Electoral methodsThis series is part of thePolitics and the Election series. A voting system allows voters to choose between options often in an Election where candidates are selected for public office. Politics Politics is the process by which groups of people make decisions An election is a Decision-making process by which a population chooses an individual to hold formal office Single memberMulti-memberProportional representationSemi-proportional representationNon-proportional multi-memberrepresentationRandom selectionSortition Politics Portal  view • talk • edit

The highest averages method requires the number of votes for each party to be divided successively by a series of divisors, and seats are allocated to parties that secure the highest resulting quotient or average, up to the total number of seats available. The most widely used is the d'Hondt formula, using the divisors 1,2,3,4. The D'Hondt method (mathematically but not operationally equivalent to Jefferson's method, and Bader-Ofer method) is a Highest averages method for . . The Sainte-Laguë method divides the votes with odd numbers (1,3,5,7 etc). The Sainte-Laguë method of the highest average (equivalent to Webster's method or divisor method with standard rounding is one way of allocating seats proportionally for The Sainte-Laguë method can also be modified, for instance by the replacement of the first divisor by 1. 4, which in small constituencies has the effect of prioritizing proportionality for larger parties over smaller ones at the allocation of the first few seats.

Another highest average method is called Imperiali (not to be confused with the Imperiali quota which is a Largest remainder method). The Imperiali quota is a formula used to calculate the minimum number or quota, of votes required to capture a seat in some forms of single transferable vote or The largest remainder method is one way of allocating seats proportionally for representative assemblies with party list Voting systems. The divisors are 2,3,4 etc. It is used only in Belgian municipal elections. The Belgian municipal elections 2006 took place on Sunday October 8, 2006. In the Huntington-Hill method, the divisors are given by $\sqrt{n(n+1)}$, which makes sense only if every party is guaranteed at least one seat: this is used for allotting seats in the US House of Representatives (while this is not strictly speaking an election, it nevertheless uses a highest average method). The Huntington-Hill method of apportionment assigns seats by finding a modified divisor D such that each constinuency's quotient (population divided by D) when rounded United States congressional apportionment is the redistribution of the 435 seats in the United States House of Representatives among the 50 states in consequence

In addition to the procedure above, highest averages methods can be conceived of in a different way. For an election, a quota is calculated, usually the total number of votes cast divided by the number of seats to be allocated (the Hare quota). The Hare quota (also known as the simple quota) is a formula used under some forms of the Single Transferable Vote (STV system and the Largest remainder method Parties are then allocated seats by determining how many quotas they have won, by dividing their vote totals by the quota. Where a party wins a fraction of a quota, this can be rounded down or rounded to the nearest whole number. Rounding down is equivalent to using the d'Hondt method, while rounding to the nearest whole number is equivalent to the Sainte-Laguë method. However, because of the rounding, this will not necessarily result in the desired number of seats being filled. In that case, the quota may be adjusted up or down until the number of seats after rounding is equal to the desired number.

The tables used in the d'Hondt or Sainte-Laguë methods can then be viewed as calculating the highest quota possible to round off to a given number of seats. For example, the quotient which wins the first seat in a d'Hondt calculation is the highest quota possible to have one party's vote, when rounded down, be greater than 1 quota and thus allocate 1 seat. The quotient for the second round is the highest divisor possible to have a total of 2 seats allocated, and so on.

An alternative to the highest averages method is the largest remainder method, which use a minimum quota which can be calculated in a number of ways. The largest remainder method is one way of allocating seats proportionally for representative assemblies with party list Voting systems.

## Comparison between the d'Hondt and Sainte-Laguë methods

### The unmodified Sainte-Laguë method shows differences for the first mandates

d'Hondt method unmodified Sainte-Laguë method parties votes quotient 1 2 3 4 5 6 seat Yellows Whites Reds Greens Blues Pinks Yellows Whites Reds Greens Blues Pinks 47,000 16,000 15,900 12,000 6,000 3,100 47,000 16,000 15,900 12,000 6,000 3,100 mandate 47,000 16,000 15,900 12,000 6,000 3,100 47,000 16,000 15,900 12,000 6,000 3,100 23,500 8,000 7,950 6,000 3,000 1,550 15,667 5,333 5,300 4,000 2,000 1,033 15,667 5,333 5,300 4,000 2,000 1,033 9,400 3,200 3,180 2,400 1,200 620 11,750 4,000 3,975 3,000 1,500 775 6,714 2,857 2,271 1,714 875 443 9,400 3,200 3,180 2,400 1,200 620 5,222 1,778 1,767 1. 333 667 333 7,833 2,667 2,650 2,000 1,000 517 4,273 1,454 1,445 1,091 545 282 47,000 47,000 23,500 16,000 16,000 15,900 15,900 15,667 15,667 12,000 12,000 9,400 11,750 6,714 9,400 6,000 8,000 5,333 7,950 5,300

### With the modification, the methods are initially more similar

d'Hondt method modified Sainte-Laguë method parties votes quotient 1 2 3 4 5 6 seat Yellows Whites Reds Greens Blues Pinks Yellows Whites Reds Greens Blues Pinks 47,000 16,000 15,900 12,000 6,000 3,100 47,000 16,000 15,900 12,000 6,000 3,100 mandate 47,000 16,000 15,900 12,000 6,000 3,100 33,571 11,429 11,357 8,571 4,286 2,214 23,500 8,000 7,950 6,000 3,000 1,550 15,667 5,333 5,300 4,000 2,000 1,033 15,667 5,333 5,300 4,000 2,000 1,033 9,400 3,200 3,180 2,400 1,200 620 11,750 4,000 3,975 3,000 1,500 775 6,714 2,857 2,271 1,714 875 443 9,400 3,200 3,180 2,400 1,200 620 5,222 1,778 1,767 1. 333 667 333 7,833 2,667 2,650 2,000 1,000 517 4,273 1,454 1,445 1,091 545 282 47,000 33,571 23,500 15,667 16,000 11,429 15,900 11,357 15,667 9,400 12,000 8,571 11,750 6,714 9,400 5,333 8,000 5,300 7,950 5,222

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