Parliamentary Dynamics

What is the optimal size of a parliament? What factors affect parliamentary efficiency?

We apply tools from network theory and complexity science to unravel the emerging dynamics of representative democracy.

An important question in representative democracies is how to determine the optimal parliament size of a given country. Currently, this is a particularly hot topic a number of western democracies are looking into downsizing their chambers’ size whilst some, Italy for instance, are already starting to cut down on the number of MPs.

According to an old conjecture, known as the cubic root law, there is a fairly universal power-law relation, with a 1/3 exponent, between the size of an elected parliament and the country’s population. Empirical data in modern European countries support such universality but are consistent with a larger exponent. Recent theoretical works also point to the same direction.

Our work discusses this intriguing regularity and the current state of social/political science research on the topic through the medium of a growing network model for a complex society organised in electoral constituencies. Following our novel network approach, we are able to predict the optimal number of representatives and show that it naturally scales as the square root of the size of the population - a finding that is qualitatively confirmed by the empirical analysis of real-world data and in line with the new “square root law” paradigm arising from the quantitative political science literature.



  • Dept. of Mathematics King's College
    London Strand London WC2R 2LS
    United Kingdom

  • +44 020 7848 2864