The Simple Analytics of Progressive Redistribution

Some of us were lucky to have Robert Waldmann http://rjwaldmann.blogspot.com/2007/06/possible-efficiency-gains-due-to-taxes.html in an adjoining room on the third floor of Weld Hall our freshman year. Others of us went to Yale.

Michael Froomkin writes:

Discourse.net: I Wish Robert Waldmann Had Been My Freshman Economics Teacher: What do you think the world would look like if freshman micro-economics students were routinely taught by Robert Waldmann? Instead of carrying around an Austrian model in their heads in which we assume total selfishness, zero transactions costs, and conclude that transfer payments are suspect, they’d be hearing about Possible efficiency gains due to taxes and transfers,

A little bit of altruism changes everything. If people care about their own physical well being (pleasure minus pain) plus that of those they love plus 0.00001 times the well being of strangers redistribution can be Pareto improving. Non poor agent A doesn’t need taxes and transfers to give his money to the poor. However, after he has chosen my level of private giving, he doesn’t want to give any more via taxes. However he wants to give rich agent B’s money to the poor. He cares a tiny bit about the small cost (in pleasure minus pain) to B and the same tiny bit about the large benefit to the poor. Increasing taxes and transfers from zero will make everyone happier if the population is large enough so that taxing one me is more than balanced by taxing lots of you

I’m pretty sure I had to wait until sophomore year to hear this stuff, and even then it was said with much less enthusiasm, as an embarrassing exception to an otherwise tidy result. (Or course, Robert couldn’t have been my freshman economics teacher, we graduated the same year from different universities, but you know what I mean.)

Comments

[anne]

http://www.calvorn.com/gallery/photo.php?photo=5544&u=4|15|...

Female House Sparrow Feeding Chick
New York City--Central Park, Maintenance Field.

Yes; this was so nice. Robert Waldmann needs to continue to approach economics as Ernst Mayr approached biology, from an philosophical base that tends to Aristotle rather than Plato. Nice.

[anne]

The Benthamite base for economics simply does not allow for the nuances in explanation that economic historians must after all rely on. Ernst Mayr knew that Charles Darwin needed a philosophical base other than Plato, for biological thinking differs from physics thinking on the level of the orgamism, no two of which organisms are the same.

[Robert Waldmann]

Brad you explained the fact that altruism implies that Laissez Faire is not Pareto efficient to me (and long after freshman year). Also please don't mention the bit about how the adjoining suits became communicating suits when I fell through the fire door (twice).

[Tomas]

What is it with this obsession with pareto efficiency in welfare economics? Almost no relevant policy initiatives will ever be pareto effecient, but will, arguably, be very a great net welfare improvement.

Why this fear of interpersonal utility comparisance? Is it cause needs (as opposed to wants) might sneak in an muddy the waters or is it an atavistic leftover from a time when the liberalistic market was sacrosankt in economics?

[David]

>> Some of us were lucky to have Robert Waldmann in an adjoining room on the third floor of Weld Hall our freshman year. Others of us went to Yale. <<

OK, Brad. You win. I give up.

Tomas: Good point about Pareto Efficiency.

[Neel Krishnaswami]

Tomas, the reason people hate interpersonal utility comparisons is because they don't work. For example, if you multiply anyone's utility function by a constant, and their observable behavior won't change at all. This means that people don't have uniquely determined utility functions, which means you can't compare them.

That is, if you try to compare two people's utilities directly, then you get to make up any result you want, because you can multiply one guy's utility by whatever constant makes the right person's utility bigger.

[anne]

Yes; you cannot quite compare them, which is sort of like, yes, we have no bananas. Robert Waldmann can be quietly subversive.

[Chris Marcil]

Others of us went to Yale.

Yes, but we're not always mentioning that fact within the first thirty seconds of meeting someone.

[Jacob T. Levy]

Since when is zero transaction costs an Austrian model? Since when are Austrians distinctively concerned about Pareto-optimality?

[anne]

Oh, please, the office next door is loosely inhabited by a Yalie who would sooner be naked, yuch, without a Yale cap. Duh.

[D-Slam]

Neel: "That is, if you try to compare two people's utilities directly, then you get to make up any result you want, because you can multiply one guy's utility by whatever constant makes the right person's utility bigger."

