Thursday, April 28, 2016

models and language

All models are wrong, but some models are useful; the purpose of a mathematical model is to simplify a complicated phenomenon so that it can be more easily and thoroughly understood, and a good model should therefore be simple enough to be readily understood and complex enough to display the phenomena of interest, making it reasonably clear what the origins of those phenomena are. The two kinds of mistakes that can be made from forgetting that All models are wrong, but some models are useful are
  • using a model outside of its domain of applicability — forgetting that is it wrong
  • criticizing a model solely for being wrong, without specifying that it substantially fails to serve the purpose to which it's being put.
For both reasons, it is typically useful for a model to be clear about its domain of applicability; it should be clear where the approximations are going to break down.

Humans are model-builders; while we use a lot of simple behavioral models that other organisms use, we are better than[1] other organisms at managing hypotheticals, especially hypotheticals that are fairly well outside of our direct experience, in part because we tend to carry around deeper models of the world with which we interact.  This comes through in our uniquely[2] human language; perhaps the barest is the use of labels, hierarchical categories ("animal" includes "dog" includes "that kind of little dog that looks like a mop with its handle missing"), and abstraction ("three apples plus two apples equals five apples" and "three oranges plus two oranges equals five oranges"; for that purpose, number can be abstracted away from the thing being counted), but it's perhaps on better display in the use of metaphorical language.  What's key about a metaphor is not that the thing being compared to the other thing is identical to it, merely that it shares certain characteristics that are relevant to some purpose; All metaphors are wrong, but some metaphors are useful, and they're perhaps more useful when it's clear in what ways they are useful and in what ways they are wrong. This is true, also, of categorical systems; if we classify movies, for example, into action movies, comedies, etc., we may sometimes find a movie that seems to sit on the edge of one category or another, or that clearly doesn't fit any of the categories we had before, or clearly fits into multiple categories that we might have thought of as largely disjoint from each other. Typically the category system will be of some use as long as the exceptions aren't too common, and as long as the use to which it's being put isn't too brittle when an exception comes along.

There are two somewhat more concrete examples I want to end with.  The less concrete is that an analogy between X and Y will sometimes be met with "You can't compare X to Y," typically in a situation in which X and Y are in fact very similar in the relevant way but different in an obvious but irrelevant way.  I'm certainly careful not to use "Nazis" as "Y" because I expect to trigger this fallacy, but even there it comes off to me as a sign that the respondent either isn't paying much attention or is more interested in some kind of point-scoring debating game than in furthering a serious discussion.  The more concrete example I want to give has to do with religion; in particular, the terms Muslim and Christian.  There's a certain politeness in taking at face value a person's own label[3] for his or her own religious beliefs, and that certainly seems like as good a way to handle edge cases as any, but it also seems to me that the labels become uselessly circular[4] if the term Muslim means "person who considers him/herself to be a Muslim".  Asking whether ISIS is "Islamic" is ultimately a semantic question; asking whether it is more useful to have a term for most Muslims that includes ISIS or one that excludes ISIS is at least somewhat clearer when it's clear what the relevant "use" is.  In any case, if we do call ISIS "Islamic" that certainly doesn't mean that their beliefs or practices are exactly those of other Muslims (and, accordingly, the fact that those beliefs and practices aren't exactly the same doesn't by itself mean we shouldn't call them Islamic).  I similarly see the occasional assertions that, because someone has identified him or herself as Christian, it is mandatory that they adopt a particular vision of Christianity, or it is "hypocritical" if they don't.  Christianity is not so narrow a category that the use of that label implies precisely a set of moral beliefs, but it is occasionally a broadly useful label nonetheless.

[1] almost?  I'm not up on animal cognition research.

[2] again, I think uniquely; perhaps not quite, though certainly I mean something more by "language" than would admit simple alarm calls etc.; "language" in my mind requires an ability to express at least some degree of abstraction.  In fact, if you're not slightly critical of my claim that language comprises model-building on the grounds that it's at least very nearly tautological, then I'm not being clear about what I mean by those words.

[3] There's a big issue, too, of our not just using labels but, for the purposes of language, having to use shared labels, i.e. we need to be using labels in approximately the same way, or at least to be able largely to understand the labels each of us is using. For the time being, I'm relegating that to this footnote.

