Home > 3.2 Proportional systems > Report on Electoral Systems - Overview of available solutions and selection criteria
 
 
 
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Paragraph 62
 

It is rarely possible to distribute all the seats using quota methods. At the end of the first distribution, there very often remain unrepresented votes and seats to be allocated. Accordingly, a second distribution has to be carried out using one of the following methods:


- The largest remainder method: using this system, the list with the highest number of unrepresented votes at the end of the first distribution obtains one seat. The operation is repeated until all the seats unfilled at the end of the first distribution have been allocated. 


This method is by far one of the most favourable for small lists, thereby tending to encourage a proliferation of small parties. Moreover, the lower the number of available seats, the more this system favours small political groupings. The largest remainder method also suffers from the disadvantage that it does not take account of the relative strengths of the parties, that is to say the number of seats obtained during the first distribution. On top of this, a number of paradoxes, such as the “Alabama paradox”, are associated with this method.


- The strongest lists method: this system provides for those seats which remained unfilled at the end of the first distribution to be allocated to the lists or list obtaining the greatest number of votes cast. This system markedly favours the large parties. This method, which was only infrequently used in the past, is not used any more today.


- The highest average method: this is the system in most widespread use internationally. Under this method, the number of votes cast for each of the lists (V1) is divided by the number of seats which the list in question obtained during the first distribution (S1), to which a fictitious seat is added. The list which has the highest average per seat is then allocated the seat at stake. This operation is repeated as many times as necessary until all the vacant seats have been allocated. During the first distribution of seats, either the simple quota or theHagenbach-Bischoff quota may be used.


Average votes per seat = V1/(S1+1 fictitious seat)

This system tends to put large parties at an advantage and to exclude small parties from the distribution of seats. It also guarantees that coalitions will obtain at least as many seats as they would have obtained if the parties belonging to them had stood as single parties. Lastly, mention should be made of a variant of the highest average method, the Balinski-Young method. First, an initial distribution of seats is carried out using the Hare quota. Next the highest average method is used as described above with one variant. The division is carried out once only and the seats go to the lists with the highest average. Consequently, no party obtains more than one of the remaining seats; this has the effect of reducing the overrepresentation of large parties.