So, I redistribute 10 bucks from Bill Gates to the guy in front of my building with the "lost job, need help, God Bless" sign... and you lack the common sense necessary to determine that net utility has been increased?

Meh. Since virtually no policy is a Pareto improvement, can we then conclude that no policies are justifiable?

[Robert Waldmann]

Excellent point Tomas. 'Nother excellent point Neel Krishnaswami. I think the (valid) argument that interpersonal comparisons of utility are impossible has had immense influence on economists.

There are two ways to make interpersonal comparisons. One is explained by Jean Francois Mertens (this is a joke as "explained by Jean Francois Mertens" is an oxymoron). As far as I can tell after listening to him for 90 minutes, his proposal is as follows. First consider people whose happiness is definitely bounded above and below so there is an epsilon so small no outcome so wonderful that they would trade 90% of their lifetime wealth for epsilon chance of that outcome and vice versa there is none so horrible so that they would trade 90% of their lifetime wealth to avoid an epsilon risk of that outcome. This is reasonable, otherwise one can get to a St Petersburb paradox (warning pdf)
http://www.springerlink.com/content/d0k7604j263788ht/

if so, for each agent say the upper bound of his utility is 1 and the lower bound is zero. The rest can be filled in observing his choices over lotteries. Now we have interpersonally comparable utility.

This can also work even if happiness is, in principle, unbounded, so long as, for each person there is an upper and lower bound of technologically feasible happiness (misery).

Finally, it can work even if there are no psychological or technological limits, there can be limits based on some non utilitarian principle of fairness (say starving to death is infinitely horrible but we believe as a moral principle that before we begin adding up utils we have to save everyone from starvation if we can(or maybe torture is infinitely awful but also before we think about utils we must respect peoples right to not be tortured as a prior and absolute moral principle)). The 0 is the lower bound of misery which we can morally allow someone to suffer (even if technology makes a much more horrible outcome possible).

This is really a simple method to arrive at comparable numbers which are linear in happiness such that your argument does not apply.

I wonder why this idea is not more influential (again a joke, Mertens may be the worlds worst lecturer).

The other is an "assume we have a can opener" approach based on absolutely absurd assumptions about mega rationality. Imagine being someone else (a super mega rational being can do this). Now imagine your soul being removed from you and planted in a random person (a super duper mega ratoinal being can do this). Now, if you can make rational choices under risk, you can decide how to maximize the sum of human happiness e voilà (this approach is advocated by a friend of mine, Peter Hammond, so I am being polite).

Of to be really picky now that no one is reading, Tomas
technically you are arguing that Pareto improvements are impossible in the real world Pareto efficiency just occurs when no Pareto improvement is possible so there are many many Pareto efficient outcomes (slavery was Pareto efficient or else slaveowners would have freed their slaves). Pareto improvements are always impossible in the real world which is complicated (in simple models there can be simple Pareto improvements). Thus Pareto efficiency is just about nothing. It gets attention because of the result that, under very strong assumptions, the market outcome is Pareto efficient. Arrow proved this and has been trying to explain (to no avail) that the proof amounts to just about nothing ever since.

[John Emerson]

If you can't compare utilities, it's possible to believe that a dollar brings as much utility to Bill Gates as it does to a undernourished African. Questions of social justice, equality, and general welfare become impossible to express. And it becomes easier to make economics into a beautiful formal system.

I'm convinced that this is the reason for the rule of non-comparison, not a side-effect. The technical difficulties could have been treated either as a technical problem to solve, or else as a rough spot to smooth over with kludges and jimmies and shims -- if that had been what economists wanted to do. But what they wanted to do was quit talking about individual utility except as expressed in consumer choices.

[Lee A. Arnold]

Others of us dropped out of Yale.

[Cranky Observer]

> If you can't compare utilities, it's
> possible to believe that a dollar brings
> as much utility to Bill Gates as it does
> to a undernourished African.

Robert X. Cringley's history of the personal computer industry has the anecdote of Bill Gates keeping people waiting at 7-11 while he digs through his pocket for a cents-off coupon. That may (and may not) be apocryphal but coworkers of mine were in line behind Gates at a discount burrito stand at O'Hare and observed him carefully counting the pennies in his change [1].

