Cecily Zamora
The cube root law is an observation in political science that states that the number of members of a unicameral legislature, or of the lower house of a bicameral legislature, is about the cube root of the population being represented. The rule was devised by Estonian political scientist Rein Taagepera in his 1972 paper The size of national assemblies. The cube root law has been used to propose increasing the size of the United States House of Representatives so that the number of representatives would be the cube root of the US population as calculated in the most recent census. However, it has been claimed by Giorgio Margaritondo that the experimental data, including the dataset originally used by Taagepera in 1972, actually fits better to a function with a higher exponent, and that there is sufficient deviation from the cube root rule to question its usefulness.
| Characteristics | Values |
|---|---|
| Name | Cube Root Law |
| First described by | Galileo Galilei |
| Year first described | 1638 |
| Formula | A2 = A1(l2/l1)2 |
| Formula | V2 = V1(l2/l1)3 |
| Formula | P = ma/A |
| Formula | P' = x3ma/x2A |
| Formula | A = 0.1P^E |
| Formula | E = 0.45±0.03 |
What You'll Learn
- The cube root law is an observation in political science that the number of members of a unicameral legislature, or of the lower house of a bicameral legislature, is about the cube root of the population being represented
- The cube root law was devised by Estonian political scientist Rein Taagepera in his 1972 paper The size of national assemblies
- The cube root law has been used to propose increasing the size of the United States House of Representatives so that the number of representatives would be the cube root of the US population as calculated in the most recent census
- The cube root law has been criticised for being conceptually flawed
- The cube root law has been applied to the study of dust explosions
The cube root law is an observation in political science that the number of members of a unicameral legislature, or of the lower house of a bicameral legislature, is about the cube root of the population being represented
However, the cube root law has been criticised for its underlying reasoning being profoundly flawed. Firstly, it is derived from a mathematical average of a broad range of nations, which may be a plausible way to establish a benchmark but certainly does not establish an ideal standard given the heterogeneous mix of nations relative to their forms of government and the quality thereof. Secondly, it is said that the sizes of most of the national legislatures map closely to its cube root prediction, but this depends on what is meant by "close".
In a 2021 paper, physicist Giorgio Margaritondo evaluated Taagepera's original paper and concluded that the cube-root law was not derived from its data and the corresponding fit was arbitrarily forced. Margaritondo also observed that Taagepera's model assumed that each representative spends, on average, equal times for communications inside and outside the parliament, an arbitrary hypothesis that has unrealistic consequences. Margaritondo concluded that "accurately evaluating the 'optimal' size of a national assembly is illusory. And trying to inject additional factors besides the population cannot solve the above problems".
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The cube root law was devised by Estonian political scientist Rein Taagepera in his 1972 paper The size of national assemblies
The cube root law was first devised by Estonian political scientist Rein Taagepera in his 1972 paper, 'The Size of National Assemblies'. The cube root law is an observation in political science that the number of members of a unicameral legislature, or of the lower house of a bicameral legislature, is about the cube root of the population being represented.
The cube root law was derived from a mathematical average of a broad range of nations. While this may be a plausible way to establish a benchmark, it does not establish an ideal standard given the heterogeneous mix of nations relative to their forms of government and the quality thereof. The cube root law has been criticised for its underlying reasoning, which is profoundly flawed. The resulting increase in representation would not ameliorate any of the problems it is supposed to address.
The cube root law has been cited in numerous papers and articles, and is frequently used to determine the optimal size of legislative bodies. The cube root model was proposed by Taagepera, who posited that "efficiency is optimised" if the size of a national legislature is equal to the third root, or cube root, of that nation's total population. The cube root law is not a law, but a suggestion.
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The cube root law has been used to propose increasing the size of the United States House of Representatives so that the number of representatives would be the cube root of the US population as calculated in the most recent census
The cube root law is an observation in political science that the number of members of a unicameral legislature, or of the lower house of a bicameral legislature, is about the cube root of the population being represented. The cube root law has been used to propose increasing the size of the United States House of Representatives so that the number of representatives would be the cube root of the US population as calculated in the most recent census.
