The conservative social welfare function

“Social welfare functions” are a good example of the payoff to thinking abstractly. They are answers to a very large question, which might be put: How should human beings live together in society, and what should society’s goals be? If you want to focus on the government, you could frame the question as: What should the government’s objective be? How should it decide between alternative policies? Not every answer to this question lends itself to being summarized in a social welfare function, but many do, some rather precisely, some loosely.

Thus, the political philosophy of John Rawls might be summarized in the social welfare function V=min(U1, U2, U3, …, Un), where V is what society is trying to maximize, and U1, U2, … Un represent the utilities of individuals 1, 2, …, n, where n is the population. Similarly, the utilitarian political philosophy might be summarized in the social welfare function V = U1 + U2 + … + Un. From these social welfare functions, with a little bit of careful further thinking, one can make several deductions. First, both Rawlsians and utilitarians will tolerate some inequality, basically for the same reason: allowing some individuals to get ahead of others gives them the incentive to create wealth. A utilitarian values the self-enrichment of individuals per se. A Rawlsian doesn’t, but he will value it indirectly if the wealth creation spills over and benefits the poorest. Second, both Rawlsians and utilitarians almost certainly would support some redistribution. The Rawlsian does so because he only values the welfare of the poorest, and no matter how much he reduces the welfare of everyone else, if he can benefit the poorest at all, he will do so. The utilitarian will support some redistribution, even if, as is probably the case, it is inefficient and reduces the total wealth of society, because the marginal utility of a dollar is higher for the poorest individuals. But the Rawlsian will support more redistribution than the utilitarian. If we call the amount of redistribution T, there will be some T’>0 that maximizes total utility, and some T”>T’ that maximizes the welfare of the poorest. The utilitarian will prefer redistribution T’, the Rawlsian, T”.

There are more games you can play with social welfare functions (SWFs). You could call democratic any SWF that places equal value on all individuals’ utility, and aristocratic any SWF that places much greater weight on some individuals’ utility than others. (Both the Rawlsian and utilitarian SWFs are democratic, by this definition.) You could call an SWF relatively socialistic if it imputes to individuals highly risk-averse utility functions: that is, a socialistic society will tolerate fairly low average living standards, in exchange for an equitable distribution of income. By the same token, a relatively capitalistic SWF would impute to individuals utility function much closer to risk-neutrality, maximizing incentives for wealth creation while tolerating extreme destitution for some members of society. Now, I want to introduce the concept of a conservative social welfare function. While I thought it up myself, I’m not surprised that a Google Scholar search reveals it has been thought of before, and with the same motivation that made me think of it a few years ago: trade policy. The concept applies directly to immigration. But first, let me try to state it mathematically. Imagine a society which seeks to maximize:

(1)  V(t+1) = f(U1(t+1) – U1(t)) + f(U2(t+1) – U2(t)) + … + f(Un(t+1) – Un(t))

That is, in choosing how to allocate resources at time t+1 it takes into account how resources were allocated at time t. Thus the conservative SWF is backward-looking. But of course, you don’t really know anything about the conservative SWF until you know something about f(). So here’s a bit of characterization of f():

(2) (a)  f(0)=0, (b) f(x)>0 if x>0, (c) f(x)<0 if x<0, and most subtly, (d) f(x) + f(-x) <<0

Conditions 2(a) through 2(c) are rather obvious. Society likes it when people’s utility improves, dislikes it when people’s utility deteriorates, is indifferent when it stays the same. The really defining feature of a conservative SWF is condition 2(d), which implies that society is much more opposed to anyone seeing their utility fall, than it is in favor of seeing people’s utility rise. If a policy harms A while benefiting B by an equal amount, under a conservative SWF, the policy will be rejected. Even if a policy raises A’s utility by considerably more than it reduces B’s, the policy is likely to be rejected.

Now, if you believe that open borders would have an economic impact anything like what, say, John Kennan’s model predicts, then they should pass a Rawlsian or utilitarian test very easily. But open borders might still be rejected from the perspective of a conservative SWF, since in Kennan’s model it reduces wages of all non-migrant workers, while roughly doubling world GDP through huge gains to owners of capital and migrants. Whether this is the “real” reason (if that means anything) for migration restrictions, I don’t know. However, I do have a sort of hunch that conservative SWFs are an important part of the way democratic politics operate.