In any case, human preferences aren't transitive which kills most arithmetic-based arguments right off the bat. And while humans are not very good at calculating probabilities, risks, etc intuitively they for the most part have very finely tuned "money-pump" detectors and refuse to get caught in such traps even though their preferences are not transitive.

Cranky

[1] Before the Microsoft BOD forced him to buy a private jet a few years ago Gates often seen changing planes at O'Hare.

[Robert Waldmann]

What John Emerson said. Also what cranky said about the money pump detector. This means that our preferences are not consequentialist as defined by Peter Hammond (again) that is our choices are not a function of the situation we are in and the options open to us but also of the history of how we got there. I am cribbing from Mark Machina who challenges the normative status of such consequentlialism (here understood as rationality not ethics) "consider the ultimate normative authority -- your mom. Let's say a mother has a treat which she can give to her son or to her daughter. To be fair she flips a coin and is about to give the treat to her daughter when her son says 'mom you have demonstrated a preference for the 50-50 lottery over giving the treat to her, so, to be rational, you must flip the coin again and give me another 50% chance.' What would your mother say ?"

[Matt]

If they cheat at the right side of the distribution, then a redistribution rebalances.

If they are not cheating at the
right side, then it is no economic model I ever heard of. They are correlated cheaters on the right side, it is avoiding these price fixing, bribe taking royalists that created the modern economy. Humans always knew that and created the redistribution scheme as a balance, to keep price fixing in check.

[Tomas]

Thanks Robert and Neel, excellent points.

Always educational to post here.

[kharris]

D-slam,

In the real world, improved outcomes from policy, or lack of policy, are by assumption. Heck, read just about any policy discussion on the internet and that is the unavoidable conclusion.

Pareto and Arrow are fine for your heritage-tomato-eating, small-run-wine-drinking, PhD-toting scholar. For the rest of us, we know what will improve outcomes by simple reference to our party manifesto. Saves time.

[mk]

A few thoughts on interpersonally valid utility measure:

1) It seems reasonable (though very fanciful) to posit that everyone has some way to order all possible "world-states" in strictly increasing order of utility. Then, the interpersonally comparable metric is "what percentile of goodness is this world-state?" So if this current world is better for me than 75% of all possible worlds, my number is .75. Then, the "maximize utility" criterion would say something like "maximize the expected value of this statistic given a uniform distribution over all human beings"-- i.e., if you are behind a "veil of ignorance" and don't know which human you are, what is your expected value of personal utility when you remove the veil?

Now, this analysis is full of holes:
a) Should the percentile statistic be evaluated given a uniform distribution of all world-states? Or should we take into account the fact that some world-states (the state in which I can fly) are very unlikely and should not be counted heavily?

b) Why should we maximize the expected utility of this statistic? Why not take the variance into account? How do we decide this? You have to sort of play god behind the veil of ignorance and decide what type of statistic is important to you. But that just means we aren't really behind the veil, right? We're imposing our own preferences.

c) It's wildly impractical.

Nevertheless, it may be fruitful as an indicator of the type of logic we want to be applying here.

2) I had something else to say, but I forgot.

[mk]

2) Oh yeah-- what about subjective measures of well-being?

[marcus]

Pareto optimality, mathematical utility orderings based on the consequences of actions, etc. are all part of trying to turn political economy from a cultural questions of values into a science that would compel assent through pure reason. That has been the project of economics. However, culture is not so easily evaded, and enters through the back door of assumptions.

But there are still facts of the matter. Social statistics, not economic theory, have been the biggest contribution of the policy "sciences".

[marcus]

And oh yeah -- interpersonal utility comparisons really are impossible. How can you possibly know how much pleasure Bill Gates gets from a dollar? Maybe he's like Scrooge McDuck and spends all his time fondling his hoard of riches. Who knows, is the point.

However, that doesn't mean that it's unreasonable for a culture to decide that a dollar is more valuable in the hands of a poor single mother than it is as part of the Gates hoard. That is pretty obvious, and a policy discipline should at least have a way of systematically discussing the definition of "reasonable" involved there. Beyond tagging it as "inefficient", yet possibly "equitable".