The negotiations that produced the US constitution left us with a democracy that's not quite representative. Even the most sparsely populated states have a single representative, and every state has ended up with two senators. That means that very populous states, like California, have fewer representatives per capita than places like Wyoming.

According to an analysis released by PNAS, being well represented pays off. States with the most representatives per capita also end up taking home the most federal cash per capita. And this isn't just a peculiarity of the US system; comparisons across nine countries shows that the same thing happens in Europe, South America, and Australia.

The authors aren't the first ones to look at this issue, but the previous studies have often been limited and US-centric. In contrast, the authors built a database for nine countries in which representation on a state or provincial level is disproportionate: Argentina, Australia, Brazil, Canada, Germany, Mexico, Spain, Switzerland, and the United States. They also obtained several decades worth of fiscal data on each of them, providing a broader perspective that covers time periods before or after reapportionment brought representation closer into line with population.

The analysis is quite simple: take the total representatives and the national population, and figure out how many legislators per capita there are. Then do the same calculation with individual states and provinces, and figure out how badly they differ from the national value. That creates a simple index for representation, and a similar process can provide an equivalent index for the amount of national budget expenditures that flow to each state. With those in hand, it's a simple matter to see if there's a correlation between the two.

The initial analysis showed that over-represented states are clearly the beneficiaries of fiscal largesse—they take home more national money than their less-represented peers. The cross-country analysis might suggest that this effect is robust, but the authors did extensive controls, looking at whether money flows disproportionately to poorer provinces, the impact of reapportionment of representation, the impact of sparse population, etc. None of these were sufficient to change the overall conclusion: if you're better represented, you get more money.

The authors were even able to confirm that this wasn't simply a hangover from whatever compromise produced the disproportionate representation in the first place. With the exception of Spain, all of the countries have added additional provinces since their representation system originated—in Germany's case, it added all of East Germany. Even though these late-comers didn't participate in making the rules for representation, their budgetary situation fell right in line with the states and provinces that had been there from the start.

How much money is involved? The most extreme case is in Brazil, where states in the northeast of the country get five times the amount of money per capita compared to the most under-represented state, Sao Paulo. Argentina has similar examples. Things are less severe elsewhere, but in the US, Australia, and Europe, the most underrepresented states only get about half the per-capita expenditures of the most over-represented ones.

On some level, these inequalities violate our general impression of democratic fairness. But for most countries, they've been around for decades, if not centuries, and the populaces involved have become very comfortable with them, with only very sporadic and poorly heeded calls for reform. Many nations, however, are just beginning to experiment with representative democracy, and the road for a number of them has already been bumpy. The authors warn that the sorts of trends we see in mature democracies might cause problems there, writing, "It is possible that in an unstable new federation characterized by mutual mistrust and hostility, highly visible and disproportionate fiscal flows to overrepresented regions could generate a challenge to the legitimacy of the union."

PNAS, 2011. DOI: 10.1073/pnas.1019061108 (About DOIs).