Saturday, March 17, 2007

So Far, So Good?

Background: the Monty Hall paradox (here are some of my tips for understanding and explaining it). Optional: David Sklansky, Theory of Poker.


I was at my neighborhood pub last night when I overheard a snippet of conversation that nearly made me pick my first bar fight. (I've been in plenty of bar fights, just never picked one before.)

WOMAN: "Do you think you made the right decision?"

MAN: "So far."

So far? I shook my head and took a drink. This guy sounded just like all the lousy poker players I've ever known: people who think drawing to an inside straight is fine as long as they hit their hand. They confuse the payoff with the play. His decision was right, I fumed, if it was arrived at in the right way, not if it does or doesn't pay off in the actual event. (Many a fisticuff has arisen over this important point of principle.)

This very idea had just come up in my Rediscovering Math class. We were playing the Monty Hall game, with me as the host, and with an imaginary jeep as the prize behind one of the doors. The student who was the game's contestant said, "OK, I'll switch because I believe the math, but if the jeep is behind my first guess, I'll be pissed." In reply I said, "But would you be pissed, really?" And here another student said, "Personally I think it would be OK even if I lost, because by switching my guess, I at least put myself in a position to win." That's how you keep the payoff separate from the play.

When the woman asked, "Did you make the right decision?", why is it so much to ask that the man should answer, "Well, I made the best decision I could based on the information I had at the time; it's working out so far, but win or lose, I think I made a sound decision on this one." More head shaking, another sip of my drink.

But as I sat there longer, I continued to reflect on the man's "so far" answer. My hackles went back down as I registered the helplessness behind his words. What decision had he been facing, and how did it feel to be still waiting for the other shoe to drop, wondering if everything would turn out all right? It struck me that there is a cruelty in this common view of decisions, this picture of accounts that remain open until the final score is tallied. But when you don't know how to assign yourself points for making rational and careful decisions, what other way is there to keep score?

***


Rational and careful is not synonymous with mathematical or robotic, and in fact, being rational demands that we pay attention to emotional factors. Good decision-making doesn't ask us to quantify emotions and values, nor does it ask us to ignore them in favor of "objective" considerations. But it does demand that we gain some distance from these emotions and values by naming them, and by investigating them as factors in our decision-making process. This is not something we often do naturally, but it is, I hope, something we can be educated to do, and something we (I) can improve at throughout the course of our lives. Another thing I hope to teach my students in Rediscovering Math is that a momentous decision with real consequences for ourselves and for others is not only a process of sorting through emotions and values, but also a process of discovering crucial facts, of being creative about options, and of bringing our clearest sort of thinking to bear. One of my students today pointed out that it is especially in a problem fraught with emotion that thinking systematically can help us cope.

If I could reclaim the last point for a mathematician: Poker is a poor metaphor for life, but it illustrates one essential feature of the rational life, which is that even the major life decisions are about (as my student put it) "putting yourself in a position to win", not winning or losing in the event. If this message helps us not to feel regret when the world inevitably fails to give us what we ask for, then there is a way in which the rational is in fact the most human option, because the most merciful.

3 comments:

Anonymous said...

Recommended: Barry Schwartz’s book “The Paradox of Choice. Why More is Less.” -- he goes in to some interesting research on why people make the decisions they do and why they frame them they do

a different Anonymous said...

Glad to hear that your hackles decided to rest because, as you seemed to recognize at the end of this segment, unlike poker and other gambling choices, life decisions don't come with a universal or even a clear method for calculating Expected Value. One cannot truly estimate the reverse implied odds of *not* pressing charges against an alcoholic and abusive spouse; the implied odds of waiting for That One Perfect Someone rather than pursuing frequent serial monogamy or playing the field; or the direct pot odds of allowing a new friend into your network.

The most important factor in most life decisions is the emotional content because the decision maker and the people in her life must live with the repercussions or the threat of them (evidently as in the bar patron's case). Professional gamblers will tell you that emotional decisions are sucker plays. In life, though, it seems foolish to behave as dispassionately as a robot, Vulcan, algorithm, or seasoned gambler: where is the LIFE in that process?

JasonZimba said...

This piece will probably grow a lot over time.

With respect to the last comment: I was trying to say that there's another way to more easily "live with the repercussions" of a major decision, and that is to be (as I put it) "rational and careful" about the decision in the first place. This doesn't reduce to maximizing EV, and of course it involves unquantifiable emotions and values. (It also involves much more fact-finding and systematic thinking than people are used to doing.) Rational and careful is not synonomous with mathematical or robotic, and in fact, being rational demands that we pay attention to emotional factors. Poker is a reductionist way to look at life, but it illustrates the essential feature I was trying to emphasize, which is that even major life decisions are about (as my student put it) "putting yourself in a position to win", not winning or losing in the event. If this message helps us not to feel regret when the world inevitably fails to give us what we ask for, then there is a way in which the rational is the most human option, because the most merciful.0