Proportional Voting Systems

There are a handful of different proportional voting and allocation systems, specifically

Quota Methods

The Hare Niemayer or Vinton is the largest remainder method, which is sometimes generalized with the use of different quotas:

The largest remainder method requires the numbers of votes for each party to be divided by a quota representing the number of votes required for a seat (i.e. usually the total number of votes cast divided by the number of seats, or some similar formula). The result for each party will usually consist of an integer part plus a fractional remainder. Each party is first allocated a number of seats equal to their integer. This will generally leave some seats unallocated: the parties are then ranked on the basis of the fractional remainders, and the parties with the largest remainders are each allocated one additional seat until all the seats have been allocated. This gives the method its name.

Hare quota (also called Hamilton): votes/seats 

Droop quota: 1+votes/(1+seats)

Hagenbach-Bischoff quota: votes/(1+seats)

Imperiali quota: votes/(2+seats)

The quota-method can also be used in an iterative approach, which mostly yields in the same result. An other alternative is too allocate all unallocated seats to the largest party.

Divisor Methods

The highest quotient and highest averages methods is defined as follows:

The highest averages method requires the number of votes for each party to be divided successively by a series of divisors. This produces a table of quotients, or averages, with a row for each divisor and a column for each party. The n'th seat is allocated to the party whose column contains the n'th largest entry in this table, up to the total number of seats available

The series of devisors are defined as follows (D'Hondt is also called Jefferson in the US and Hagenbach-Bischoff in Switzerland, Sainte-Lague is also called Webster in the US:

Generally D`Hondt (round-down) favours large parties while Adams (round-up) favours smaller parties while Sainte-Lague (artithmetic avergae), Hill Huntington (geometric mean) and Dean (harmonic mean) or generally almost identical in their outcome.

In a future post we will look at the actual implications.