida, Julio; Camou, Antonio. Globalización, identidad y democracia: México y América Latina (I edición). México: Siglo Veintiuno Editores. p. 94. ISBN 968-23-2300-2.
  3. ^ Huneeus, Carlos. "Chile: A System Frozen by Elite Interests" (PDF). International Institute for Democracy and Electoral Assistance. Archived from the original (PDF) on 5 January 2015. Retrieved 17 March 2015.
  4. ^ Carey, John M.: "Las virtudes del sistema binomial", en Revista de Ciencia Política, Vol.26 N°1 (2006), pp. 226–235.