Monday, 31 October 2011

Prompted Pareto improvements

I'm going to attempt to introduce a new concept here. It is a bit technical, but I'll try to provide background for non-economists first. I may indulge in some modelling to help me understand it better, so if that's not your thing, feel free to skip the equations and just read the words.

I'm also struggling for the name of this concept. The title of the post, "Prompted Pareto improvements" is a name I'm reasonably happy with, but catchier suggestions are welcome.

I'll start by explaining the idea of Pareto efficiency and a Pareto improvement. There's lots of information at the Wikipedia page if you'd like to know more.

Pareto efficiency is one of the standards that is often used in economic theory as something we should aspire to, because it is a standard almost nobody can disagree with. It means that we should consider any transaction, or change in an economic allocation, to be a good thing if it makes at least one person better off and nobody worse off. A transaction which meets these criteria is called a Pareto improvement, and a system in which no possible Pareto improvement can still be made is called Pareto optimal.

It is intuitively problematic in two ways, however. First, because it's hard to achieve. In practice, there are always still opportunities to improve the world, so we are never really at a Pareto optimum. Second, it demands an unlikely level of respect for rich people. Accepting this as our standard yardstick of economic goodness implies that if we could take one dollar from Warren Buffett to cure malaria and hunger, we should not do it. Even though billions of people would be better off, Warren would be a dollar worse off, so this is not a Pareto improvement.

I imagine that most people who have studied economics have wondered whether this is a good principle. It has the appeal of removing all coercion from the economic system: people only take an action if it benefits them. Thus it seems that nobody should object to a Pareto improvement.

One can certainly debate whether it's legitimate to tax Warren Buffett to make Youssou, Mike and Mary better off; strict libertarians would probably say no, while most utilitarians would say yes. Traditional economics sidesteps this question and asks what is the best we can do without such coercion.

I don't want to go into the utilitarian question right now. What I want to explore is the borderline. Why is Pareto efficiency not a useful standard in practice? The two reasons I gave above can be looked at in a single framework.

Start with the second problem: the billionaire who can solve hunger. The take-a-dollar-from-Warren example is an extreme case, but one can imagine lots of situations where a very small cost to a wealthy person would make a huge difference to one or more poor folk. Wealth need not be defined only by money: the same might apply to bone marrow or knowledge, where recipients can gain much more than the donor gives up.

Some cases are so close to the borderline that if we point out the situation to Warren, he may well voluntarily give up his resources to help the person who needs them. Without the reminder, it doesn't occur to him to seek out someone who can use the dollar better than him; but if we do the seeking and tell him about it, he will probably be amenable to a deal. In the conventional model, we could say that his preferences simply change when he gains more information about the situation: his preference for compassion then outweighs his preference to retain one extra dollar.

However this assumes away everything interesting about the problem. If we simply posit that preferences can change, then almost anything can happen; the model becomes too general to be useful. In any case, even traditional economics requires preferences to be stable - it doesn't allow them to change when new information becomes available.

There are several more useful ways to look at this situation:

  • the preferences for compassion change
  • preferences are not a constant, but a function applied to context. When the context changes, the effective utility value of the preferences change.
  • preferences are over a set of objects within the world that we know about. When the world we know about changes, we re-optimise over our newly learned preferences
  • attention is limited and we only make decisions within the scope of our current attention. A new message can shift our attention, and a decision becomes available which was not possible before.
  • the information itself creates a new preference; in the same sense as being told the first line of a joke creates a desire or demand to hear the punchline.

Regardless of which of these explanations is closest to accurate, we can certainly imagine a situation where Warren does not make a particular exchange when unprompted. However, when told about the consequences of the exchange for the other party, he chooses to make it.

I mentioned another reason why a Pareto optimum is never achieved - practicality. There is no realistic way to get to a Pareto optimum because we cannot know all the trades that are available in the world. There are probably many things I would want to buy or sell right now, and people who would willingly sell them to or buy them from me - if only I knew who they were, what was on offer and why it would benefit me.

We can look at this in exactly the same way: if I were prompted with the right information, I would choose to make the trade. Lack of information is what prevents us reaching a Pareto optimum.

The consequences of introducing this concept

So let's imagine we introduce the idea of a "prompted Pareto improvement". A trade between two parties which both parties would willingly make if they receive a certain piece of information, but without that information they do not proceed.

If this concept finds its way into our economic models, what does it allow us to do?

First, it broadens the range of economic transactions which are permissible. This may raise the welfare of the society we are studying (depending on our definition of welfare).

Second, it starts to suggest how we could incorporate the transmission of knowledge into our models. There is little place for knowledge in the main general equilibrium models of the economy. But surely in reality it is one of the most important factors that controls economic behaviour and welfare. Not just explicit knowledge - the possession of intellectual property, or knowing how to write a Java program - which has economic value. But tacit knowledge of the choices we have and the chance they'll make us happy.

How far should we bend the rules?

