## Thursday, June 13, 2013

### How constraining are completeness and transitivity assumptions, really?

OK, on Unlearningecon's blog I made a quick point without elaboration that I've made in more detail here - that while most people think economists' assumptions about "rationality" are implausibly strong they're actually quite weak. You basically need completeness and transitivity. Indeed it's impressive that you need such weak assumptions to make an optimizing agent go.

Even this was problematic for one of his commenters:
"The problem isn’t the ‘rationality’, but the completeness and rigid transitivity that economics has to assign to an agent when trying to glean insight into the workings of an economy."
I agree that completeness especially is unrealistic (transitivity, as far as I can figure, actually isn't really that bad), but honestly what changes by assuming it? The biggest problem in a world with transitivity but without completeness is that you just don't have the basis for a choice. The math doesn't work. You can't define a maximal set. But we could imagine some kind of algorithm for dealing with a world where preferences actually aren't complete (i.e. - the world we live in). A couple come to mind. First when you make pairwise comparisons you could just skip the cases where preferences aren't defined. You could also flip a coin (since transitivity holds I don't think this should cause too much trouble - the biggest problem is its randomness).

Let's say you had a bunch of agents with mostly complete preferences and you ran some simulations with these sorts of options. So we're not doing the optimization that requires the rationality assumptions Unlearningecon is uncomfortable with, we're doing more of an agent based approach. I don't do this sort of modeling but I'm guessing you get about the same results (particularly if you skip the undefined elements and the undefined elements are not maximal elements... which makes sense - why would your preferences be undefined on a bundles you highly value? Agents ought to be the foggiest about relatively low value bundles).

A more realistic approach is to assume that it takes cognitive resources to produce completeness in the preference relations. Indeed we could even think about a production function for preference relations and some way of assessing expected benefits of expending cognitive resources. If we think higher-value elements might have undefined preference relations this might be especially important. Think, for example, of grocery shopping that requires you to plan for a week's worth of meals given a huge variety of products. There are many high value bundles and you exert some effort in figuring out the best bundle but there's a point where you quit expending cognitive resources and just make the purchase. Again I'm guessing running this simulation approximates the results from more naïve optimization problems that go in assuming completeness - but of course it won't perfectly hit it.

I don't run agent based models so I'm just thinking through how these seem like they'd work. Is there any reason to temper my optimism? If we were to relax these assumptions how would things really go so wrong that adding the assumptions - for mathematical convenience - is a dangerous move? I just can't think of a reason for pessimism here. The unrealism we're dealing with seems to primarily pose problems for the math, not for the conclusion. Thoughts?

1. I am always disappointed that nobody who responds to my criticisms of utility or rationality notes my most important point:

"However, as I have previously argued, utility does not only require that preferences are complete, transitive and so forth, but also that they are fixed: that is, individuals have a set of preferences that remain the same for at least long enough to be useful for analysis (and in some neoclassical models, preferences are the same for an agent’s entire lifespan). However, evidence suggests that individual preferences are highly volatile, differing across time and being highly dependent on situation. How exactly could something so hard to pin down be useful?"

Preferences may be complete and transitive at any one point in time, but that doesn't tell us about how they are formed and how they change, which seems to be the real question if we are studying something so volatile.

There are also other problems with neoclassical expositions - someone on twitter pointed out economics assumes preferences are strictly hierarchical. But Rock-paper-scissors is an obvious example where this is not the case. Related is the idea that preferences may depend on what other people choose or on what else someone chooses.

I find it's the implicit, not explicit, assumptions which make economists prefer (!) their own framework.

1. Who says they need to be fixed? This is news to me. They might not respond because it's not a good criticism.

I would have thought preferences need to be around for about as long as it takes you to pull out your wallet. I had a very high preference for BBQ last weekend. I acted on it. I don't now. I act on that too. Prices change as these preferences change.

What's the problem?

Why do you think this is a quality criticism?

Rock paper scissors gets into the expected value (and the expected value of each should all be equal). Again, what's the issue? There is no maximal strategy in rock paper scissors. So? What's the problem?

I think the preference for the framework is obvious. It's reasonable that preferences are concave and we're complete and transitive enough to get a hell of a lot of mileage out of the framework. I don't know any competing framework that's preferable. Do you?

2. "Who says they need to be fixed? This is news to me."

Well, nobody, but as I said it's implicit.

"They might not respond because it's not a good criticism.

Possibly ;)

"Why do you think this is a quality criticism?"

