Inequality Regimes and Rawlsian Growth Rates: Some thoughts on the evolution of inequality 1960-2010, with special reference to Venezuela

(Mostly an excuse to play with the Standardized Worldwide Income Inequality Database, compiled by Frederick Solt, which I just discovered. This post also belongs, loosely speaking, to my long-running series on the quantitative history of political regimes. R code for everything in this blogpost available in this Git repository; you would need to download the dataset separately).

Inequality is difficult to measure. Socially relevant inequalities are manifold, and measurable inequalities in money income are not always especially important. (In the formerly communist states of Eastern Europe income was very evenly distributed; yet this did not mean that there were no important social inequalities). Even inequality in money income is not easy to measure properly. Most existing data is not very comparable accross countries or years, and it is often not even clear to what income concept the sorts of inequality measures people typically use to make a point in political discourse refer to: does it refer to after-tax, after-transfer income or to "market" income? Does it refer to individual or household income? What sorts of things are counted as "income"? How do we account for access to high-quality public services? At best, measures of income inequality are uncertain estimates of an unknown distribution of potential living standards, more or less valid for societies where "money income" is a useful proxy for the ability of people to enjoy various important goods, and of little value outside the context of a conception of a "just distribution" of these capabilities.

Despite the fact that estimates of what is essentially a statistical abstraction often play surprisingly big roles in current political debates (cf. the debate over The Spirit Level some years ago, or recent concern about a rise in New Zealand's gini index), I have recently become more skeptical about the importance of measured income inequality in politics: whatever importance the actual distribution of incomes has for political life in a society, it has to be mediated through complicated processes that refract local lived experience through the prism of context-dependent fairness norms that are only vaguely related, if at all, to the numbers used to measure its skewness.

Yet I'm curious: what sorts of income inequality have in fact increased, and where? How might these changes have mattered? Enter a new and shiny dataset: the Standardized Worldwide Income Inequality Database, which promises to ameliorate some of these measurement problems. The database uses the Luxembourg Income Study - very high quality income inequality data - to calibrate the much larger but less comparable United Nations University World Income Inequality Database. The result: lovely long time series estimates of both the market and the after tax, after transfer (net) gini index of inequality, including standard errors, for 153 countries. My first though on learning about this was: graphs! (Hopefully some non-obvious facts are also involved below).

Let's start by looking at a country that has often been cited as a great success in reducing inequality: Venezuela during the Chavez years. (Also, I was there recently visiting family after a long absence, and I have a personal interest in understanding the changes that have occurred during that time). One question I've been curious about concerns the evolution of inequality in Venezuela relative to other Latin American countries, especially since the coming to power of Chavez in 1999. How do changes in inequality in Venezuela compare to changes elsewhere?

In the following plot, we see changes in both the market ("equivalized (square root scale) household gross (pre-tax, pre-transfer) income", if you must know) and the net gini index of inequality (after tax, after transfer) in 19 Latin American countries from 1999 until 2010, ordered by the estimated rate of inequality reduction (countries that reduced inequality faster appear earlier; read the graph from right to left, top to bottom):

Inequality in Venezuela has indeed decreased relatively quickly since 1999 - the second fastest decrease after Ecuador, which has also had left-leaning governments (though a far more unstable political context, with five different presidents since 1998). Three things are worth noting about the context of these trends, however.

First and most important is that this reduction in inequality is not driven by direct redistribution: there is barely any difference between the "market" gini index (our measure of inequality before taxes and transfers) and the "net" gini index (our measure of inequality after taxes and transfers). To the extent that the reduction in inequality is the result of government action rather than something else, it must have come about through measures like investment in human capital and labor market policies (see Morgan and Kelly 2012, ungated here, for the proper peer-reviewed argument). This is true of all Latin American countries save for Puerto Rico (which is part of the USA in a sense) and (to a lesser extent) Brazil; indeed, redistribution in some countries (Peru) appears to have perversely increased inequality.

Second, most Latin American countries have experienced reductions in inequality during this period, though most remain highly unequal. But Venezuela was already among the most equal countries in Latin America; in 1999, only Uruguay and Costa Rica had lower measured inequality (and the difference in net gini was within the margin of measurement error, so it should probably be disregarded). This surprised me; I had expected higher levels of inequality in Venezuela when compared to other countries, given the level of class conflict on display during the Chavez era. More surprisingly perhaps, if we take a broader look we discover that inequality in Venezuela appears to have been remarkably stable over the past fifty years, fluctuating around a flat trend:

(Lines around dots represent 95% confidence intervals).

In fact, the low level of inequality in Venezuela as of 2010 only returned the country to the level of inequality it last experienced around ... 1992, the year of the February coup which made Chavez famous, and three years after the "neoliberal" paquete of 1989 (which was supposed to have triggered the Caracazo). Inequality did increase after 1992, and poverty had increased before then - the Venezuelan economy had been in decline for a while, as we can see below. Which all goes to show, I suppose, that political unrest and lived experiences of injustice are only very loosely connected, if at all, with measures of income inequality; whereas austerity and large income losses appear more immediately important to political outcomes (as Jay Ulfelder argues here):

(GDP per capita data from the Penn World Table v. 8.0).