[4] in principle. In practice, a person who doesn't fall at least close to the usual category is unlikely to claim to belong to it, which is probably at least part of why we so often fall back on it.

Tuesday, April 19, 2016

terms of trade

Suppose I have (at least) 3 oranges and you have (at least) 5 apples, and I'd consider trading three of my oranges for four apples to be a net improvement to me, and you'd consider trading five of your apples for three oranges to be a net improvement to you.  We have a situation, then, where we ought to be able to find a mutually beneficial trade, but there is a real danger that we get hung up on that fifth apple; even if our relative values are common knowledge — so that, among other things, we both know that we ought to do some kind of trade — it's quite possible we end up unable to agree to a deal, if we both dig in our heels, I insisting that you give me five apples for my oranges, and you insisting that I accept only four.

This looks like an economic model, and it is that, but it's also a model of politics, and while I think people have a tendency every four years to think that they're in the ugliest presidential race ever more from poor historical perspective than a monotonic decline in the state of American politics, it really does feel as though the "digging in our heels" bit has become worse in the last several years, especially (but not exclusively) on the right.  I also think, though, that there's less common knowledge of values than people often believe, which creates more problems, the way that my insisting on six apples would in the opening parable.

I don't think it's inconsistent for me to add, though, that I also feel as though a common and vapid form of political discourse involves essentially decrying any attempt by the other side to negotiate terms of trade; in particular, when controversial riders get attached to popular legislation, especially but not only when those riders are topical, that seems entirely fair[1] as part of negotiating a deal.  I've noted elsewhere on this blog how I might change procedures such that these gambits would be less capable of blocking consensus bills, but certainly given the rules we have, something well between unilateral disarmament and complete obstinacy should be achievable.

[1]in and of itself.  Demanding huge concessions for passing a popular or urgent bill is antisocial, while adding something that one side mildly dislikes is very different.

Tuesday, April 5, 2016

homeowners associations

One of the striking ways in which my views have changed since (say) I turned 30 is that I'm a lot more pessimistic about local government in practice than I used to be.  The principle of subsidiarity still has great theoretical appeal to me, however, and I've had some ideas in the past several ideas, many of which have other features I found unattractive when I was in my twenties as well, to try to mitigate the problems that local governments often face.

While not exactly a local "government", homeowners associations are of particular interest in this context in that there are certain sorts of problems to which they seem like obvious and even necessary solutions, and yet I think they often highlight the worst of local government.  A large part of the problem is sort of an averse selection or "attractive nuisance" feature they have, which is tied to the fact that the knowledge that someone is interested in serving on the homeowners' association tends to imply that that is not a person you would want to serve on the homeowners' association; they may attract some people who have a sense of duty that is not entirely misplaced, but they also draw anyone with an inclination toward officiousness, a certain kind of status-seeking, or peculiar axes to grind.  The equilibrium here is that they be held in check by the constraint that normal civic-minded people find the prospect of getting elected, attending the meetings, and providing whatever other service is entailed slightly more obnoxious than putting up with the current board, which thereby consists primarily of people with at least slightly antisocial motivations.

One solution is something akin to Athenian democracy: part of your "homeowners association dues" is the obligation to occasionally serve on the board, which consists of a somewhat random sample of homeowners, which, as I noted, is likely to result in a majority that is at least less pathological than the group that would volunteer.  I don't hate that solution, but I have in mind another set of solutions, driven by the same idea that what one needs is a system for attracting candidates for office who are motivated more strongly by something other than telling their neighbors what to do.  What's particularly interesting is how squarely these three solutions fly in the face of the sort of thing that various progressive (in the best-preserved century-old sense of the term) and "good government" forces would tend to put forward:
  1. Allow, encourage, and maybe require that some of the board members come from outside the community;
  2. Circumscribe the job such that actually performing it is as unburdensome as is possible while getting the actually needed tasks handled
  3. Provide a salary for the job at a level that is at least on the brink of ridiculously generous.
The latter two points should be clear in light of the preceding commentary; money may not be the motivation you would have as your first choice, but it's likely to be less malign than many intrinsic motivations, and, provided that it's sufficient to draw enough candidates to have a competitive election, is ultimately not insuperable. These provisions make the job more attractive to normal people, and hopefully enough normal people that the winning candidates are somewhat representative of the people electing them, rather than the people who were motivated enough to volunteer. The first provision is not there with the expectation that the average person from outside the community is a better candidate than the average person in the community, but simply the expectation that there are more of them; inducing forces to draw candidates from outside of petty neighborly disputes is part of it, but this provision, too, is more concerned with drawing enough candidates to get a competitive race from which the homeowners can meaningfully elect a proper subset.

