The Dalton transfer principle may not be a good way to judge increases in polarization (for a definition, see Esteban and Ray [1994] and Wolfson [1994]). To see this, begin with a society in which incomes take all values in $100 increments between $100 and $1000, and in which an equal proportion of the population (1/10) occupies each of these classes. Show this income distribution in a diagram with incomes on the horizontal axis and population proportions on the vertical axis. Now draw another diagram with half the population at the income level $250, and another half at income level $750. Intuitively rank these two income distributions: which one has more scope for social unrest, which one might display a greater awareness of inequality, and so on.

Now show that the second distribution can be obtained by a sequence of progressive Dalton transfers from the first. Do you feel that your intuition is in line with the transfer principle, in this example?