Not Quite a Blog

If you know me, you know I'm interested in the use and misuse of randomness in policy. Two recent uses of randomness in pop culture sparked some thoughts on the notion of randomness used for decision-making. The book, The Traveler, by the mysterious John Twelve Hawks and the film No Country for Old Men both use randomness in interesting ways.

Background

The Traveler is a New York Times bestselling, dystopian book about a threatened group of elite bodyguards, the Harlequin, that defend a special breed of humans, the Travelers. The Harlequin defend Travelers from the Brethren, a vast network that keeps the world under control using high-technology surveillance and who are supported by the world's dominant powers.

An interesting part of being a swift and clever Harlequin is that they use randomness to make decisions: each Harlequin carries a random number generation device that they consult when making decisions. They seem to do this when there's no rational reason to choose one option over another in a given decision. The Harlequin use randomness to ensure that the Brethren assassins cannot predict what they do. For example, in The Traveler, a Harlequin, while breaking into a fortress, has to choose between two forks in a tunnel. She consults her random number generator and depending on whether the number produced is even or odd, she goes either left or right in the fork.

In No Country for Old Men, Javier Bardem's character, the ruthless bloodthirsty hitman Anton Chigurh, flips a coin and asks potential victims to "call it". If they call it right, Chigurh allows them to live. If they call it incorrectly, Chigurh kills them.

These two uses of randomness in decision-making are exceedingly interesting. The Harelquin is taught in its training to "cultivate randomness" in order to be unpredictable; Harlequins use random number generators to support this cultivation. Chigurh uses the coin flip in a more mysterious and different manner. Presumably to do one or more of the following: to allow his potential victims to assist in deciding their fate, to submit to a higher power (fate, god, etc.) and allow that power's rules to govern and/or to inject some randomness in his rampage in order to throw off the authorities. This last mode is similar to the Harlequin's use of randomness.

Randomness "Needs"

The size of the space of randomness for these to uses differs. Chigurh needs only one of two outcomes: kill this person or let them live. But he also needs the victim to assist by calling the side of the coin. When one character refuses to call heads or tails, Chigurh presumably--although it's not clear--kills her. Only having two choices means that he only needs a 2-sided die: a coin.

The Harlequin's need for randomness can be a bit larger. The Harlequin example above is a simple binary choice, but you could very easily have a three-choice fork in the path. Relying on binary choices here quickly becomes impractical. You could take the first two paths in the fork, make a binary choice and then choose between the winner and the last fork in the path. For a 10-forked path, this can take too long; the Harlequin might be killed.

In general, the Harlequin would want to essentially take the random number modulo the number of choices (modulo is math for the remainder after dividing one number by another). That is, in general they would want to divide the random number by the number of choices and multiply all the stuff to the right of the decimal in the result by the number of choices.

Of course, only savants can do multiple-decimal arithmetic like that in their head. Harlequins might invoke the rules for divisibility. That is, they could take their number of choices (up to a reasonable number like 10) and, using the divisibility rules below, decide if their random number is divisible by their number of choices. If not, they can quickly decide what the closest number is to their random number that is evenly-divisible by their number of choices. Then they could just count the number of digits between the closest evenly-divisible number and their random number to figure out which choice to make.

Here are a set of divisibility rules:

• A number is divisible by 1 if... All numbers are divisible by one. This corresponds to no choice.
• A number is divisible by 2 if... the last digit is even, the number is divisible by 2.
• A number is divisible by 3 if... the sum of the digits is divisible by 3, the number is also.
• A number is divisible by 4 if... the last two digits form a number divisible by 4, the number is also.
• A number is divisible by 5 if... the last digit is a 5 or a 0, the number is divisible by 5.
• A number is divisible by 6 if... the number is divisible by both 3 and 2, it is also divisible by 6.
• A number is divisible by 7 if... Take the last digit, double it, and subtract it from the rest of the number; if the answer is divisible by 7 (including 0), then the number is also.
• A number is divisible by 8 if... the last three digits form a number divisible by 8, then so is the whole number. To check is the last three digits are divisible by 8, make sure it's divisible by 4 and 2.
• A number is divisible by 9 if... the sum of the digits is divisible by 9, the number is also.
• A number is divisible by 10 if... the number ends in 0, it is divisible by 10.

For example, if their generator produces 427171 and they have 6 choices to choose from, they know their number is not divisible by six. The Harlequin can add together all the digits of the number plus one (427172) and the number minus one (427170) to see if either of these numbers is divisible by three. 427170 added together is 21 which means the number below is divisible by two and three, so it's also divisible by six. So 427171 modulo 6 is 1 which means the Harlequin would take the second choice (since you add one to the modulus to get the choice to make).

Security Concerns

What if someone messes with either the Harlequin's or Chigurh's sources of randomness to bias them? In the security field, we would say, "What are the threats to randomness such that their actions would be more predictable?"

In Chigurh's case, he can just change coins often enough to not use the same one (I don't recall if the coin he used was "special"). In the Harlequin's case, she needs to be more careful. If a mercenary were to swap her random number generator with one that were biased or trigger-able in some manner, the Brethren would have a significant advantage.

In elections, we tend to use ten-sided dice or numbered ping pong balls to choose digits randomly. Obviously, the infrastructure for numbered ping pong balls doesn't comport well with a melee environment. Ten-sided dice are small and can be kept securely. However, if one is hanging from a rope and has to decide which shaft to jump down, throwing dice is quite inconvenient. So, that brings me to an idea for a decision-making device.

(Hint, hint: This would make a great promotional trinket for the release of the third book in the Forth Realm trilogy, of which The Traveler was the first.)

An Idea for a Device

I'd love to have a decent random number generator in a watch-like form to support random decision-making. Let's call it the Randnum.

The Randnum would not tell time, but simply display two things:

• A random number (between 1 and 1000000).
• The modulus of the random number and a number between 2 and 10, plus one.

These two numbers would be displayed after the user pressed one of nine buttons labeled with the numbers 2 through 10. A use case could be like this:

1. Harlequin has to decide which of 7 roads in the next few miles to take in order to stop and get some rest.
2. She pushes the "7" button on her Randnum.
3. The device displays a random number, 865418, and a modulus plus one, 2.
4. The Harlequin would take the 2nd road and get some rest.

There are various forms of electronic six-sided dice, electronic roulette and even electronic gaming dice that presumably do all types of dice. But there's nothing like this and I want one.