Let's say we have our model of the economy - an equilibrium time path. We have a set of agent or agents with given preferences, endowments, technology etc. We then map these into an outcome. Yet at no point is the possibility that preferences may change and fundamentally alter the 'time path' of the economy considered. But preferences do change,m all the time, so the model is probably irrelevant. Remember, Lucas considered preferences the 'deep parameters' of human behaviour, and the discipline's enthusiasm for microfoundations has been based on this: they presume that they 'solve' the Lucas Critique. But if preferences are liable to change with policy - or randomly - then there's no reason to believe our model holds, and therefore it will be as useless as the crude Phillips Curve.

"It's reasonable that preferences are concave and we're complete and transitive enough to get a hell of a lot of mileage out of the framework. I don't know any competing framework that's preferable. Do you?"

See Paul Omerod on network effects/copying/trend etc. I linked to him in my post.

3. I don't understand the problem. Write the same model, change the preferences, see what happens. WTF is the matter here? I am feeling really dumb.

Presumably most people don't write models like that because it's not a relevant complication of the mechanism they're modeling. None of this makes the method unreasonable because if you do care about that you just change the preferences and keep going.

Omerod does what I suggest, right? You use rules of thumb because of cognitive constraints. You're just adding another margin that you're acting on. I'm not seeing how this is different from the way most people think it works.

4. But if preferences can just change in the real world, which of your models do we use? Why not consider a model where preferences can change?

Omerod is more about network effects and how preferences are created by environment. Also see this piece, which pablo bortz linked on twitter:

http://aix1.uottawa.ca/~robinson/english/wp/consumer_king.pdf

5. Honestly, Daniel, I don't understand why you would engage this troll. Every time I've had the misfortune to be linked to his blog, he just constantly batters a construct of mainstream economics that seems to be composed of DSGE, Mas-Colell misunderstood, and whatever Steve Keen tells him it is. It's fine to criticize assumptions about stability across time and contexts...if you can give examples of work where this assumption is used, and matters. Of course, there are no concrete examples to be found here, as you never find in these kind of puerile critiques of economics.

Incidentally, there is some interesting recent work about stability of preferences across contexts using insurance data that I've been reading recently, both accepting it to an extent (Einav et al. (2012), http://www.stanford.edu/~leinav/pubs/AER2012.pdf) and rejecting it (Barseghyan et al. (2011), http://joshuateitelbaum.weebly.com/uploads/2/1/1/2/21124222/bpt.pdf).

6. 1. If changing preferences really matter - if it matters that I wanted BBQ last week but not this week - if you can't just assume that I wanted half a BBQ meal both weeks - then don't assume it. Use changing preferences. On most questions of interest we CAN just assume I want half a BBQ meal both weeks. Even if you do assume it it's still a neoclassical model.

2. Endogenous preferences are great. What's the issue here?

You don't seem to be bent out of shape about neoclassicism. You seem to be bent out of shape about some mythical view that the absolute simplest neoclassical model is the best one in all cases. Tough thing is, nobody that I know of holds that view.

7. @Pseudonymous

Getting past your whining, stereotypes and typical obsession with Keen (just because I decided to blog his book - could easily have been any other but there you go), let's find the small amount of substance in your comment:

"Of course, there are no concrete examples to be found here, as you never find in these kind of puerile critiques of economics."

Actually, I offered the example of Lucas suggesting that preferences were the 'deep parameters' of human behaviour. Otherwise, I presumed it was so well established that many DSGE models have individuals with given preferences etc, and the equilibrium maps these onto an outcome, that I wouldn't have to bother.

btw, if some papers 'accept it to an extent' and others 'reject it', it has been falsified. Cheers for proving you have anything but a scientific view of the matter.

@Daniel

1. This lost me. I don't see how it's OK to assume you want half a BBQ every week.

2. There are a lot of areas of economics, obviously, but many of the mainstream models taught to most students assume preferences are internal, fixed for long enough to matter and so forth. There is little discussion of how environment determines preferences, in my experience anyway.

8. Unfinished 3rd paragraph: fixed preferences are also used in every model taught on UG economics, afaik.

2. I have an unrelated question.

If I am a capitalist in a area with a fixed gold standard and only one coin of gold...And I take that piece of gold and split it into two pieces, half for labor, half for materials. Then if I sell my commodity on the market there is no way I am going to get more gold than I started with, (no profit)...How is this overcome?

3. Daniel Kuehn: Speaking of rationality in economics...you still have yet to respond to this.

http://unlearningeconomics.wordpress.com/2013/04/03/economists-and-the-as-if-argument/#comment-12566

All anonymous comments will be deleted. Consistent pseudonyms are fine.