Arbitrary vs. Random

I bring up this point to a lot of people, and a lot of people find it confusing. Are random and arbitrary synonymous or aren't they? I admit I'm not always entirely sure how to describe the difference between the two words, but since I insist people use them appropriately I should probably offer an explanation.

Let's start by defining them both. Arbitrary, according to answers.com, describes things that are "1. Determined by chance, whim, or impulse, and not by necessity, reason, or principle" or "2. Based on or subject to individual judgment or preference." Random, on the other hand, applies to things "1. Having no specific pattern, purpose, or objective" or "2. Mathematics & Statistics. Of or relating to a type of circumstance or event that is described by a probability distribution." I'll limit the discussion, at first anyway, to the two most widely used definitions.

What we can gather from these definitions and what we know about the words is that they're both used to describe a selection process. Decisions can be made arbitrarily or they can be made randomly. How, then, do they differ? It comes down to the outcome really - an arbitrary decision is one that doesn't matter either way. The outcome of repeatedly making a decision about something whose outcome doesn't matter can, and oftentimes does, lead to the same decision being made over and over. A good example is asking people to select a "random" number between 1 and 10, inclusive. It's been demonstrated that, usually, 7 or 3 will be chosen more frequently than most of the other numbers given a large enough pool of participants. The reason for this is that people perceive these numbers as being random: they're prime numbers, they aren't even, they aren't right in the middle, and they aren't extremes. All of that makes them very appealing as "random" choices. In reality, a random selection gives each possible option equal weight. That is the basis for a random selection as opposed to an arbitrary one. What follows is, given a large enough pool of samples, every number between 1 and 10 should, statistically, be selected as much as any other number (give or take a bit). A human's bias in the selection process is what removes the randomness.

Going back to the definitions, one might argue that an arbitrary choice can also be random because there is no "necessity, reason, or principle" behind random selection. In fact, there is. It's all in the rhetoric here, which can make it seem tricky. I would counter that argument by reminding the person that random selection necessarily gives all options equal weight. Another argument that might come up is that random numbers have "no specific pattern, purpose, or objective" and that neither do arbitrary ones, which are chosen on a whim. That argument I counter by saying that arbitrary selections do, in fact, have a pattern as I mentioned in the example above with the numbers 3 and 7. Note that there is still room for debate here (there always is), so if you can think of a good argument let me know.

So what about randomly running into a friend at the store? Or all the random people who showed up to the party? Most of the time, random isn't used to describe a selection process at all. Instead it's used in place of more appropriate words such as coincidental, assorted, or unexpected - none of which are random. However, I have to concede that this is the nature of language: if a word or phrase goes into widespread use it can become part of the language. This is still considered slang or colloquial, though, and should be treated as such.

To summarize, for those who need to explain this to others: Arbitrary describes a decision-making process in which the choice simply doesn't matter or is made on a whim. Random, on the other hand, describes a decision-making process as well, but one in which every possible option is given equal weight.