In behavioral economics, loss aversion is a recognized anomaly in people’s decision-making. People treat gains and losses asymmetrically, regretting losses more than they welcome equivalent gains, in ways that are hard to reconcile with any plausible utility function, and in that sense might be called “irrational.” For example, if I tell you that you get $100 for participating in an experiment, but can flip a coin and lose $100 for heads but win another $102 for tails, you might refuse the deal. You don’t want to “lose” $100. But if I tell you that your payoff from the experiment can be either $100 or $202, the latter payoff conditional on a coin flip coming up tails, you might take the deal. Of course, the payoff structures are exactly equivalent, but the presentation is varied to make it seem, in the first case, that you’re risking a “loss.” If you’d turn down the first deal but take the second, you suffer from the minor mental pathology called loss aversion.

Now, a conservative SWF is much like loss aversion at the level of a whole society. My hunch, though, is that loss aversion is much more pronounced at the societal level than at the individual level. I suspect that the impulse to trade protection reflects a conservative SWF, and that a lot of government programs that are basically handouts to interest groups, e.g., most farm subsidies, or excessive pensions for public sector employees, are politically sustainable because of a conservative SWF.

Mancur Olson wrote a book called The Rise and Decline of Nations: Economic Growth, Stagflation, and Social Rigidities (1984). Acemoglu and Robinson recently (2011) wrote a book called Why Nations Fail: The Origins of Power, Prosperity, and Poverty. I wouldn’t actually recommend either of these books particularly highly. In fact, I think Acemoglu and Robinson (2011) is an unfortunate book that tends to subtract from the sum of human knowledge by throwing out some good theories on inadequate grounds and then presenting their own crude and largely false theory– it’s a variation of the appealing but false notion that democracy is the cause of modern economic growth– supported neither by econometrics nor by formal theory but instead by miscellaneous historical episodes, tendentiously reported. I like Olson’s book better but it is vague and also weak in both formal theory and explicit data analysis. Still, both books stress the role of vested interests in blocking growth. For Acemoglu and Robinson, poverty is largely a function of “extractive” institutions inhibiting growth which would destabilize their rule. That that sometimes happens I can well believe. For Olson, societies tend to accumulate interest groups over time, and grow increasingly rigid. One feels vaguely that this describes France on the eve of the Revolution, with its parasitic aristocracy, or the Roman Empire in its dotage, with its parasitic senatorial elite; one is even reminded of contemporary America, with its enormous handouts to seniors that undermine savings and investment, and bleed the young just at the time of life when they badly need their earnings to pay for school and start families and buy houses. Yet the theory is hard to formalize and/or test.

I suppose I’m ambivalent about conservative SWFs. Unlike Olson, Acemoglu, and Robinson, I’m decidedly unsympathetic to revolutions. My DRITI scheme concedes a lot to the conservative SWF, striving to achieve open borders without any losers. Ultimately, though, I think conservative SWFs do a lot of damage. One of the reasons that I think open borders would be good for rich countries is that, without being actually revolutionary, it might disrupt a lot of the social rigidities and vested interests that– here I’m following Olson (1984)– accumulate over time and cause sclerosis and stagnation in society.

Two final points. 1) Conservative SWFs don’t have much to do with American conservatism as a political ideology. If anything, “liberal” Democrats are probably more beholden to vested interests in America today. 2) This post is loosely linked to my recent post “The golden age of immigration and innovation.” I suspect that Olson-style vested interests started to accumulate and rigidify the US economy after mass immigration stopped diluting them. But I’m only speculating.

Nathan Smith

Nathan Smith is an assistant professor of economics at Fresno Pacific University. He did his Ph.D. in economics from George Mason University and has also worked for the World Bank. Smith proposed Don’t Restrict Immigration, Tax It, one of the more comprehensive keyhole solution proposals to address concerns surrounding open borders.

See also:

Page about Nathan Smith on Open Borders
All blog posts by Nathan Smith

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