Finally, it's probably worth noting that Venezuela's economic fortunes are deeply tied to oil prices, and that the rapid reduction in inequality in the last decade or so should also be placed in the context of the very large rise in the value of oil and gas during this period. Here is an estimate of the per capita value of oil and gas exports for Venezuela, from Michael Ross' oil and gas dataset:

In fact, Venezuela and Ecuador, the countries that have experienced the fastest inequality decreases, have been precisely the two countries that have benefitted the most from oil and gas price increases - money that flows directly to the state (especially since the Chavez government systematically asserted control over the state oil company) and can be used to provide employment and subsidize education, healthcare, housing, staples, and other goods, however inefficiently (e.g., the varios "Misiones" and other social programs created by the Chavez government). At least some of these programs must have played some role in the reduction of inequality, but given the amount of oil and gas money flowing directly to the Venezuelan state (representing most Venezuela's exports, which have become substantially less diversified over the last 15 years) and the typical patterns of clientelism and electoral politics in Venezuela it would have taken a bloody-minded kleptocrat not to reduce inequality by some amount. At any rate, inequality and poverty also diminished quite a bit during the 1970s oil boom, likely through similar channels - massive amounts of money flowing through the state, which increased its ability to employ people and subsidize public services. (I don't mean to sound grudging; though I have doubts about the effectivenes of some of these programs, some of the new housing built during the Chavez years looks decent, for example).

Let's take a broader look, however. How does the Venezuelan experience of inequality reduction compare to some countries outside of Latin America? Just because they've been in the news, let's look at the Venezuelan experience in coparison to Turkey and Egypt; and add the USA and New Zealand to see how two "developed" countries look as well.

That's right: Egypt and Turkey apparently reduced inequality faster than Venezuela in this period (though the error estimates of the gini index for both are also larger), and were less unequal than Venezuela by the end of the period! Also, despite the fact that the degree of "market" inequality was higher in the USA and NZ than in Venezuela, and did not decrease or even increased a little during this period (as measured by the net gini index), both countries remain less unequal than Venezuela (as measured by the net gini index), due to the effectiveness of their redistributive measures.

Now, this is perhaps surprising, but a bit of an aberration, and really, we are dealing with imperfectly estimated quantities (rates of decline) based on measurements with error. So there's really no point in arguing about whether inequality in Venezuela has in fact decreased faster than in Egypt or not; our methods of measuring inequality don't allow us to give a very precise answer to this question (error bars are large, etc.). In any case, it is clear that income inequality has declined pretty fast in Venezuela over the last 15 years, even allowing for some meaurement and estimation error, as we can see by calculating the trend rate of change in the net gini coefficient (the slope of a regression of log(gini_net) on year, to be technical, which yields the estimated trend annual percent rate change in the gini index) for all countries in the dataset:

(I took out countries that had too few datapoints, since the trends didn't look to me like they could be informative. The error estimates in the graph are nevertheless probably too small, since one would need to use the proper rules for error propagation to calculate them, which I have not done. Interestingly, the estimate of the rate of change in the net gini index for New Zealand and the USA since 1998 suggests basically that they have experienced no significant change in measured inequality from 1999 until 2010, contrary to popular belief; their important increases in inequality occurred earlier. More on this in a minute).

What strikes me about this graph is that countries that have achieved very fast reductions in inequality over this period appear to be quite disparate; though left governments are in evidence among these, many countries apparently achieved fast reductions in inequality with supposedly "neoliberal" policies (e.g., Egypt and Turkey) that are now in turmoil. Maybe this is evidence that the gini index does not capture socially relevant changes in inequality; but then it would also fail to capture changes in inequality in non-neoliberal Venezuela and Ecuador. (Of course, other confounding factors may be at work too).

It is also curious that many of the fastest reductions in inequality have occurred in states that do not engage in a lot of explicit redistribution. In fact, a simple correlation between the average redistributive capacity of a state (measured by the percentage difference between the "market" gini and the net gini coefficient) and the rate of decrease in measured "final" inequality over the period is slightly negative (so fastest reductions in inequality have occurred in states that are unable to affect market gini very much at all, or that even increase it through perverse redistribution):

It's probably not worth making too much of this correlation (measurement errors, the relatively short time period under consideration, and confounding factors are not taken into consideration), though it does suggest that many changes in inequality seem beyond the control of most governments. But even when we expand the period of observation all the way to 1960, the correlation does not entirely disappear, though it weakens greatly:

Ultimately, however, the more directly and explicitly redistributive the state has been, the more equal it also appears to be over the long run:

Or, to put it crudely, since 1960 at least market inequality has only been reliably reduced in states that take from the rich and give to the poor. And yet actually taking from the rich and giving to the poor seems to put nontrivial demands on state capacity and political life (witness the existence of robber states that take from the poor and give to the rich). The degree of change in the market distribution of income even appears to be a fair measure of that capacity; from the graph above, it's likely that a state that can consistently reduce gini index of market inequality by at least 30% is a pretty "strong" state (in the "infrastructural" sense of strong), whereas a state that cannot make a dent on the market distribution of income is more likely to be "weak" (with some communist exceptions like the USSR that did not engage in a great deal of explicit redistribution, since, to put it crudely the state owned everything and everyone more or less got paid the same).

And abilities to redistribute income appear to be remarkably "sticky." Few countries appear to become more able to affect the gini distribution over time:

(I've deleted cases with very few data points to make the graph look prettier. See the code for the details). What is striking about this graph is how stable the redistributive capacity of most states has remained over a period of more than six decades: many countries show basically zero change in their ability to change the income distribution. To be sure, some countries have increased their redistributive capacity -- France is a good example -- and others experience wild swings in redistributive capacity, probably related to big political conflicts -- note Bangladesh and Chile, the latter with a big bump around the time of Allende. But at best we can detect a long-term decline in redistributive capacity for the majority of cases (even if the decline is often slight); and often, after a decline, we see long periods of stability rather than change: countries settle into an "inequality regime," with some occasional big bumps which indicate new equilibria.

Note that in many cases the redistributive capacity of the state does not change even while inequality increases: thus, for example, while the net gini has increased over the past six decades in the USA and New Zealand, their capacity to affect the gini coefficient has remained approximately the same (New Zealand has been able to reduce the market gini by about 27%, though there's a slight downwards trend in this number; the USA by about 22%). The structure of their economies changed (by political action, in part), producing more inequality, but their redistributive capacity as states remained basically the same. To decrease inequality by redistribution in cases where the market gini increases substantially seems to require either a big political shock, or a long-run increase in state capacity.

