Pareto or log-normal? A recursive-truncation approach to the distribution of (all) cities

Traditionally, it is assumed that the population size of cities in a country follows a Pareto distribution. This assumption is typically supported by nding evidence of Zipf's Law. Recent studies question this nding, highlighting that, while the Pareto distribution may t reasonably well when the data is truncated at the upper tail, i.e. for the largest cities of a country, the log-normal distribution may apply when all cities are considered. Moreover, conclusions may be sensitive to the choice of a particular truncation threshold, a yet overlooked issue in the literature. In this paper, then, we reassess the city size distribution in relation to its sensitivity to the choice of truncation point. In particular, we look at US Census data and apply a recursive-truncation approach to estimate Zipf's Law and a non-parametric alternative test where we consider each possible truncation point of the distribution of all cities. Results con rm the sensitivity of results to the truncation point. Moreover, repeating the analysis over simulated data con rms the di culty of distinguishing a Pareto tail from the tail of a log-normal and, in turn, identifying the city size distribution as a false or a weak Pareto law.

The Liberal Ethics of Non-Interference and the Pareto Principle

We analyse the liberal ethics of non-interference applied to social choice. A liberal principle capturing noninterfering views of society and inspired by John Stuart Mill s conception of liberty, is examined. The principle captures the idea that society should not penalise agents after changes in their situation that do not a¤ect others. An impossibility for liberal approaches is highlighted: every social decision rule that satis es unanimity and a general principle of noninterference must be dictatorial. This raises some important issues for liberal approaches in social choice and political philosophy.