To illustrate the problem, I have calculated a figure of relative poverty for a hypothetical re-united Austro-Hungary. I have taken income, measured in price-level-adjusted US dollars, from a recent OECD report. Unfortunately, the income distribution is only reported per decile instead of per percentile, so I have had to make the assumption that within each decile the distance between any two percentiles is the same. Nevertheless, there is enough information to provide a pretty good estimate.
Officially, poverty in Hungary (12.3%) is currently more than a full percentage point lower than in Austria (13.4%). But after re-unifying the former Habsburg Empire, the new median income earner either belongs to the second-poorest decile of Austria, or to the second-richest decile of Hungary (these strata overlap).
In Austria, only 14% earn less than the new median income, compared with 83% in Hungary. The relative poverty rate of Austro-Hungary is 26%. However, the poverty threshold, set at 60% of the median income, is lower than the average income of the lowest income decile in Austria. Under the assumption explained above, the poverty rate falls to just 3% in Austria but almost quadruples to 46% in Hungary.
In absolute terms, no individual has got richer or poorer. Yet a simple boundary change has apparently driven 3 million Hungarians into poverty. This demonstrates how easily relative poverty data can be manipulated. Clearly public policy should not be based on such flawed measures.