1.13.2006

Optimization problems

I'm going to venture into math nerdiness for a very short time, because sometimes it's just how I think. Don't worry -- it won't be too painful. :) I'm just going to use some terms from very basic game theory to frame a few questions I want to explore. If you want a better explanation of the theory than what I'm going to give, see this page.

Before I get to the questions, I want to define just a couple of "strategies" for decision-making (believe me, there can be many more!).

1. Maximax -- essentially, you look at the best payoff that each option provides, and you take the option that gives the best of these best payoffs. In other words, you aim to get the best "best" consequence.
2. Maximin -- essentially, you look at the worst payoff that each option provides, and you take the option that gives the best of these worst payoffs. In other words, when following this strategy, you aim to get the least "worst" consequence.

Now, here are the questions: When choosing a option from a set of alternative options, which of these two strategies do you tend to use? Why? And does the particular strategy you use depend on your situation?

I'll give an example of how this may be applied. Say that you're out "spouse-shopping." (Sounds weird, doesn't it? Oh well.) Realistically speaking, you know that marriage is going to produce both highs and lows. These peaks and valleys are inevitable in marriage -- or so I hear. So given that you know that you will experience both highs and lows with any person, what drives you to decide to settle down with person A instead of person B? Are you prone to choose a person who is most likely to maximize the intensity or duration of your highs (the maximax strategy) or a person who is most likely to minimize the intensity of your lows (the maximin strategy)? Do you want to make life more happy and fulfilling when things are good or do you want to make life less difficult and painful when things are bad?

Of course, there are situations in which applying either strategy will produce an identical result -- it would be great to find a spouse who is going to make your good times great and your bad times not all that bad. I'm sure it's possible, even. But still, a lot of marital problems seem to stem from seemingly unbalanced scenarios: "He makes me really happy and we're passionately in love, but when we fight things turn extremely ugly." Or, "You know, we often are good at working through our problems together and we occasionally disagree a bit, but I just never feel any passion in our marriage -- everything seems completely dull."

Now, choosing a spouse is just one (potentially silly) example to highlight some differences between the two strategies. You can apply this to all sorts of choices we make in life, from grocery shopping to investing in stocks. But even more intriguing than the strategies themselves is the question of what these strategies might reveal about ourselves. If we apply the maximax strategy, we're focusing on the positives. Seems nice, but does it mean that we're being ignorant or avoiding important negatives? If we apply the maximin strategy, we're focusing on the negatives. Seems practical, but does it mean that we're letting ourselves be controlled by fear?

Finally, do you use different strategies for different types of choices? If so, why? For particular types of choices, are you sometimes seeking fulfillment and other times seeking security? Does fulfillment provide security? Does security provide fulfillment?

Ack, too many questions. Okay, I'm going to stop rambling for now. :)

4 Comments:

Anonymous Anonymous said...

One question: would we still think logically and strategically when we're in love? :P

1/14/2006 12:48 PM  
Blogger Al said...

Does fulfillment provide security?
No.

Does security provide fulfillment?
No.

Would we still think logically and strategically when we're in love?
Isn't that the definition of self-control? To exercise wisdom in the middle of emotionally charged situations?

1/16/2006 5:54 PM  
Anonymous Anonymous said...

I understand the dilemma; I'm just glad it's never occurred to me to look at situations in such a way. I think I'd be hopelessly deadlocked into never deciding which way was best. :)

Course, I guess if I look at my own situation, marrying Dean was by far the best decision of my life. I love my hubby to pieces. At the same time, it also had the effect of making things extremely miserable with my family. Had I gone with the maximin strategy, Dean and I never would have gotten married. I'd be without the pain of seeing family relationships shattered, but I'd also be without the person I know I'm meant to be with. So I guess without really thinking of it that way I've gone with the maximax strategy.

Trying to live life with as little pain as possible is of course understandable, but is it really a way to live? I know I've made plenty of screw-ups and I've had situations that have been quite painful to say the least, but even so I don't think I'd go back and change anything if I was offered the chance. Aside from learning from your mistakes, it's the dreary days that make you appreciate the sun, ya know?

1/17/2006 12:44 PM  
Anonymous Anonymous said...

Is it possible to choose a more middling strategy -- to choose someone who doesn't spike at both ends of the spectrum, yet doesn't completely flatline? Is that a real math thing?

2/12/2006 11:26 PM  

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