Friday, August 24, 2012

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 19th 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 any (that is, the median income of the richest class is a times the median income of the poorest class) and 1/anx 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 kth income class would have 1/ak 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.

[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 anx 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).


  1. random thought: in labor economics it is a fairly well established fact that income and years of education are positively correlated. in this sense, a system of the kind you propose would somehow take away political power from a good number of those who could arguably make better decisions because they are smarter. of course, the problem with this type of argument is that smart/educated people are not necesarily altruistic in their intentions, so it may not be such a bad idea to take away some of their voting power in order to compensate for their economic power. what i think would be nice would be to have an socioeconomic indicator or index that is:
    (1) positively correlated with income (after all, taking away some political influence from the people with the economic muscle tends to restore justice at least a bit in my view);
    (2) however, in order not to dilute too much the political influence of those with higher intelligence (because of the positive correlation between intellgigence and income), it would also be nice to have this indicator to be negatively correlated (or somehow inversely related) with a measure of the degree to which a person acts/thinks altruistically. this way, the influence of richer/smarter people who still hold the common good in high esteem are not excessively punished in terms of political power.

    of course, finding a dataset with a variable satisfying condition (2) is not easy. but i hear people at chicago are doing something called the national altruism study where they measured altruism by means of surveys (interesting read!). so i guess a very crude refinement to your model incorporating my remarks would be to use Income/Altruism instead of just Income. That way I guess some philantropists would have the kind of political power they so much need.



    1. Raul, yes, that's a question here: if giving more power to the lowest income group is also giving power to the least well informed, then the epistemic quality of decisions might suffer. (This is kind of the opposite of Mill's system for giving extra votes to the more educated in the 19th century). But the modeling can be complicated; if the votes of the poorest matter more, they might have more incentives to become informed, and parties might have more incentives to provide information (a la Wittman's "Myth of Inefficient Democracies") though also disinformation. (This is all highly speculative, of course).

      Unfortunately I think the sort of indicator you suggest does not exist at the level of universality and public justification for this sort of system to be possible. But one might have other adjustments to representation in a second chamber (e.g., randomized constituencies, for example) to improve the incentives of regularly elected representatives to look to broader interests.

  2. Anonymous9:50 AM

    For ****'s sake. Simplify the law and translate the it into first order logic, predicate calculus, and remove contradictions. The laws ought to be deducible from a handful of statements. It now takes a group of CPAs to tell you if what you want to do for tax purposes is legal, and even they're not sure. An eloquence of lawyers still cannot predict how a judge will rule. Our legal complexity and the non-precision of legal jargon gives large corporations a tremendous advantage over everyone.

    Utah UCA 76-7-104, , says sex outside of marriage is illegal. Of course, everyone has sex outside of marriage, which makes everyone a criminal and gives the state the ability to selectively enforce laws and create all kinds of corruption. There are many, many examples of that in all areas.

    Additionally, electing people, no matter who they are, is not the solution to anything. Maybe it is time for some kind of bounded direct democracy since we have Internet access.