You're using an outdated browser. Please upgrade to a modern browser for the best experience.
Huntington–Hill Method
Edit

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. 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 D=n(n+1), 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. 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 – and the Census Bureau calls it the method of equal proportions. It is credited to Edward Vermilye Huntington and Joseph Adna Hill.

vermilye huntington–hill census

1. 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 could be the Hare quota[1], or

totalvotestotalseats,

where

  • total votes is the total valid poll; that is, the number of valid (unspoilt) votes cast in an election.
  • total seats is the total number of seats to be filled in the election.

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

exclusionthreshold[percentage](totalvotes100).

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:

exclusionthreshold[percentage](totalseats100)

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

An=Vs(s+1)

where:

  • V is the population of the state or the total number of votes that party received, and
  • s is the number of seats that the state or party has been allocated so far.

1.1. 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.[1] 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.

Denominator Votes Is the party eligible or disqualified?
Party A 100,000 Eligible
Party B 80,000 Eligible
Party C 30,000 Eligible
Threshold 28,750
Party D 20,000 Disqualified

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 another 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). If the "Total Seats" column is less than the "Proportionate seats" column (Parties C[2] and D in this example) the party is under-represented. Conversely, if the "Total Seats" column is greater than the "Proportionate seats" column (Parties A and B in this example) the party is over-represented.[3]

Denominator 1.41 2.45 3.46 4.47 5.48 6.48 7.48 8.49 Initial
seats
Seats
won (*)
Total
Seats
Proportionate
seats[4]
Party A 70,711* 40,825* 28,868* 22,361 18,257 15,430 13,363 11,785 1 3 4 3.5
Party B 56,569* 32,660* 23,094 17,889 14,606 12,344 10,690 9,428 1 2 3 2.8
Party C 21,213 12,247 8,660 6,708 5,477 4,629 4,009 3,536 1 0 1 1.0
Party D Disqualified 0 0.7

If the number of seats was equal in size to the number of votes cast, this method would guarantee that the apportionments 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[5]. 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:

Party Votes Huntington–Hill D'Hondt[5] +/–
(hypothetical) (actual)
Last Priority[6] Next Priority[7] Seats Seats
width=2px bgcolor="Template:Likud/meta/color" | Likud 985,408 33408 32313 30 30 0
  Zionist Union 786,313 33468 32101 24 24 0
width=2px bgcolor="Template:Joint List/meta/color"| Joint List 446,583 35755 33103 13 13 0
bgcolor="Template:Yesh Atid/meta/color" | Yesh Atid 371,602 35431 32344 11 11 0
bgcolor="Template:Kulanu/meta/color" | Kulanu 315,360 37166 33242 9 10 –1
bgcolor="Template:The Jewish Home/meta/color" | The Jewish Home 283,910 33459 29927 9 8 +1
bgcolor="Template:Shas/meta/color" | Shas 241,613 37282 32287 7 7 0
bgcolor="Template:Yisrael Beiteinu/meta/color" | Yisrael Beiteinu 214,906 39236 33161 6 6 0
bgcolor="Template:United Torah Judaism/meta/color" | United Torah Judaism 210,143 38367 32426 6 6 0
bgcolor="Template:Meretz/meta/color" | Meretz 165,529 37013 30221 5 5 0
Source: CEC