There is another historical pattern that struck me as interesting: both levels of inequality and redistributive capacities seem to be highly correlated accross regions. Neighboring countries appear to have both similar levels of inequality and similar redistributive capacities. Linked economic and political histories seem to produce both the equilibrium level of inequality and the long-run redistributive capcity of the state.

Here, for example, we see the average redistributive capacity of states per region:

(Cases to the right of the solid line are states that on average made their income distribution more equal; the dashed line indicates the median redistributive capacity).

And here is a graph of net gini per region (all observations since 1960):

No great surprises here, perhaps: Sub-Saharan Africa and Latin America have been the world's most income-unequal regions over the last six decades, whereas Europe has been consistently equal - the home of both Northern social democracy and Eastern European communism, both of which have been able to keep the distribution of incomes relatively equal through explicit redistribution, though in somewhat different ways.

But perhaps this is of little importance. On one (vaguely Rawlsian) view, what matters is not the income distribution per se, but the ways in which it affects the prospects of the worst off in society. How much does it matter whether or not inequality declines in any given society, especially for the poorest? This will depend on the growth rate of the economy; high growth with declining inequality will be better for the poor than low growth with increasing inequality, though the outcome of the comparison is ambiguous for high growth with increasing inequality or low growth with decreasing inequality.

Now, it occurs to me that with the average income for these countries as well as their level of inequality, we can make an informed guess (technically, a wild guess) about the average income of various deciles for the years in which data is available. To do this properly would be too painful for a blog post, but I assume that empirical income distributions more or less fit a lognormal distribution (even though they fit more exotic distributions better, like the Singh-Maddala distribution or the generalized Beta distribution). With a little help from R, I can then simulate the average income of each decile of every country in the SWIID dataset. (Take a look at the code for the gory details. Also: this is a VERY rough and ready simulation, extremely inefficient to run and cooked up in a day. Do not take these numbers too seriously). We can then provide some vaguely informed answers to a Rawlsian question: which countries have most increased the prospects of the poorest over the last six decades?

The question admits of two more precise formulations, which we'll take on in turn: what countries have had the highest growth rate of income for the lowest deciles of the population? And second, in which countries do the poor have the highest incomes? (The first corresponds to a sort of dynamic version of the difference principle, which I find more interesting). Let's start with looking at the Rawlsian growth rate (the rate of income growth for the lowest decile, which we'll assume represents the group whose position must be maximized in Rawls' theory); the higher the long-run Rawlsian growth rate, the more the country fulfills the dynamic version of the difference principle. Though in theory the long-run growth rate of the economy as a whole and the long-run growth rate of the income of the lowest decile should perhaps converge, in practice they diverge, even over long time periods - some groups do well over some time frame, others do badly. Now, what we would actually want to know from a strict Rawlsian perspecive is the highest long-run growth rate of income for a representative person in the lowest decile of a given country relative to the potential growth rate of the whole economy (in other words, what degree of inequality would produce the highest income growth for that representative person, given the particular structure of that economy), but this is a counterfactual quantity we cannot estimate, so we'll make do with simulating the incomes of the lowest decile for the actual combinations of growth and inequality in existing economies. (I repeat my warning: this is only a simulation!)

First, we estimate the long-run Rawlsian growth rate (for countries with data going back far enough - so we drop countries that don't have long enough time trends, say at least 30 years):

The "Asian Tigers" unsurprisingly top the list: over the last six decades, Taiwan, Singapore, and South Korea had the highest (simulated) Rawlsian growth rate (in countries with at least 30 years of both GDP and gini data). South Korea and Taiwan are below average in inequality, which makes sense, but Singapore is not. Over the long run, in other words, a high enough growth rate of income seems to compensate for higher than average inequality. But one surprise among the top countries is Egypt - where the poorest decile, if we believe this simulation (and you shouldn't), had a pretty good run over many decades, despite Egypt not being considered a big performer in terms of its average per capita growth. At the bottom, by contrast, we find that Venezuela has essentially experienced zero Rawlsian growth over six decades (in fact, its long-run trend in regular per-capita annual growth is also zero). Though below average in inequality, its income has suffered so many ups and downs (mostly following oil price changes) that the trend is flat; no wonder Venezuelans eventually got tired of all their politicians before Chavez.

Now, there obviously is a correlation between Rawlsian growth and regular growth, as well as between Rawlsian growth and average inequality, but it is not perfect, simply because the Rawlsian growth rate is a function of both the average growth rate and the gini index by construction, and these two things are not perfectly correlated; a high enough growth rate in the whole economy can overcome a large gini coefficient to produce high Rawlsian growth rates and vice-versa. But it's worth noting that extremely high levels of inequality do appear to be associated with plain low growth over the long run, bad for both the poor and everyone else except perhaps tiny kleptocratic elites:

We can now repeat the exercise for the last 15 years and see how Venezuela stacks up since then:

As we can see, the Chavez years (up to 2010; the data does not tell us what happened for the last three years) were quite good for the poor, according to this simulation: the combination of declining inequality and relatively high growth rates (due in great part to rising oil prices) made Venezuela a top ten Rawlsian performer - better even than China, which also had torrid growth rates but increasing inequality during this period. To be sure, this good "Rawlsian" growth rate is only relevant if we ignore the equal liberties principle, which from a strict Rawlsian perspective  is meant to have priority over the difference principle; and increasing disregard of classic liberal rights during this period counts against Venezuela. (I vaguely wondered whether perhaps a "Rawls index" could be constructed, using data like the UDS to measure compliance with the first principle, fair equality of opportunity using the gini index, and the difference principle using the rate of growth of the income of the lowest decile; but since the two principles are supposed to be lexicographically ordered, a combined Rawlsian index would be pointless, useful only if we relax that assumption. Nevertheless, if we relax that assumption, then we would have to face the question of how much the improvement in the condition of the least well off ought to count against the decline in the "equal liberties" of the first principle; and I don't know of any good principled answer).

