Huntington–Hill method

Last updated

The Huntington–Hill method of apportionment assigns seats by finding a modified divisor D such that each constituency's priority quotient (its population divided by D), using the geometric mean of the lower and upper quota for the divisor, yields the correct number of seats that minimizes the percentage differences in the size of subconstituencies. [1] When envisioned as a proportional electoral system, it is effectively a highest averages method of party-list proportional representation in which the divisors are given by , n being the number of seats a state or party is currently allocated in the apportionment process (the lower quota) and n+1 is the number of seats the state or party would have if it is assigned to the party list (the upper quota). Although no legislature uses this method of apportionment to assign seats to parties after an election, it was considered for House of Lords elections under the ill-fated House of Lords Reform Bill. [2]

Contents

The method is how the United States House of Representatives assigns the number of representative seats to each state – the purpose for which it was devised. It is credited to Edward Vermilye Huntington and Joseph Adna Hill. [3]

Allocation

In a legislative election under the Huntington–Hill method, after the votes have been tallied, the qualification value would be calculated. This step is necessary because in an election, unlike in a legislative apportionment, not all parties are always guaranteed at least one seat. If the legislature concerned has no exclusion threshold, the qualification value would be the Hare quota, or

,

where

In legislatures which use an exclusion threshold, the qualification value would be:

.

Every party polling votes equal to or greater than the qualification value would be given an initial number of seats, again varying if whether or not there is a threshold:

In legislatures which do not use an exclusion threshold, the initial number would be 1, but in legislatures which do, the initial number of seats would be:

with all fractional remainders being rounded up.

In legislatures elected under a mixed-member proportional system, the initial number of seats would be further modified by adding the number of single-member district seats won by the party before any allocation.

Determining the qualification value is not necessary when distributing seats in a legislature among states pursuant to census results, where all states are guaranteed a fixed number of seats, either one (as in the US) or a greater number, which may be uniform (as in Brazil) or vary between states (as in Canada).

It can also be skipped if the Huntington-Hill system is used in the nationwide stage of a national remnant system, because the only qualified parties are those which obtained seats at the subnational stage.

After all qualified parties or states received their initial seats, successive quotients are calculated, as in other Highest Averages methods, for each qualified party or state, and seats would be repeatedly allocated to the party or state having the highest quotient until there are no more seats to allocate. The formula of quotients calculated under the Huntington-Hill method is

where:

Example

Even though the Huntington–Hill system was designed to distribute seats in a legislature among states pursuant to census results, it can also be used, when putting parties in the place of states and votes in place of population, for the mathematically equivalent task of distributing seats among parties pursuant to an election results in a party-list proportional representation system. A party-list PR system requires large multi-member districts to function effectively.

In this example, 230,000 voters decide the disposition of 8 seats among 4 parties. Unlike the D'Hondt and Sainte-Laguë systems, which allow the allocation of seats by calculating successive quotients right away, the Huntington–Hill system requires each party or state have at least one seat to avoid a division by zero error. In the U.S. House of Representatives, this is ensured by guaranteeing each state at least one seat; in a single-stage PR election under the Huntington–Hill system, however, the first stage would be to calculate which parties are eligible for an initial seat.

This could be done by excluding any parties which polled less than the Hare quota, and giving every party which polled at least the Hare quota one seat. The Hare quota is calculated by dividing the number of votes cast (230,000) by the number of seats (8), which in this case gives a qualification value of 28,750 votes.

DenominatorVotesIs the party eligible or disqualified?
Party A100,000Eligible
Party B80,000Eligible
Party C30,000Eligible
Threshold28,750
Party D20,000Disqualified

Each eligible party is assigned one seat. With all the initial seats assigned, the remaining five seats are distributed by a priority number calculated as follows. Each eligible party's (Parties A, B, and C) total votes is divided by 1.41 (the square root of the product of 1, the number of seats currently assigned, and 2, the number of seats that would next be assigned), then by 2.45, 3.46, 4.47, 5.48, 6.48, 7.48, and 8.49. The 5 highest entries, marked with asterisks, range from 70,711 down to 28,868. For each, the corresponding party gets a seat.

For comparison, the "Proportionate seats" column shows the exact fractional numbers of seats due, calculated in proportion to the number of votes received. (For example, 100,000/230,000 × 8 = 3.48) [4]

Denominator1.412.453.464.475.486.487.488.49Initial
seats
Seats
won (*)
Total
Seats
Proportionate
seats
Party A70,711*40,825*28,868*22,36118,25715,43013,36311,7851343.5
Party B56,569*32,660*23,09417,88914,60612,34410,6909,4281232.8
Party C21,21312,2478,6606,7085,4774,6294,0093,5361011.0
Party DDisqualified00.7

If the number of seats was equal in size to the number of votes case for the qualified parties, this method would guarantee that the appointments would equal the vote shares of each party.

