Saturday, December 31, 2011

Fiction is now either Science Fiction or Historical Fiction. The present doesn't last long enough.

I just finished reading "The Wind up Bird Chronicle," and the plot of it requires that the main character be unreachable by phone when he is outside of his house. How different a world that was, where going out into the world to meet other people actually isolated you in some ways. This dated the novel entirely. It became a novel about sometime last century instead of just a novel.

Consider writing a story about someone who gets lost on a road trip or a walk. This is an archetypical setup, but how difficult it would be to do that today, to set that up in a way that rules out all the obvious ways of getting directions in an entirely uninteresting way from our smart phones? I can imagine it now: "My battery was too low to get signal, and between my two companions, one doesn't have a nationwide data plan, and the other is with a second tier carrier with poor 3g coverage, so miraculously, we have to talk to another person, and thus move the plot forward in an interesting way." Even after all those awkward contortions, that setup probably has a half-life of 5 years.

All of us spend a lot of our lives on our computers, but what we do on them can't be written about in a way that is both poetic and accurate. We just don't have enough words for it. Every humble tool in a leatherworker's arsenal has its own name (the awl for instance.) These things have been around for long enough for that to happen, and to gain the gravity that makes them candidates for metaphor. The pen is still mightier than the sword, even though we no longer use either. The keyboard may be mightier than the cruise missile, but I can't imagine saying that with any dramatic weight.

The basic ways we do common things are not only different, but changing from year to year. Henceforth a novel will have to choose a time period in which to take place, and choosing "now" will make it historical fiction by the time it is published.

Tuesday, March 08, 2011

Why big organizations don’t take risks proportionate to their size (a theoretical argument)

TLDR version: People optimize E(Log(x)). Big organizations should optimize E(Log(Σ x)), but because they are composed of many people, they optimize ΣE(log(x)).

Logarithmic Utility Curves

Suppose someone offers you a 50% chance of a $1M prize, or a 10% chance of a $10M prize. Most people who don’t already have a lot of money would take the first, more certain option, even though the expected value of the second is double that of the first. ($0.5M vs $1M). $1M would improve my life a lot. $10M would also improve my life a lot, but not so much more than $1M that I’m willing to risk getting nothing. Economists call this “risk aversion.” and model it using a “utility curve.” Though quite abstract, it corresponds pretty well to intuition. The idea is that $10M isn’t “worth” 10x as much to me as $1M, so I have to account for that before I take the expected value. The most common utility curve used in simple models is logarithmic, both because it’s mathematically simple, and close enough to reality for most purposes. Intuitively, no matter how much money I make, I’m willing to put in a linear amount of additional effort in order to raise my income level by 10%, so you end up with logarithmic utility.

To compare these two offers, before we take the expected value, we’ll take the log of the outcomes.
log(1M) ~ 6,
log(10M) ~ 7,
0.5 * 6 > 0.1 * 7, so we take the first offer as observed.

Rather than optimizing E(x), we optimize E(log(x)) and get behavior somewhat like what a real person would do.


It makes sense that an organization should have a utility curve looking like a log. Going out of business (log 0) is -infinity as observed, and companies care about percentage improvements rather than absolute improvements just like individuals do. I apologize for not having better arguments that this is the way organizations should behave. This is a blog post, not a research paper. :)

This means that if the output of each employee is x, the outcome for the company as a whole is Σ x, and the company should be optimizing E(log(Σ x)).

How do they actually behave? The company will behave in the way that the aggregate of its individuals behave. If individuals are rewarded in proportion to their personal outcomes rather than the company’s outcomes, they’ll behave by optimizing their personal utility function. As a result, the company as a whole will optimize Σ E(log(x)).

Big organizations apply the risk-aversion of an individual to losses that are teeny relative to the size of the organization, because people care more about their individual risk than the risk to the company. Ideally, a company should have many people working on huge improvements with a small probability of success. In reality, it's almost impossible to structure incentives so that doing things with a small chance of success is a good personal strategy. It’s hard to reward competence and not outcomes. If you reward outcomes, the company will be risk averse. Having a few engineers work for years on something that doesn’t finally work is a teeny risk to the company, but potentially a huge risk to the careers of those engineers.