At the same time, it is interesting to note the countries at the very top are not precisely all left-wing governments; Azerbaijan, Mongolia, and Ukraine appear there. This may be because the simulations are risibly wrong (an important possibility), or the data are wrong; or simply that policies of the kind the Chavez government tried out are not the only possible ones to bring about growth in the income of the poor (and now, with high inflation, sporadic shortages, a large black market premium for dollars, and other problems, they don't look especially sustainable either). Nevertheless, the high Rawlsian growth rate makes it easy to understand why many of the Venezuelan poor felt that Chavez improved their position, regardless of how much responsibility we ought to attribute to his government for that outcome, or how sustainable its policies may be with lower oil prices.

Regardless, a good growth rate for the poorest decile matters: if inequality had remained at its maximum level during the Chavez years instead of declining but the growth rate had stayed the same, I estimate that the a representative of the poorest decile would have earned about $2000 less over the entire period than they actually did. We can call this quantity the "Rawls gap": the amount of income the poorest decile would have gained (or lost) in a given period had inequality remained the same as at the beginning of the period. Of course, since the growth rate would have been different had inequality remained the same, this is merely a fiction; we can't really estimate this counterfactual.

Nevertheless, just for fun, here is the Rawls gap for Latin America, per year:

This allows us to say that in Venezuela, the reduction of inequality that occurred during the Chavez period (assuming, per impossibile, that the growth rate would have stayed exactly the same had inequality remained at the 1999 level) gained a representative person in the poorest decile a total of about $1500-$2500 over 10 years, or about $200 per year, whereas the increase in inequality over the same period in Costa Rica cost a representative person in the poorest decile about $800-$1200 in income, or about $100 per year. This is nothing to sneeze at for the poorest decile (whose average yearly income is only about $3000 per year).

(It's kind of fun, though conceptually pointless and computationally expensive in my system given my crappy code, to calculate various Rawlsian gaps for arbitrary years and countries; for example, the "Rawls gap" for NZ is something like $2000 per year lost in income for the poorest decile if we assume the same growth trajectory but the level of inequality of the early 80s. Which of course we shouldn't - had inequality remained the same, the growth trajectory would have been different. As Adam Przeworski has said, everything is endogenous).

(We could also imagine even more exotic quantities, though I have no time to test them out here. Consider the Rawlsian compensatory growth rate, for example. This would be the growth rate that would compensate the poorest decile for an increase in inequality: if we want to say that some reform x would lead to higher income growth but higher inequality, then the compensatory Rawlsian growth rate is the growth rate where the income growth rate of the poorest decile at the higher level of inequality is identical to their income growth rate at a lower level of inequality but a lower overall growth rate for the economy; you would need a reform to produce at least the compensatory Rawlsian growth rate for it to be justified in terms of the difference principle. Which you may of course think is bogus).

Now, absolute incomes matter too; the difference principle in Rawls is not usually understood in terms of growth rates (though I think that should be the more natural interpretation). But the second version of the Rawlsian question above (where do the poor have the highest incomes?) has a much more obvious and boring answer: the Scandinavian countries, due to both generally high incomes and low levels of inequality due to high redistribution; and most of the countries at the top also score well in terms of the first principle (measured inexactly here by the UDS, which perhaps ought to be discounted a bit given recent developments in some countries). I include it here for completeness:

The roots of that ranking of countries are much older and deeper than this dataset allows us to see.

In theory, both the first ("equal liberties") and the second principle of Rawls' theory ("fair equality of opportunity" plus the "difference principle") ought to go together. In practice, however, Rawls himself thought that they did not always do so, though his reasons for thinking this were not always clear. Though I don't really have the tools to tackle the question of the relationship between liberal rights and the rest of the components of Rawls' theory properly (certainly not here), it looks as if we see a kind of inverted-U relationship in the data:

In other words, over the last half-century, the income of the poor has risen fastest under regimes that have not been on average highly democratic, but also has grown least in these regimes; non-democracy looks like a (potentially quite bad) gamble, though both democracy, long-run inequality, and the long-run growth rate of the income of the poor are probably determined by (or are a reflection of) some deeper social fact, like state capacity, which is not really susceptible to policy intervention. Whatever state capacity is (I have argued it is a kind of development of political technologies) it emerges out of political struggles that take a very long time to work themselves out with many tragic consequences along the way; and in any case the rate of improvement of state capacity is at times immeasurably low.

[Update 12/7/2013 - fixed a reference to a non-existing graph]

Impossible Political Systems: Further Adventures in Rawlsian Constitutional Design

I am somewhat amazed, now that I think of it, that no “serious” political philosopher I know of has ever proposed an electoral system like the one I proposed in this post last week, where individual voting power is inversely proportional to income. (By all means enlighten me if anyone has proposed something like it; I would be delighted to know. I’m pretty certain that among the many forgotten pamphleteers of the 19^th century someone must have come up with a similar idea but I don’t have the knowledge to locate these potentially existing antecedents). This probably means that it is a bad idea (and judging by the few reactions I got, most people think so); but if it is a bad idea, I would like to explore in more detail the reasons why it is bad, since it is not obvious to me that a system like that would not meet Rawls’ principles of justice.[1] (And I sort of would like to see a few more responses).

A recap: I suggested (more or less tongue in cheek) that Rawls’ difference principle could potentially be met by a political system where everyone has a vote, but the formal value of your vote declines the more you earn. There are a number of different ways of achieving this, but the most interesting (at least to me!) version of this system is the following.