The cube root law was devised by Estonian political scientist Rein Taagepera in his 1972 paper "The size of national assemblies". The cube root law has been described as "profoundly flawed" and "conceptually flawed" by critics, who argue that it is derived from a mathematical average of a broad range of nations, and that it does not establish an ideal standard given the heterogeneous mix of nations relative to their forms of government and the quality thereof.
The cube root law has been used to propose increasing the size of the United States House of Representatives. The House of Representatives has had 435 members since the Reapportionment Act of 1929 was passed. If the US followed the cube root law, there would be 693 members of the House of Representatives based on the population at the 2020 Census. This proposal was endorsed by the New York Times editorial board in 2018.
However, critics argue that the cube root law is not a meaningful solution to the problem of increasing the size of the House of Representatives. Firstly, the cube root law does not take into account the diverse forms of government that comprise the nations to which it is applied. Secondly, the cube root law would result in far too few Representatives to have any material impact on the problems it is supposed to address. For example, if the size of the US House were increased to that indicated by the cube root law, it would have 692 Representatives, resulting in an average district size of 478,480. This would still be the largest congressional districts in the world and almost twice as large as second-place Mexico.
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The cube root law has been criticised for being conceptually flawed
The cube root law, also known as the cube-root model, is a concept in political science that suggests that the number of members of a unicameral legislature, or of the lower house of a bicameral legislature, is about the cube root of the population being represented. The cube root law was proposed by Estonian political scientist Rein Taagepera in his 1972 paper "The size of national assemblies".
- The cube-root law was not derived from its data and the corresponding fit was arbitrarily forced.
- The theoretical steps that were used to derive the cube-root formula incorrectly evaluated one of its key factors.
- The model assumed that each representative spends, on average, equal time on communications inside and outside the parliament, an arbitrary hypothesis that has unrealistic consequences.
- No evaluation of the "optimal" size based on a power law, including the cube-root one, can reach a meaningful accuracy.
Margaritondo's analysis revealed that the cube-root law was force-fitted onto the dataset, which helps to explain the significant disparities between the actual legislature sizes and their cube-root benchmarks. Furthermore, Margaritondo argued that no such equation can accurately determine the "optimal" size of a national assembly. He concluded that the cube-root law's foundations are fatally undermined and that it should not be used to evaluate the "optimal" parliament size for a country.
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The cube root law has been applied to the study of dust explosions
In the context of dust explosions, the cube root law is used to determine the optimal size of explosion relief vents. The law suggests that the area of the vent is proportional to the volume of the vessel raised to the two-thirds power. This approach takes into account the relationship between the vessel's volume and the flame thickness, which becomes significant when the flame thickness is comparable to the vessel's radius.
However, the cube root law has limitations when applied to dust explosions. It is only valid for geometrically similar vessels and when certain conditions are met, such as negligible flame thickness compared to the vessel radius. Additionally, the flame surfaces must be geometrically similar, and the burning velocity must be independent of pressure and temperature.
In the case of dust explosions, the flame thickness can be significant, and the cube root law may not hold. To address this limitation, a three-zone model has been developed to account for flame thickness and provide more accurate predictions of pressure evolution in confined dust explosions. This model considers the unburnt fuel ahead of the flame, the flame itself, and the burnt fuel behind it.
While the cube root law provides a starting point for understanding dust explosions, it should be used with caution and in conjunction with other models or experimental data to make accurate predictions.
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Frequently asked questions
The cube root law is an observation in political science that the number of members of a unicameral legislature, or of the lower house of a bicameral legislature, is about the cube root of the population being represented.
The cube root law formula is:
> {\displaystyle A_{2}=A_{1}\left({\frac {\ell _{2}}{\ell _{1}}}\right)^{2}} where
>
> {\displaystyle A_{1}} is the original surface area and
>
> {\displaystyle A_{2}} is the new surface area.
>
> {\displaystyle V_{2}=V_{1}\left({\frac {\ell _{2}}{\ell _{1}}}\right)^{3}} where
>
> {\displaystyle V_{1}} is the original volume,
>
> {\displaystyle V_{2}} is the new volume,
>
> {\displaystyle \ell _{1}} is the original length and
>
> {\displaystyle \ell _{2}} is the new length.
The cube root law is a mathematical principle that can be applied to a variety of scientific fields. It is not limited to high or low gravity.
