More Trilemmas

Looking into the trilemma subject from last week's entry, I stumbled across Jason Kottke's post about what he calls a "Pick Two" system, using the "good, fast, or cheap, pick two" example to start, but then listing out a whole bunch more:
Elegant, documented, on time.
Privacy, accuracy, security.
Have fun, do good, stay out of trouble.
Study, socialize, sleep.
Diverse, free, equal.
Fast, efficient, useful.
Cheap, healthy, tasty.
Secure, usable, affordable.
Short, memorable, unique.
Cheap, light, strong.
I don't know if I agree with all of those, but regardless of their authenticity, Kottke is right to question why the "Pick Two" logic appears to be so attractive. Indeed, I even devised my own a while back when I was looking at my writing habits.
Why is "pick two out of three" the rule? Why not "one out of two" or "four out of six"? Or is "pick two out of three" just a cultural assumption?
He also wonders if there is some sort of underlying scientific or economic relationship at work, but was unable to find anything that fit really well. Personally, I found the triangle to be closest to what he was looking for. In a triangle, the sum of the interior angles is always 180 degrees. If you "pick two" of the angles, you know what the third will be. Since time and money are both discrete, quantifiable values, you should theoretically be able to control the quality of your project by playing with those variables.

In a more general sense, I tend to think of a system with three main components as being inherently stable. I think this is because such a system is simple, yet complex enough to allow for a lot of dynamism. As one of the commmenters on Kottke's post noted:
Seems like two out of three is the smallest tradeoff that's interesting. One out of two is boring. One out of three doesn't satisfy. Two out of three allows the chooser to feel like s/he is getting something out of the tradeoff (not just 50/50).
And once you start getting larger than three, the system begins to get too complex. Tweaking one part of the system has progressively less and less predictable results the bigger the system gets. The good thing about a system with three major components is that if one piece starts acting up, the other two can adjust to overcome the deficiency. In a larger system, the potential for deadlock and unintended consequences begins to increase.

I've written about this stability of three before. The steriotypical example of a triangular system is the U.S. Federal government:
One of the primary goals of the American Constitutional Convention was to devise a system that would be resistant to tyranny. The founders were clearly aware of the damage that an unrestrained government could do, so they tried to design the new system in such a way that it wouldn't become tyrannical. Democratic institions like mandatory periodic voting and direct accountability to the people played a large part in this, but the founders also did some interesting structural work as well.

Taking their cue from the English Parliament's relationship with the King of England, the founders decided to create a legislative branch separate from the executive. This, in turn, placed the two governing bodies in competition. However, this isn't a very robust system. If one of the governing bodies becomes more powerful than the other, they can leverage their advantage to accrue more power, thus increasing the imbalance.

A two-way balance of power is unstable, but a three-way balance turns out to be very stable. If any one body becomes more powerful than the other two, the two usually can and will temporarily unite, and their combined power will still exceed the third. So the founders added a third governing body, an independent judiciary.

The result was a bizarre sort of stable oscillation of power between the three major branches of the federal government. Major shifts in power (such as wars) disturbed the system, but it always fell back to a preferred state of flux. This stable oscillation turns out to be one of the key elements of Chaos theory, and is referred to as a strange attractor. These "triangular systems" are particularly good at this, and there are many other examples...
Another great example of how well a three part system works is a classic trilemma: "Rock, Paper, Scissors."