We divide voters into n income (or wealth) equal classes (or quantiles). Voters in the first (poorest) class have median income y and a single vote each, whereas voters in the nth (richest) class have median income a_ny (that is, the median income of the richest class is a times the median income of the poorest class) and 1/a_n^x votes each, where x is a number between 0 and 1 that determines the extent of the “disenfranchisement” of high income voters. “Income” here is post-tax, post transfer income.[2] The value of a person’s vote thus depends on their income class; more specifically, it is inversely proportional to the ratio between the median income of their class and the median income of the poorest class. For n > 1, if x = 0 then every voter has one vote, and the system reduces to the normal “one person, one vote” system; if x = 1 then the extent of rich voter disenfranchisement is strictly proportional to the average income of their income class, so a voter in the k_th income class would have 1/a_k votes.

A numerical example may be useful. Imagine that this system had been in place in the USA in 2008, with x = 1 (so the value of the votes of the richer classes is strictly inversely proportional to their income), and n = 10 (so there are ten classes of voters). According to the Luxembourg Income Study, the income ratio between the bottom and the top decile of the income distribution in the USA in 2010 was 6.154 (so a₁₀=6.154). In this imaginary political system, in other words, the poorest decile of the income distribution would have had about six times the voting power of the highest decile. About 75% of these people voted democratic in the 2008 congressional elections, according to the American National Election Study, whereas only about 33% of the people in the highest income decile did so. A very quick and dirty simulation (see code and explanation here) suggests that if this system had been in place in 2008, the Democratic party would have won about 62% of the two-party vote (61% if we assume turnout rates would have stayed the same, with poorer voters voting at lower rates than richer voters), rather than the 54% that it actually won – an 8% difference, which one imagines would have been translated into somewhat different policies. A system like this would thus have amplified the influence of the bottom decile of the income distribution (and of the lower half of the income distribution generally), though of course parties would have behaved very differently in the new environment, so the example is merely illustrative. (A simulation for New Zealand is a bit harder to do given our different electoral system and my inability to use the NZ Election Study, but I’d love to see one).

Note that we could in principle consider systems where x > 1 or x < 0, though I doubt such regimes would pass Rawlsian muster. If x is much greater than 1, the votes of the richer classes are discounted very quickly: with a small number of classes (say n = 4) we then get a “dictatorship of the proletariat”; with a larger number of classes and a very large value for x, we get basically a simple dictatorship of the very poorest people in society. Similarly, if x > 0 and the number of classes is small, we get a régime censitaire, where the rich have more formal voting power than the poor (like the Roman republic of Cicero’s time); if x is much smaller than -1 and the number of classes is large we simply get a dictatorship of the richest people in society.

Note also that if n = 1 then the system reduces to the usual "one person, one vote" system; for n = 2 voters below the median income each get one vote, while voters above the median income each get  votes, where a₂ is the ratio of the average income of voters above the median income to the average income of voters below the median income; and so on. The smaller n, the more abrupt differences in voting power are (though they are ultimately less steep), whereas the larger n, the more gradual and steeper the differences in voting power. So, for n = 2, the superrich end up with the same voting power as the middle class, and the lower middle class ends up with the same voting power as the very poorest, though the poor and the lower middle class end up with more voting power than the upper middle class and the rich; for n = 100, the superrich end up with much less voting power than the middle class, but the middle class in turn ends up with less voting power than the very poorest, even though voters in adjacent income classes end up having similar voting power. If n is high but x is close to zero we have smooth differences in voting power but a small gradient, so that rich and poor end up having similar voting power per person but there are many small gradations. All of this would be easier to show in a simple interactive simulation (a Mathematica notebook, perhaps?) with a couple of sliders for n, x, and some choice of potential income distributions, but that is beyond my ability to do right now; for now, all I can offer is some R code here if people want to play with various choices of parameters.

So how should we choose the parameters n and x? Current voting systems in democracies at least pay lip service to the idea that each elector is formally equal, i.e., that n should be 1 and x should be 0, even if in practice the value of some voters’ votes is larger than the value of others. (In elections to the US senate, the million or so Montana citizens have about 37 times the voting power of the 37 million or so California citizens, a ratio that is much higher than the ones contemplated in the numerical example of this system above. this is an approximation - I should look up the actual numbers of voters, not just the populations - but it will do for a ballpark figure). But would a person choose these exact parameters for an electoral system from behind a veil of ignorance? Rawls himself notes that one must evaluate political institutions by their tendency to produce just outcomes (they are forms of “imperfect procedural justice,” like jury trials); and it is not clear that n = 1 and x = 0 yield the most just outcomes. And the advantages, from a Rawlsian point of view, of choosing larger values for both n and x seem considerable.

Most people (including Rawls) would say that the rich have more influence than the poor in politics, influence that is disproportionate to their numbers (though not everyone thinks this is a bad thing). The reasons are obvious. Standing for elections costs money, and the need for financing campaigns from moneyed private interests may push certain issues to the forefront of the public agenda, and make others invisible. The rich can lobby representatives more easily, and have more ability to coordinate and spread their ideas than the poorest. In the USA, Martin Gilens has argued  that the views of the poor have almost no influence on the actions of their representatives when these views diverge from those of the rich. To be sure, not all of these things are necessarily negative. The ability of the rich to lobby can be construed as an informational subsidy to legislators. If the rich are better informed than the poor, policy that is nonresponsive to the views of the poor might be of better quality by some measures. But it is difficult to deny that political inequalities exist; the question is whether they are arranged to the benefit of the worst off. If they are not arranged for the benefit of the worst off, then it is possible that changing the values of n and x, i.e., giving more formal influence to the poorest, would serve as appropriate compensation for their economic inequality.

