science

Huntington–Hill method

Huntington–Hill method is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Huntington–Hill method rather than just read about it. In short: The Huntington–Hill method, sometimes called method of equal proportions, is a highest averages method for assigning seats in a legislature to political parties or states. Since 1941, this method has been used to apportion the 435 seats in the United States House of Representatives following the completion of each decennial census.

Key takeaways

Huntington–Hill method belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Huntington–Hill method to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Huntington–Hill method from memory before moving on to harder problems.

Reference excerpt

The Huntington–Hill method, sometimes called method of equal proportions, is a highest averages method for assigning seats in a legislature to political parties or states. Since 1941, this method has been used to apportion the 435 seats in the United States House of Representatives following the completion of each decennial census. The method minimizes the relative difference in the number of constituents represented by each legislator. In other words, the method selects the allocation such that no transfer of a seat from one state to another can reduce the percent error in representation for both states.

Apportionment method In this method, as a first step, each of the 50 states is given its one guaranteed seat in the House of Representatives, leaving 385 seats to be assigned. The remaining seats are allocated one at a time, to the state with the highest average district population, to bring its district population down. However, it is not clear if we should calculate the average before or after allocating an additional seat, and the two procedures give different results. Huntington-Hill uses a continuity correction as a compromise, given by taking the geometric mean of both divisors, i.e.:

A n = P n ( n + 1 ) {\displaystyle A_{n}={\frac {P}{\sqrt {n(n+1)}}}}

where P is the population of the state, and n is the number of seats it currently holds before the possible allocation of the next seat. Consider the reapportionment following the 2010 U.S. census: after every state is given one seat:

The largest value of A1 corresponds to the largest state, California, which is allocated seat 51. The 52nd seat goes to Texas, the 2nd largest state, because its A1 priority value is larger than the An of any other state. The 53rd seat goes back to California because its A2 priority value is larger than the An of any other state. The 54th seat goes to New York because its A1 priority value is larger than the An of any other state at this point. This process continues until all remaining seats are assigned. Each time a state is assigned a seat, n is incremented by 1, causing its priority value to be reduced.

Division by zero 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 party-list representation, small parties would likely be eliminated using some electoral threshold, or the first divisor can be modified.

Example Consider an example to distribute 8 seats between three parties A, B, C having respectively 100,000, 80,000 and 30,000 votes. 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 √2 • 1 ≈ 1.41, then by approximately 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.

See also Edward Vermilye Huntington Highest averages method Joseph Adna Hill

References

Illustrations

Worked examples

Example 1 — a first encounter with Huntington–Hill method

Start with the simplest possible case. Write down what Huntington–Hill method claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Huntington–Hill method before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Huntington–Hill method ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Huntington–Hill method

In research: Huntington–Hill method appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Huntington–Hill method in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Huntington–Hill method is common in secondary-school and first-year university syllabi. It links to neighbouring topics Apportionment methods, so understanding it makes those chapters shorter.
In everyday life: Look for Huntington–Hill method outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Huntington–Hill method in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Huntington–Hill method means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Huntington–Hill method out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Huntington–Hill method in simple terms?

Why does Huntington–Hill method matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Huntington–Hill method?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Huntington–Hill method.