In this example, the results of the apportionment is identical to one under the D'Hondt system. However, as the District magnitude increases, differences emerge: all 120 members of the Knesset, Israel's unicameral legislature, are elected under the D'Hondt method. Had the Huntington–Hill method, rather than the D'Hondt method, been used to apportion seats following the elections to the 20th Knesset, held in 2015, the 120 seats in the 20th Knesset would have been apportioned as follows:

PartyVotesSeats (actual results, D'Hondt)Seats (hypothetical results, Huntington–Hill)Upper quota (Huntington–Hill)Geometric mean (Huntington–Hill)+/–
Likud 985,40830303130.500
Zionist Union 786,31324242524.500
Joint List 446,58313131413.490
Yesh Atid 371,60211111211.490
Kulanu 315,360109109.49–1
The Jewish Home 283,91089109.49+1
Shas 241,6137787.480
Yisrael Beiteinu 214,9066676.480
United Torah Judaism 210,1436676.480
Meretz 165,5295565.480
Source: CEC

Compared with the actual apportionment, Kulanu would have lost one seat, while The Jewish Home would have gained one seat.

Related Research Articles

Party-list proportional representation

Party-list proportional representation systems are a family of voting systems emphasizing proportional representation in elections in which multiple candidates are elected through allocations to an electoral list. They can also be used as part of mixed additional member systems.

Single transferable vote Proportional representation voting system

The single transferable vote (STV) is a voting system designed to achieve or closely approach proportional representation through the use of multiple-member constituencies and each voter casting a single ballot on which candidates are ranked. The preferential (ranked) balloting allows transfer of votes to produce proportionality, to form consensus behind select candidates and to avoid the waste of votes prevalent under other voting systems.

The electoral threshold, or election threshold, is the minimum share of the primary vote which a candidate or political party requires to achieve before they become entitled to any representation in a legislature. This limit can operate in various ways. For example, in party-list proportional representation systems an electoral threshold requires that a party must receive a specified minimum percentage of votes, either nationally or in a particular electoral district, to obtain any seats in the legislature. In multi-member constituencies using preferential voting, besides the electoral threshold, to be awarded a seat, a candidate is also required to achieve a quota, either on the primary vote or after distribution of preferences, which depends on the number of members to be return from a constituency.

The Droop quota is the quota most commonly used in elections held under the single transferable vote (STV) system. It is also sometimes used in elections held under the largest remainder method of party-list proportional representation. In an STV election the quota is the minimum number of votes a candidate must receive in order to be elected. Any votes a candidate receives above the quota are transferred to another candidate. The Droop quota was devised in 1868 by the English lawyer and mathematician Henry Richmond Droop (1831–1884) as a replacement for the earlier Hare quota.

The D'Hondt method or the Jefferson method is a highest averages method for allocating seats, and is thus a type of party-list proportional representation. The method described is named in the United States after Thomas Jefferson, who introduced the method for proportional allocation of seats in the United States House of Representatives in 1792, and in Europe after Belgian mathematician Victor D'Hondt, who described the methodology in 1878. There are two forms: closed list and open list.

The Webster/Sainte-Laguë method, often simply Webster method or Sainte-Laguë method, is a highest quotient method for allocating seats in party-list proportional representation used in many voting systems. It is named in Europe after the French mathematician André Sainte-Laguë and in United States after statesman and senator Daniel Webster. The method is quite similar to the D'Hondt method, but uses different divisors. In most cases the largest remainder method with a Hare quota delivers almost identical results. The D'Hondt method gives similar results too, but favors larger parties compared to the Webster/Sainte-Laguë method; the Webster/Sainte-Laguë method is generally seen as more proportional but risks an outcome where a party with more than half the votes can win fewer than half the seats. Often there is an electoral threshold, that is a minimum percentage of votes required to be allocated seats.

The highest averages method or divisor method is the name for a variety of ways to allocate seats proportionally for representative assemblies with party list voting systems. It 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 nth seat is allocated to the party whose column contains the nth largest entry in this table, up to the total number of seats available.

The largest remainder method is one way of allocating seats proportionally for representative assemblies with party list voting systems. It contrasts with various highest averages methods.

An apportionment paradox exists when the rules for apportionment in a political system produce results which are unexpected or seem to violate common sense.

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 largest remainder method party-list proportional representation voting systems. It is distinct from the Imperiali method, a type of highest average method. It is named after Belgian senator Pierre Imperiali.

The Hare quota is a formula used under some forms of the Single Transferable Vote (STV) system and the largest remainder method of party-list proportional representation. In these voting systems the quota is the minimum number of votes required for a party or candidate to capture a seat, and the Hare quota is the total number of votes divided by the number of seats.

