** Analyzing a classic paper that has influenced the size of parliaments for almost half a century, an EPFL physicist discovers major flaws with its methodology, challenges its fundamental assumptions, and calls for a complete and careful re-think of its government-governing rule. **

What is the best size of a parliament? That is a question at the center of many countries today, including the 2020 referendum in Italy where almost 70% of voters selected to slash the number of members of parliament by about a third. Among others, the complex issue involves matters of governing efficiency, logistics, and financial costs.

But one thing many people might not realize is that there is a science behind all this. In 1972, political scientist Rein Taagepera published a seminal paper proposing that the ideal size of a parliament corresponds to the cube root of the country’s population: *A=αP _{o}^{1/3}*, where A is the parliament size, P

_{o}is the population size, and α is a constant. In general terms, the bigger a country’s population, the bigger its parliament ought to be.

Taagepera’s famous -cube-root law- was quickly taken up by governments, but hasn-t been without critics: In 2007 and 2012, researchers used empirical data to come up with a square-root relationship rather than a cube-root, while another paper in 2019 questioned the actual cause-effect sequence that lies at the foundation of Taagepera’s law. So while all agree that a bigger parliament would be needed for a bigger country, the exact relation has remained a matter of dispute.

Now, physicist Giorgio Margaritondo, Professor Emeritus with EPFL’s School of Basic Sciences, has published a paper analyzing Taagepera’s model. Published in *Frontiers in Physics* , his findings challenge the math behind the paper and the accuracy of its predictions, and raises concerns about the way the data was used.

-I was astonished,- says Margaritondo. -The law has been, - and still is - widely used, but the paper’s flaws have gone undetected for half a century.- He points out that Taagepera’s original paper actually evaluates the actual size of a parliament not its -optimal- size.

**Four fatal flaws**

-The original derivation of the -cube-root law- is affected by fatal mistakes, unnoticed for half a century,- says Margaritondo. Taking a physicist’s view, he analyzed the 1972 paper, and discovered four flaws.

First, that the cube-root law was not derived from the paper’s data and that the corresponding trend that led to the formula was -arbitrarily forced-.

Second, that the theoretical steps used to derive the formula incorrectly evaluated one of its key factors.

The third flaw has to do with real-world politics: Taagepera’s model assumes that each member of parliament spends on average an equal amount of time communicating inside and outside parliament, which Margaritondo describes as a -an arbitrary hypothesis that has unrealistic consequences.-

Finally, there is generally no evaluation of -optimal- size based on a power law that can reach meaningful accuracy, and that includes the cube-root law.

**Square, not cube**

Margaritondo’s suspicion was that the paper’s data could better fit a broader, more -general- formula that the cube-root law. But in the paper, Taagepera challenged this notion by claiming that the it would be a -dead end- and that it would be -*more fruitful to look for a plausible theoretical model which would fit the observed general trend*-.

-This argument is fundamentally flawed from a physicist’s point of view,- writes Margaritondo. -It considers only one hypothesis, renouncing *a priori* to demonstrate its superiority with respect to others.- Spurred on, Margaritondo used the paper’s original data and applied to them the same statistical fitting method that Taagepera had in 1972. Except that here, he used a similar, but more general formula to fit the data: *A=αP _{o}^{n}*. Here the cube root changes and the exponent is n.

Applying this equation to the 1972 data, Margaritondo discovered that n equals 0.45 Â± 0.03. This is actually closer to a square-root law, already proposed in 2012 by the researchers Emmanuelle Auriol Robert J. Gary-Bobo. -Even the original data did not support the cube-root law,- says Margaritondo. -The fit was arbitrarily forced.-

**Beyond math**

In short, it seems that, at least for now, physics cannot decide what the optimal parliament size is based on math alone, but it might be time to abandon a cherished rule that has governed governments for almost half a century.

-To think that we can accurately derive the -optimal- parliament size with a power law is an illusion,- says Margaritondo. -It-s akin to fake news: the wrong use of -scientific- arguments to propagate political notions.-