The thing about a system where n > 1 and x > 0 is that the value of any one person’s vote changes as society becomes more or less equal. Regardless of how many classes we choose, and what value we give to x, the more income-equal the society, the more equal the value of the vote of rich and poor, and in a perfectly income-equal society everyone would have exactly one vote. By the same token, the higher the level of inequality, the higher the value of the votes of the poor relative to the votes of the rich, and as inequality increases, the more political power the poor gain. x thus represents a kind of “sensitivity parameter”: the higher its value, the more sensitive the political system will be to inequality.

Moreover, a system like this would bypass debates about which economic policies actually reduce inequality or produce the most benefits for the worst off, i.e., which policies would meet the “difference principle” (assuming, of course, that the difference principle is the right principle of justice for socioeconomic matters; and it may not be). It makes no assumptions about which kinds of economic policy actually do help the poor; if laissez faire improves their position, then the poor would be in the best position to approve of it; and if some other policy worsens their relative position, then the poor would get a right of “first refusal.” (As inequality increases in a society, the poorest would gain more and more formal political power). In the spirit of the difference principle, the rich are thus allowed to benefit from (economic) inequality so long as the poor approve (with x and n setting the “approval parameters” of the system). Thus, the higher the level of inequality, the more disenfranchised the rich become, and the greater the compensation to the poor in the form of political inequality (benefiting the worst off the most), which in turn might enable them to change those policies. Of course, if your political theory does not depend on Rawlsian assumptions, this point might leave you cold; but even utilitarians might see potential benefits here. (And your choice of x and n might say something about how much a person is willing to give up for the sake of economic equality).

Now, there are many potential problems here. The rich might underreport their income. (Though this should only be a serious problem if n is large). The poor might choose policies that are not in the interest of society as a whole. (But so can the rich; the question is whether, on average, granting more political power to the poor would result in more just decisions). They might redistribute property. (Which would result in their losing political power as economic inequality decreases). If we start tweaking n and x who knows where we might end up. (We could end up with political systems that grant more political power to the rich). Loss of formal political influence by the rich might have unanticipated consequences in the form of additional corruption and so on. Formal distinctions in voting power are an affront to the equality of citizens, and offend our sense of fairness. (True, though people take very large inequalities in elections to the US senate, for example, completely in stride. Also see next point). Perhaps the most important objection to a proposal like this, which Jay Ulfelder raised in conversation on G+ when I posted the original idea, is that politics is not  only about economic issues; it is also about many other issues, which we evaluate from the point of view of equal citizenship. Issues about religion, civil liberties, etc. should not be subject to the predominant influence of one social group; they concern all as equal citizens.

I grant that this is a powerful objection to a scheme like this. But here’s a refinement that bypasses or at least mitigates it. Imagine a bicameral legislature. The lower chamber is selected through an electoral system like the one described above, where x = 1, and n = 10, for example. We could call this the “Chamber of the Difference Principle.” The upper chamber, by contrast, is selected through an electoral system of universal equal suffrage (x = 0, n = 1), perhaps including some of the “random constituency” ideas I discussed in an earlier post to ensure the representation of suitably general interests. We could call this the “Chamber of Equal Citizenship.” Determining the exact relationship between these two chambers is beyond the scope of this post; but the (Rawlsian) idea would be that these two chambers would represent the two standpoints from which we evaluate social institutions, and work together to produce law and policy.

Now, I myself don’t know for sure whether to take this idea seriously. I lean toward thinking that a system like this is not only too shocking to our normal ideas of fair representation to be ever politically possible, but is likely to have some bad unanticipated public choice consequences. So I don’t know where I would set x and n, if not at 0 and 1, even if I’ve half convinced myself that higher values for both would be somewhat desirable. But I would like to know where others would place these values. Do you think that voting power should be inversely proportional to income? If you’ve read this far, it would be great if you could answer this poll.

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[1] Rawls does say in section 36 of ToJ that the political constitution of the just society would honor “the precept of one elector one vote” as far as possible; but he could be wrong about that, even by his own lights; and anyway a Rawlsian could argue that departures from the one elector, one vote precept are justified in nonideal situations (as Rawls himself does). Furthermore, Rawls does express concern about maintaining the “fair value” of political liberty under conditions of economic inequality, a problem which this system would potentially eliminate.

[2] This is mathematically equivalent to a system in which the members of the richest income class each have one vote, and members of the poorest class each have a_n^x votes; it doesn’t matter which description we use, except that in the second x should perhaps be called an “empowerment” parameter (for the poor) rather than a disenfranchisement parameter (for the rich).

More Rawlsian Thought Experiments: An Inverse Income Voting System

(For some unknown reason, re-reading Rawls stimulates my weird idea generator. Another politically impossible proposal here, presented as a thought experiment)

[Update 25 August 2012: see the more detailed discussion of this proposal here]

Thinking about the difference principle today, it occurred to me that most of the discussion on the topic tends to be overly focused on the economic institutions that would ensure that the least advantaged group in society would fare best. Yet the difference principle is not restricted in its application to economic inequalities; in fact, the principle specifies that inequalities of authority and political power must also be justified to the worst off group in society: “[t]he second principle applies, in the first approximation, to the distribution of income and wealth and to the design of institutions that make use of differences in authority and responsibility” (§11, p. 53, emphasis mine). Is a standard democratic system – with its panoply of elections, constitutional protections, and so on –justified in those terms? Rawls seems to assume so, even though standard democratic institutions entail clear inequalities in authority and responsibility which are not obviously to the maximum benefit of the worst off.

Moreover, to the extent that Rawls discusses the connection between political and economic inequalities, he tends to think of the direction of causation as going from economics to politics. Unjustifiable political inequalities in authority and responsibility (as, for example, when the rich have undue influence in the political process) would be remedied, in his view, once objectionable economic inequalities are taken care of, which seems reasonable enough; after all, he notes, such inequalities are correlated with one another (§16, p. 83). With low levels of economic inequality, widely dispersed ownership of the means of production, and a healthy dose of public campaign finance, Rawls argues, whatever differences in authority and responsibility political institutions would still produce would be justifiable to the least advantaged (cf. §13, p. 71, §36, p. 198).

