The highest averages method is one way of allocating seats proportionally for representative assemblies with party list voting systems. The plurality voting system is a Single-winner voting system often used to elect executive officers or to elect members of a legislative assembly which is based on single-member The two-round system (also known as the second ballot or runoff voting) is a Voting system used to elect a single winner The exhaustive ballot is a Voting system used to elect a single winner This article is about voting systems that use ranked ballots For alternative meanings see Preferential voting (disambiguation. The Condorcet candidate or Condorcet winner of an Election is the candidate who when compared with every other candidate is preferred by more voters A Condorcet method is any single-winner election method that meets the Condorcet criterion, that is which always selects the Condorcet winner, the candidate Copeland's method is a Condorcet method in which the winner is determined by finding the candidate with the most pairwise victories The Kemeny-Young method is a Voting system that uses Preferential ballots Pairwise comparison counts and sequence scores to identify the Minimax is often considered to be the simplest of the Condorcet methods It is also known as the Simpson-Kramer method, and the successive reversal method The Borda count can be combined with an Instant Runoff procedure to create hybrid election methods that are called Nanson method and Baldwin method. Ranked Pairs (RP or Tideman (named after its developer Nicolaus Tideman) is a Voting method that selects a single winner using votes that express The Schulze method is a Voting system developed in 1997 by Markus Schulze that selects a single winner using votes that express preferences. Bucklin voting is the name of a Voting system that can be used for single-member and multi-member districts. The Coombs' method, also called the Coombs rule is a Voting system created by Clyde Coombs used for single-winner Elections in which Instant-runoff voting ( IRV) is a Voting system used for single-winner elections in which voters have one vote and rank Candidates in order of The Borda count is a single-winner election method in which voters rank candidates in order of preference Approval voting is a single-winner voting system used for Elections Each voter may vote for (approve of as many of the candidates as they wish Range voting (also called ratings summation, average voting, cardinal ratings, score voting, 0–99 voting, or the score A voting system allows voters to choose between options often in an Election where candidates are selected for public office. Proportional representation (sometimes referred to as full representation or PR is a category of electoral formula aiming at a close match between the percentage of votes Cumulative voting (also accumulation voting or weighted voting) is a multiple-winner Voting system intended to promote Proportional representation Mixed member proportional representation, also termed mixed-member proportional voting and commonly abbreviated to MMP, is an ' additional member ' Party-list proportional representation systems are a family of Voting systems used in multiple-winner Elections (e Open list describes any variant of Party-list proportional representation where voters have at least some influence on the order in which a party's candidates are elected Closed list describes the variant of Party-list proportional representation where voters can (effectively only vote for political parties as a whole and thus The D'Hondt method (mathematically but not operationally equivalent to Jefferson's method, and Bader-Ofer method) is a Highest averages method for The largest remainder method is one way of allocating seats proportionally for representative assemblies with party list Voting systems. 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 Single transferable vote (STV is a preferential Voting system designed to minimize Wasted votes and provide Proportional representation The Quota Borda System or Quota Preference Score is a Voting system that was devised by the British philosopher Michael Dummett and first published in 1984 in his The matrix vote can be used when one group of people wishes to elect a smaller number of persons each of whom is to have a different assignment The Additional Member System (AMS is a branch of Voting systems in which some representatives are elected from geographic constituencies and others are elected under Parallel voting describes a mixed Voting system where voters in effect participate in two separate elections using different systems and where the results in one election have Cumulative voting (also accumulation voting or weighted voting) is a multiple-winner Voting system intended to promote Proportional representation The single non-transferable vote or SNTV is an Electoral system used in multi-member constituency elections Limited voting is a Voting system in which electors have fewer votes than there are positions available Sortition, also known as allotment, is an equal-chance method of selection by some form of lottery such as drawing coloured pebbles from a bag Party-list proportional representation systems are a family of Voting systems used in multiple-winner Elections (e A voting system allows voters to choose between options often in an Election where candidates are selected for public office.

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 , 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

With the modification, the methods are initially more similar