So there's my advice: turn it into a well-paid sinecure open to outsiders in order that it best serve the electorate.

Saturday, March 26, 2016

regressions on selected populations

Suppose there are two different sets of factors that affect some kind of outcome, and each moves toward optimizing the outcome, but in a noisy way.  I'm imagining two gradual processes, each affecting a subset of factors that affect the outcome, drifting generally toward values of those factors that increase some real-number-valued function of the factors; the function itself may move, somewhat gradually and smoothly, requiring the processes to chase it.  We might imagine them as multi-dimensional factors, but the language might be easier and more concrete if we imagine that each of them is simply a real number as well; x and y follow stochastic processes that drift in a direction of higher f(x,y).

Suppose, though, that x tends to move more quickly than y; it will, at any given time, tend to be closer to its optimal value.  Imagine, now, an ensemble of these, each trying to optimize the same function but otherwise moving independently of each other.  Cross-sectional differences in y will tend to capture differences in the extent to which the y values have adapted to the most recent function; if the optimal value of y has been increasing, there will be a pronounced tendency for higher values of y in the ensemble to be closer to the optimal value of y, with perhaps some overshooting, but, if y adjusts slowly compared to the rate at which its optimal value changes, probably relatively few points that have too high a value of y.  Values of x, on the other hand, will be scattered more or less randomly around the optimal value of x; if the noise now exceeds the residual mismatch between the average value of x and its current optimum, then the highest values of f will be associated with values of x near the middle of the distribution, rather than near one of its ends.

This is all assuming more or less the right ratios — that adjustment of x isn't too slow compared to changes in its optimum, that adjustment in y is fairly slow compared to changes in its optimum, and that in some practical sense they are each intrinsically of similar importance to f(x,y) relative to the noise in each variable.  The upshot, though, is that if we do a standard linear regression on how f varies with x and y within the observed cross-section, we find that x has little to no linear effect, while y does have one; even if we add nonlinear terms to the regression, x contributes only second-order terms, while y has both first- and second-order terms, and in general if you can pick to know only either x or y from a datapoint sampled from the population, knowing only y will enable you to predict f(x,y) with much more accuracy than knowing only x would.

There's literature suggesting that parenting is less important to a child's outcomes than genes are.  This is, however, conditional on most parents' trying to be decent parents; it is certainly the case that environment can matter, as we see with the victims of Romanian orphanages and other examples of violence and neglect.  It seems likely to me that parenting isn't, in some sense, "less important" than genes; it's just that most people have mostly done a decent job of adjusting their parenting to modern times, such that observed variations tend to have second-order effects, while our genes haven't caught up in the same way, and that differences there tend to be first-order.

Thursday, March 24, 2016


Three and a half years ago, I was looking into the idea of doing research on people's desire for privacy.  I kind of gave up, though others have not, and perhaps I'll go back in that direction some day.  Today's post is triggered by recent news from my school that a student has a strain of meningitis, which information the school may be required to make public, though of course other regulations require that they not announce which student.  This seems like a useful example in which to lay out some spare thoughts I've had over the years.

The essential point is that there would be some public health justification for releasing the name of the building in which the student lives, the classes the student attends, possibly even student organizations in which the student has been active.  If you release all of those, it seems likely that the student would be uniquely identified.  Privacy is, at first order, less of a concern if you release any single one of those pieces of information; what I mostly want to note here is that, however you might try to place value on the student's privacy, one of the primary costs of releasing one of those pieces of information is that you thereby make it more expensive to release one of the others (and, similarly, more costly if one of them comes out by accident).  While there is perhaps some extent to which different information can be released to different people, insofar as the information is likely to spread, it seems likely that their decision not to release any of those extra bits of identifying information is probably the right cost-benefit decision, regardless of what legal liability rules HIPPA might impose as well.