Can we say that giving ANY message to the individual is permitted? Imagine you told Warren that you had kidnapped his daughter and would kill her if he doesn't give a billion dollars to buy malaria nets. No doubt his preferences would be changed, but on the basis of a false picture of the world (I'm assuming you have not actually kidnapped his daughter. If you have, please contact me and I'll correct this post). But I am loth to add a condition that the information must be "true" - because of the difficulty of defining what that means. Indeed, many messages will have no defined truth value (like "I suggest you go onto the following website...").

Passing a message of this kind would have consequences. Presumably you would be arrested; giving the message in itself would therefore result in a diminution of your utility. Thus you would become a party to the Pareto transaction, and your interests would need to be considered in whether it is a permissible transaction.

This is an unusual case. But it highlights a factor we will have to consider: the provider of information may incur a cost to provide it. A more straightforward example than the above is if A wants to sell a product to B, but in order for B to know it is available, A must pay to advertise it.

Another relevant example may be the threat of force from the legal authorities. In a typical economic model, payment of an income tax is not a Pareto transaction, as the taxpayer does not benefit from it and does not choose to participate. However, most self-employed people pay tax not because they are physically forced to, but because of information that has been communicated to them about the consequences if they don't. The communication of this information affects the choice that the taxpayer makes, even though they never actually suffer the consequence.

More generally, it is logical to suppose that people do not form preferences without receiving information. Some information is directly received by experiencing a product, some is communicated from other people.

With all these interesting factors, how might we design a tractable and useful model?

What we'd need to model to include information in our view of the world:
  • State K of knowledge of an agent (setting aside the question of whether this "knowledge" is all true)
  • Message M which can be received by agent A and will alter K
There exists some M which can be received by A which will induce A to choose to make an exchange of goods with agent B.

We can define three different kinds of improvement:

  • One-sided prompted-Pareto improvement (if B prefers the new allocation unprompted, but A needs prompting).
  • Two-sided prompted-Pareto improvement (if both parties need prompting).
  • Zero-sided prompted-Pareto improvement (an ordinary Pareto improvement without any prompting)
Questions to think about:

  • does B know what the message M is?
  • does A know what the message M is?
  • is there a cost to transmitting M?
  • does M depend on source, timing, other context as well as content?
  • can there be messages N which contradict M? What if multiple messages affect the preferences differently?
 Finally, what might be the generalisations of a Pareto optimum?
  1. An unprompted Pareto optimum; where no pair of agents wish to make an unprompted exchange
  2. A prompted Pareto optimum; where every possible prompted Pareto improvement has been made (does this mean they have all been prompted? Presumably yes)
  3. An intermediate optimum, where every improvement that has so far been prompted has been made, but other prompted Pareto improvements are still possible
These are nice, elegant concepts but they ignore some of the more difficult questions listed immediately above.

What are the consequences?

We are able to start constructing an economic model where information flows are explicitly modelled and their effect on preferences can be understood. To be useful, the model will certainly need to make further assumptions about the relationship between information and preferences. For example, might preferences for goods be made up by composing different product benefits along with some knowledge of how they will satisfy other pre-existing preferences?

It will give us a richer understanding of a real world in which traditionally Pareto efficient outcomes are not reached.

It will allow us to see how a system can get closer to Pareto efficiency - or whatever standard of welfare we decide is appropriate - by becoming more open to the flow of messages that can more effectively allow people to make welfare-maximising choices.

Just as conventional economics has a standard of allowing the maximum voluntary exchange, cognitive economics could develop a standard of maximum information transparency, which in turn would improve the operation of voluntary exchange in practice.

"Maximum transparency" is only, of course, a theoretical goal - no more realistic than "perfect information" in the neoclassical model. Passing messages has a cost. So a model which lets us see what types of information unlock Pareto-improving transactions will help determine what kind, or amount, of information, should be passed. No doubt there will be an indifference point at which the marginal cost of providing one more piece of information will outweigh the marginal benefit from enabling one more Pareto improvement. What will that point look like?

Is this original?

Finally, I would welcome anyone more familiar with the information economics literature than I to say whether this concept has been examined already. Greenwald and Stiglitz proved that a Pareto optimum cannot necessarily be reached when there are information asymmetries; and I am aware of the idea of a "constrained Pareto optimum" which is the best that can be achieved given a certain state of information held by agents. The idea of a prompted Pareto improvement may help to solidify those concepts and provide a more useful framework to implement them in practice.

2 comments:

PunditusMaximus said...

I haven't published anything, but I have sketched out a model of persuasion that looks almost exactly like what you're talking about here. Unfortunately, I've been too ill for the past five years to do anything with it. If you're serious about discussing this, let me know and I'll give you some of what I have. Maybe we can work together, I dunno.

Diane Coyle said...

Interesting idea but I'm unclear about who is changing the information sets of whom. In the welfare econ lit, Pareto optimality is an assessment by 'benign dictator', or rather some kind of 'objective' assessment. I can see how you introduce constraints into that framework, but not quite how you introduce change via prompts. Kaushik Basu's book http://press.princeton.edu/titles/9299.html was interesting on possible welfare approaches, although it was quite hard going. I reviewed it on my blog http://www.enlightenmenteconomics.com/blog/index.php/2011/01/do-we-need-to-go-beyond-the-invisible-hand/(Am probably slow about it, as it's not my field.)