But why wait until such inequalities are fully remedied? Imagine that instead of the standard, one person, one vote system, we had a voting system where the poorest person with any income got 1 vote, the person with twice the income of the poorest person got ½ a vote, and a person with 20,000 times the income of the poorest person got 1/20,000^th of a vote. “Income” here includes any government transfers; people with no income would have 1 vote, just as the poorest people with any income. The specific value of the vote would be linked to the income records on file with the national tax agency, and no one could vote who was not linked in some way to the tax system. We might use broad categories instead of specific incomes – say, people making less than $10,000 a year get one vote, people making up to $20,000 half a vote, and so on; and of course we might decide that a different weighting of votes is required. [Update: it occurs to me that using the median income would be easier to set up. For example, voters below the median income each get one vote, voters between the median and twice the median get half, and so on.] Whatever the case, poorer people would have more formal influence than richer people.

In a fully income-equal society, everyone would have 1 vote; in an extremely unequal society, the very poorest would have the most political influence. High-flying hedge fund managers with extremely high incomes likely would have an infinitesimal vote, though they would of course still have many means of exercising influence. After all, elections cost money, and the rich are more able to run for election and lobby legislators. But the idea is that the least advantaged groups would have compensating advantages, as politicians would have to cater to the greatest mass of votes; yet these advantages would diminish as transfer payments increased, or society became more equal. Note also that the specific value of a person’s vote would fluctuate throughout their lifetime, being very high when the person is very young or very old, and very low during their peak earning years. (The system might work kind of like an automatic means test for politically distributed benefits, baked right into the political structure).

Would there be anything wrong with this system, from a Rawlsian point of view? Everyone can still vote and run for office, so the first principle of Rawls’ theory - the principle guaranteeing the equal basic liberties - is not overtly violated; and it seems to me that the inequalities of authority and responsibility produced by this system are more clearly justifiable to the worst off group in society than the inequalities produced by a standard democratic system. For one thing, it provides the least advantaged in society with the fair value of their political liberties in a direct, unmediated way that complicated systems of campaign finance cannot match. Moreover, a political system along these lines bypasses the theoretical discussion about which economic system would best produce outcomes in conformity with the difference principle; different proposals can be tried, and if they worsened the lot of the least advantaged, the poor would gradually acquire sufficient political clout to overturn them. (In theory, this is compatible with pure libertarian laissez faire, so long as such laissez faire actually does improve the condition of the least advantaged group).

Like any oddball proposal, this is very likely a bad idea. (I can imagine all kinds of bad incentives to underreport income, for example, and I’m not sure it would fit with the well-entrenched idea that having an equal voice is a mark of respect of equal citizenship.) But I’m curious: are there specifically Rawlsian grounds to reject this sort of system? (I'm sure there are other grounds). And what are the obvious problems I’ve missed in here? Does this lead to a sustainable politico-economic equilibrium, or simply to an intensification of class conflict?

[Update 2, 20 August 2012: fixed some minor typos. Also thought of some further refinements. Suppose we divide the income distribution into N equal quantiles. The voters in the lowest class have one vote, and the voters in the highest class have (1/(N^x)) fractional vote, where x is a parameter determining how extreme the disenfranchisement of the rich is. When x=0 everyone has one vote, as today; when x=1, the disenfranchisement is strictly proportional to class position, so the each person in the nth quantile has 1/n votes; but we could set x between 0 and 1, leading to a range of different weightings of formal influence for the poorest depending both on the number of "classes" and on the extent of disenfranchisement with income. With few classes and low x, the system is close to our own; with many classes and large x, there is a very steep disenfranchisement curve. What values of these parameters would be chosen behind the veil of ignorance?]

Musical Chairs, Veto Constituencies, Accountability Juries, and other Random Ideas: Further Thoughts on Randomizing Electoral Constituencies

(Attention conservation notice: some more thoughts on this proposal, which gained a modest amount of internet attention in the last couple of days – see Dylan Matthews here, Matt Yglesias here, and Evan Soltas here).

Having slept on it and seen a few responses, I am not yet convinced that the proposal I sketched in the post below would actually be a bad idea (though it probably is!). The basic idea is that the electoral constituency or electorate – the group of people who “selects” the legislator – should be separated from the accountability constituency or electorate – the group of people who “disciplines” the legislator¹ – in such a way that neither the legislator nor the electors would know in advance who the latter group would be. Such a system would (in theory) mimic some of the structural features of a Rawlsian “veil of ignorance,” so that legislators could not tailor their appeal to any particular group of people but are instead incentivized to speak and act in ways that can be publicly justified to any group in society. But there are a variety of ways of accomplishing this, as I hinted at in the original post. Some of these are very close to current practice; others are not so close. I want to consider here in detail a few of these variations:

1. “Musical chairs” representation. This is the simplest form of the proposal. (My original idea was in fact closer to option 2 below, “random veto constituencies,” though it seems to have been quickly simplified into this form, which is at any rate simpler and more elegant). Under musical chairs representation, non-incumbent candidates can run in any constituency they choose, but incumbent candidates running for re-election are randomly assigned a constituency shortly before the election date (say, a month or so earlier). The random constituency can be their original electoral constituency (let’s call this the “initial” constituency). We do not need to imagine that the incumbent draws any constituency with equal probability; a system where the incumbent has a higher probability of drawing his/her initial constituency could strengthen the incentive to do the kinds of constituent service that a lot of people seem to find valuable.
   