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

References

  1. Other quotas could be used instead, such as the Droop quota.
  2. Party C's proportion is actually 1.04
  3. While this example favors the largest parties (Parties A and B), if a different number of seats were apportioned, other parties would be favored. In short, the largest party is not always favored.For example, if there were 12 seats instead of 8, then Party C would be the only over-represented party (since Party D would have qualified) with two full seats while proportionately deserving only 1.6 seats.
  4. This proportionality is based on the total votes. If instead it was based on the qualified votes (i.e., reducing the total 230,000 votes by the disqualified 20,000 votes for Party D), the proportionate seats would be: Party A - 3.8 seats, Party B - 3.0 seats, and Party C - 1.1 seats.
  5. The method used for the 20th Knesset was actually a modified D'Hondt, called the Bader-Ofer method. This modification allows for spare vote agreements between parties.
  6. This is each party's last priority number which resulted in a seat being gained by the party. Likud gained the last seat (the 120th seat allocated). Each priority number in this column is greater than any priority number in the Next Priority column.
  7. This is each party's next priority number which would result in a seat being gained by the party. Kulanu would have gained the next seat (if there were 121 seats in the Knesset). Each priority number in this column is less than any priority number in the Last Priority column.
More
Related Content
A partially ordered set (or a poset, for short) is a set endowed with a partial order relation, i.e., with a reflexive, anti-symmetric, and transitive binary relation. As mathematical objects, posets have been intensively studied in the last century, coming to play essential roles in pure mathematics, logic, and theoretical computer science. More recently, they have been increasingly employed in data analysis, multi-criteria decision-making, and social sciences, particularly for building synthetic indicators and extracting rankings from multidimensional systems of ordinal data. Posets naturally represent systems and phenomena where some elements can be compared and ordered, while others cannot be and are then incomparable. This makes them a powerful data structure to describe collections of units assessed against multidimensional variable systems, preserving the nuanced and multi-faceted nature of the underlying domains. Moreover, poset theory collects the proper mathematical tools to treat ordinal data, fully respecting their non-numerical nature, and to extract information out of order relations, providing the proper setting for the statistical analysis of multidimensional ordinal data. Currently, their use is expanding both to solve open methodological issues in ordinal data analysis and to address evaluation problems in socio-economic sciences, from multidimensional poverty, well-being, or quality-of-life assessment to the measurement of financial literacy, from the construction of knowledge spaces in mathematical psychology and education theory to the measurement of multidimensional ordinal inequality/polarization.
Keywords: incomparability; formal concept analysis; Hasse diagram; lattice; multidimensional ordinal data; multi-indicator system; order relation; ranking; socio-economic assessment; synthetic indicators
The increasing complexity of social science data and phenomena necessitates using advanced analytical techniques to capture nonlinear relationships that traditional linear models often overlook. This chapter explores the application of machine learning (ML) models in social science research, focusing on their ability to manage nonlinear interactions in multidimensional datasets. Nonlinear relationships are central to understanding social behaviors, socioeconomic factors, and psychological processes. Machine learning models, including decision trees, neural networks, random forests, and support vector machines, provide a flexible framework for capturing these intricate patterns. The chapter begins by examining the limitations of linear models and introduces essential machine learning techniques suited for nonlinear modeling. A discussion follows on how these models automatically detect interactions and threshold effects, offering superior predictive power and robustness against noise compared to traditional methods. The chapter also covers the practical challenges of model evaluation, validation, and handling imbalanced data, emphasizing cross-validation and performance metrics tailored to the nuances of social science datasets. Practical recommendations are offered to researchers, highlighting the balance between predictive accuracy and model interpretability, ethical considerations, and best practices for communicating results to diverse stakeholders. This chapter demonstrates that while machine learning models provide robust solutions for modeling nonlinear relationships, their successful application in social sciences requires careful attention to data quality, model selection, validation, and ethical considerations. Machine learning holds transformative potential for understanding complex social phenomena and informing data-driven psychology, sociology, and political science policy-making.
Keywords: machine learning in social sciences; nonlinear relationships; model interpretability; predictive analytics; imbalanced data handling
A mixed-methods approach combines qualitative and quantitative research methodologies to provide a comprehensive understanding of complex social phenomena in healthcare. This approach leverages the strengths of both methodologies to address research questions that cannot be fully answered by a single method. While quantitative data offer measurable patterns and generalizability, qualitative research provides critical insights into the human experiences, cultural contexts, and systemic factors that underlie these patterns, and such elements are often missed by purely statistical analyses. Notably, qualitative components can uncover why interventions succeed or fail in real-world settings, adding explanatory power to quantitative results. By integrating numerical data analysis with in-depth contextual insights, mixed-methods research enables researchers to explore, explain, and generalize findings in healthcare settings more holistically than either method could achieve alone.
Keywords: mixed-methods research; healthcare; qualitative research; quantitative research; social phenomena; triangulation
World Population Day is an annual observance held on July 11 to raise awareness about global population issues, including population growth, reproductive health, gender equality, and sustainable development. Established by the United Nations Development Programme (UNDP) in 1989, the day commemorates the approximate date when the world's population reached five billion in 1987.
Keywords: World Population Day; reproductive health; gender equality
Historical sociology is a subfield of sociology that examines how social structures, institutions, and processes evolve over time. It integrates historical analysis and sociological theory to understand long-term social transformations, including changes in power, economy, culture, and social relations. Historical sociology draws from classical sociological traditions, including the works of Karl Marx, Max Weber, and Émile Durkheim, and is used to analyze phenomena such as state formation, revolutions, capitalism, colonialism, and social movements.
Keywords: Historical Sociology; Social Change and Continuity; Comparative-Historical Analysis; Sociology of Modernity
Upload a video for this entry
Information
Subjects: Others
Contributor MDPI registered users' name will be linked to their SciProfiles pages. To register with us, please refer to https://encyclopedia.pub/register :
View Times: 2.1K
Entry Collection: HandWiki
Revisions: 2 times (View History)
Update Date: 06 Dec 2022
Academic Video Service