Friday, March 4, 2016


I'm making less of an effort than usual with this post to be interesting to people who aren't me.  I'm just formalizing the idea of "unravelling" of certain employment markets, in particular markets where there's some sense in which it's best for all firms and workers to be making offers that are in some sense simultaneous, but where individual agents might have an incentive to cheat, making deals before the thick market; in particular, under what conditions might a firm make a take-it-or-leave-it offer to a prospective employee before the market rather than waiting for the market?  In particular, it should be clear that, if the offer were really enticing, the employee would have accepted it in the regular market, and if it's not enticing enough, the employee won't accept it anyway.

Suppose there are two prospective firms hiring an employee, and let's examine the consequences of their making offers sequentially or simultaneously (in the sense of game theory).  Ex ante, the employee attaches probabilities p1 and p2 of getting offers from them, and gets utility u1 or u2 from accepting an offer. (The value of unemployment is set to 0, and may be assumed lower than either ui.)  If firm 1 makes an offer that must be accepted or declined before receiving a response from firm 2, then declining the offer is worth p2u2; conditional on firm 1's offer, the expected payoff is
max{u1,p2u2} or p2u2.
If the offers are simultaneous, then those conditional values are
max{u1, u1(1-p2)+p2u2} or  p2u2.
If the first firm fails to make an offer, the structure of the game is immaterial. Similarly, if the first firm is the worker's first choice, the structure is immaterial. If the worker gets an offer from the first firm but u2>u1, then the simultaneous game payoff, which can be written as u1+max{0, p2(u2-u1)}, is u1+p2(u2-u1)=p2u2+u1(1-p2); the simultaneous game payoff in these circumstances is higher by min{p2(u2-u1),u1(1-p2)}.

The first firm gets the hire in the sequential game whenever it does in the simultaneous game, but also when
  • It makes an offer
  • firm 2 makes or would have made an offer
  • u2 > u1 > p2u2
where the last condition is the condition in which the worker would choose firm 2 over firm 1 if given both choices but will choose firm 1 rather than take the chance that the other offer isn't coming.  This condition essentially captures the intuition of the last sentence of the first paragraph; by exploiting the worker's uncertainty as to whether a better offer would be forthcoming, the employer can induce the worker to take the "bird in the hand", but as the probability of another offer gets close to 1, there's an increasingly narrow range of offers the worker would accept now but not later.

the value of money

Let's continue on the idea of eggs as a medium of exchange.  In particular, while they make a decent store of value for a short period of time, they're terrible at storing value for very long; even if you boil them, they won't be a way to stockpile wealth on the scale of a generation or something.  They hold their value well enough, though, that one could reasonably use them to facilitate a couple of trades before they end up with their final consumer; eventually, though, their value is that of a straight consumable.

Now consider an agricultural economy with limited currency of other sorts such that eggs pick up at least some of the slack.  The consumer of the eggs presumably sees some gain from trade in the final transaction; that person values the eggs at least as highly as what is being exchanged for them.  The penultimate owner presumably values what is being received from the final owner more highly.  Now consider the trade between the antepenultimate owner and the penultimate owner of the eggs.  We suppose
  • the transaction couldn't have happened had the eggs not been available as a medium of exchange
  • there was a substantial gain from trade in the eyes of both parties
  • if it is common knowledge that the eggs are deteriorating, the terms of trade should reflect this.
Young eggs, in particular, with three or four transactions left in them, might be worth more than eggs with only one or two transactions left in them — "eggs" may not be a unit of account (by which I really mean "standard of value"), exactly, even though they're a medium of exchange. At all both points, though, the eggs can acquire a liquidity premium in excess of the value that any consumer puts on them, essentially incorporating some of the gains from the trades they will facilitate into their initial value.

Now let's go back to money that is expected to last, in some practical sense, forever.  The social value of a dollar is the value of the transactions it can facilitate; a dollar that is return-dominated is, in some neutral unit of account, depreciating, but as long as the present discounted value of the gains from trade of the trades it will mediate is at least (say) a few dollars, the dollar can kind of steal that.  The more slowly the dollar deteriorates, the more marginal trades it can intermediate; a dollar that depreciates quickly will only be accepted as payment if the gains from trade are large.