   More formally, let’s say there are N constituencies or districts in the system; come election time, incumbents can draw their own initial constituency with probability p, where p > 1/N, and any other constituency with probability (1-p)/(N-1). (More complicated assignments of weights are of course possible). When p = 1, the system works identically to current practice – the incumbent always draws his own constituency; when p = 1/N, the incumbent can draw any constituency with equal probability. We might thus think of p as a measure of “localism” in the system. The lower p, the more the re-election seeking politician will need to act in ways that can be publicly justified to any constituency in the country, but he will of course have less incentive to do constituency service or to represent his locality. p can also serve as a measure of incumbent advantage; the higher p, the higher the advantage, all other things equal.
   
   What might be the benefits of a system where p < 1? By facing the possibility of having to compete for re-election in a constituency other than the one where he has been originally elected, a politician would of course need to avoid acting in ways that can incur disapproval beyond his constituency. But he would still have incentives to represent his constituency, pace Dylan Matthews. For one thing, the chance of drawing his initial constituency is nonzero, and a reputation for serving the constituency one is representing would still be a valuable asset in a race in a different district. Indeed, they might still be able to too easily promise to extract rents on behalf of local interests, as Evan Soltas notes, though I imagine it would be harder to promise this credibly when they don’t know which district they would be representing in the next election. At any rate, promises of local rents aren’t the only criterion by which electorates judge the suitability of candidates, and this system would weaken the appeal of these promises. Moreover, while a district or electorate could insist on electing candidates with purely local appeal, these would, I suspect, tend to be one-term wonders, as would “extreme” candidates. Assuming the distribution of voter preferences is not itself polarized for other reasons, the system would tend to moderate polarization over time as candidates strategically target the “modal” constituency to a greater or lesser extent, depending on the strength of their convictions and their level of risk aversion.
   
   Elections might nevertheless become more competitive under this system, since p < 1 implies a lower level of incumbent advantage, which might be a good thing (more competitive elections tend to be associated with more public goods provision, though this varies depending on the kind of competition). More importantly, as Matt Yglesias notes, the forms of public justification themselves would shift. An incumbent US congressman who defended agricultural subsidies in Iowa during his term, for example, would need to do so in terms that would resist potential sceptical examination by an electorate in New York. And one should not discount the satisfaction electors would get from giving a sound thumping to a politician they find particularly obnoxious but would not, under current practices, normally be able to defeat. (Soltas’ objection that it “weakens accountability structures to have your performance judged by someone else than whoever installed you” is I think overstated; electors judging the performance of a non-local candidate can always opt for the local challenger, or judge the non-local candidate on the basis of his/her record on issues or national significance, as they often seem to do anyway, and as is perhaps appropriate for candidates to a national legislature). Nevertheless, it is probably safe to say that in the aggregate this system would not produce large shifts in policy from the status quo; after all, many mixed-member proportional systems (New Zealand!) try to achieve similar balances of “national” and “local” concerns, even if they use somewhat different mechanisms and have somewhat different effects on the forms of public justification.


2. Random veto constituencies. My original proposal tried to preserve local representation in a slightly different way. Perhaps the simplest form of it is the following: non-incumbent candidates are elected according to the vote totals in the constituency they are running, but incumbent candidates are subject to a veto in a randomly selected constituency (assigned shortly before the election). In essence, the challenger must win only in the local constituency, but the incumbent must win in both the local and the randomly selected constituency. If the incumbent loses in the randomly assigned constituency but wins in the local constituency, the challenger takes power; hence the idea of a veto. The system could make allowance for extremely popular incumbents, so that getting, say, 60% of the vote in their local constituency means that they only have to get 40% of the vote in their randomly-assigned constituency, and getting 80% of the vote in the local constituency means they only have to get 20% of the vote in the randomly assigned constituency. (Again, the chances of drawing a particular constituency could be suitably weighted to favour nearby constituencies, for example).
   
   It seems to me that this system would have most of the advantages of the previous one while preserving the possibility of strongly-rooted local representation. Races remain local, but politicians cannot act in ways that have a strong probability of being disapproved of elsewhere in the country; and incumbent advantage is strongly diminished. Nevertheless, it seems possible that a system of vetoes could create a lot of ill-will; I’m sure people in say, rural South Carolina, would not relish having their choices of representatives vetoed by people in San Francisco or vice-versa. So it does not seem politically sustainable in the long run, even if it would enable the schadenfreude of spectators to see politicians having to justify themselves to hostile electorates beyond their home turf (a benefit that is not to be underestimated; see Jeffrey Edward Green’s The Eyes of the People for a full academic defence).


3. Accountability juries. One problem with the proposals above is that they favour geographical units of representation at the expense of other possibilities. While randomization of such geographical units may have some benefits, certain interests are never going to be well represented on that basis. One could, however, modify the idea of veto constituencies so that the veto would be exercised by juries selected on the basis of some non-geographical criterion. For example, imagine that before each election, we drew five juries of 500 people each selected on the basis of income – the first jury being composed of 500 people randomly selected from the first income quintile, the second from the second, and so on. Each incumbent candidate is then randomly assigned, shortly before the election, to make his/her case before one of these juries; you could be assigned to speak before a jury of the poor, or before a jury of the rich, but you would not know which one in advance. We could have weeklong, televised trials, perhaps presided over by special investigating magistrates, in an echo of the “audits” Ancient Athens subjected its officials to at the end of their terms. The jury could then vote (perhaps with some suitable supermajority requirement) on whether or not the incumbent should be allowed to run for re-election (in that election; no permanent disqualification is envisioned). The possibilities here are, of course, much more various: how we would organize such juries, run the trials, and so on would be crucial questions. I suspect a system like this would shift policy more radically, but I like the idea of having representatives having to justify themselves to randomly selected constituencies that do not have a geographical basis.

Anyway, I’m sure there are huge problems with all of these proposals, which I don’t expect to be political reality any time soon; this is more a thought experiment than anything else. I would nevertheless be interested to hear what some of these problems are, or what alternatives people can come up with.