The Hagenbach-Bischoff quota is a formula used in some voting systems based on proportional representation (PR). It is used in some elections held under the largest remainder method of party-list proportional representation as well as in a variant of the D'Hondt method known as the Hagenbach-Bischoff system. The Hagenbach-Bischoff quota is named for its inventor, Swiss professor of physics and mathematics Eduard Hagenbach-Bischoff (1833–1910)

The single transferable vote (STV) is a voting system based on proportional representation and ranked voting. Under STV, an elector's vote is initially allocated to his or her most-preferred candidate. After candidates have been either elected (winners) by reaching quota or eliminated (losers), surplus votes are transferred from winners to remaining candidates (hopefuls) according to the surplus ballots' ordered preferences.

Leveling seats, commonly known also as adjustment seats, are an election mechanism employed for many years by all Nordic countries in elections for their national legislatures. In 2013, Germany also introduced national leveling seats for their national parliament, the Bundestag. Leveling seats are seats of additional members elected to supplement the members directly elected by each constituency. The purpose of these additional seats is to ensure that each party's share of the total seats is roughly proportional to the party's overall shares of votes at the national level.

Wright system

The Wright system is a refinement of rules associated with proportional representation by means of the single transferable vote (PR-STV) electoral system. It was developed and written by Anthony van der Craats, a system analyst and life member of the Proportional Representation Society of Australia. It is described in a submission into a parliamentary review of the 2007 Australian federal election.

Schulze STV is a draft ranked voting system designed to achieve proportional representation. It is a single transferable vote (STV) voting system. It was invented by Markus Schulze who developed the Schulze method for resolving ties under the Condorcet method. It is similar to CPO-STV in that it compares possible winning sets of candidate outcomes pairwise and selects the Condorcet winner. However, unlike CPO-STV, it only compares outcomes that differ by a single candidate. Comparing outcomes that differ by more than one candidate is accomplished by finding the strongest path.

Electoral system Method by which voters make a choice between options

An electoral system or voting system is a set of rules that determine how elections and referendums are conducted and how their results are determined. Political electoral systems are organized by governments, while non-political elections may take place in business, non-profit organisations and informal organisations. These rules govern all aspects of the voting process: when elections occur, who is allowed to vote, who can stand as a candidate, how ballots are marked and cast, how the ballots are counted, how votes translate into the election outcome, limits on campaign spending, and other factors that can affect the result. Political electoral systems are defined by constitutions and electoral laws, are typically conducted by election commissions, and can use multiple types of elections for different offices.

Party-list representation in the House of Representatives of the Philippines

Party-list representation in the House of Representatives of the Philippines refers to a system in which 20% of the House of Representatives is elected. While the House is predominantly elected by a plurality voting system, known as a first-past-the-post system, party-list representatives are elected by a type of party-list proportional representation. The 1987 Constitution of the Philippines created the party-list system. Originally, the party-list was open to underrepresented community sectors or groups, including labor, peasant, urban poor, indigenous cultural, women, youth, and other such sectors as may be defined by law. However, a 2013 Supreme Court decision clarified that the party-list is a system of proportional representation open to various kinds of groups and parties, and not an exercise exclusive to marginalized sectors. National parties or organizations and regional parties or organizations do not need to organize along sectoral lines and do not need to represent any marginalized and underrepresented sector.

Hare–Clark electoral system

Hare-Clark is a type of single transferable vote electoral system of proportional representation used for elections in Tasmania and the Australian Capital Territory. The method for the distribution of preferences is similar to other voting systems in Australia, such as for the Australian Senate.

Apportionment in the Hellenic Parliament refers to those provisions of the Greek electoral law relating to the distribution of Greece's 300 parliamentary seats to the parliamentary constituencies, as well as to the method of seat allocation in Greek legislative elections for the various political parties. The electoral law was codified for the first time through a 2012 Presidential Decree. Articles 1, 2, and 3 deal with how the parliamentary seats are allocated to the various constituencies, while articles 99 and 100 legislate the method of parliamentary apportionment for political parties in an election. In both cases, Greece uses the largest remainder method.

References

  1. "Congressional Apportionment". NationalAtlas.gov. Archived from the original on 2009-02-28. Retrieved 2009-02-14.
  2. Draft House of Lords Reform Bill: report session 2010-12, Vol. 2. Google Books. 23 April 2012. ISBN   9780108475801 . Retrieved 6 November 2017.
  3. "The History of Apportionment in America". American Mathematical Society. Retrieved 2009-02-15.
  4. Note the slight favouring of the largest party over the smallest (if we subtract Proportionate seats from Total Seats Party A - the largest party - gets the highest total (0.5) while Party B only gets 0.2, Party C gets 0 and Party D gets -0.7)