Essay:Privileging the hypothesis

Although some of this is taken from the Yudkowsky post of the same name, I wanted to put my own spin on this fallacy and also construct an essay based on the most common objection I've seen to it.

Hypothesis testing

Hypothesis testing is a core part of the scientific method, and forms the basis of how we go about collecting evidence to support or demolish theories. By understanding how best to test hypotheses, we can more accurately and efficiently focus down on correct models of the universe and discard the incorrect ones. Knowing the main logical fallacies is key to to this, as it prevents us from, at best, inefficient thinking and, at worst, completely incorrect thinking. Privileging the hypothesis, or giving undue weight to a single idea without prior evidence (or any compelling reason to do so) is one of those fallacies. In short, prior to gaining any evidence at all we can say that all possible answers to a question are equally probable, or more accurately, we have equal confidence in any of these answers being correct. If we have a thousand ideas or potential solutions, then without any evidence our confidence in any particular one is simply expressed as 1-in-1000. Remember that this is without any evidence or examination, we're generating new ideas and assigning basic confidence values to them based on simple guesswork rather than actually going in and getting evidence.

So simply put, considering that we can have confidence in a single hypothesis as low as 1-in-1000 and we have 999 competing ideas all equally improbable, it makes no sense to single one out. These seems fair enough, and the solution is to start searching for evidence to narrow our ideas down and improve our confidence. Our problem, however, arises not from this starting position but the mechanism we choose to go around gaining our evidence. It's this aspect that I think is often lost on people who find themselves guilty of performing this fallacy.

Murders and Deal or No Deal?

While Yudkowsky's analogous post explains privileging the hypothesis with a murder. If someone is killed in a small town, then without any evidence (because she's only just received the phone call about it, has made no interviews and hasn't even seen the crime scene) the detective in charge of the case has no reason to suspect anyone above anyone else. Her confidence in arresting or investigating any one person is, roughly, equal. While you can narrow this down to realistic possibilities like anyone in the local town of about 5,000 people, there are 7 billion people on the planet. So to immediately pick John Q Cloggs of 32b Main Street to investigate would be utterly illogical, as our detective only has a 1-in-7,000,000,000 confidence. This is often cues the most common objection: "well, the detective may as well start somewhere!". Unfortunately, this "may as well start somewhere" gambit is not a solution to the fallacy, and nor is it invalidating this act as fallacious. In fact, it's an application of the fallacy itself.

So to illustrate, I want to move a more simple model system to demonstrate privileging the hypothesis. Most people, unless they've had the good fortunate to be trapped under a pop-culture rock for the best part of the last decade, will be aware of Deal or No Deal?. 22 identical boxes, one top cash prize, and if you're following the American-style adaptation lots of identically "nondescript but hot" models, and if you're following the UK version Noel Edmonds and his cosmic ordering crap. Okay, so there are other versions and it started in the Netherlands but I'm hear for snark, not a history of appalling television game shows. Anyway, if we throw out most of the rules and focus on the hunt for the top prize ($1 million in the US, £250,000 in the UK) the game mechanics are almost a complete personification of privileging the hypothesis. This isn't just contestants focusing on their lucky numbers and Edmonds talking about how the Banker is playing a "shrewd" game, the actual selection process and game mechanics reflect it with respect to hypothesis testing.

Given the usual spread of a few dozen boxes that you have no prior information about, you have a very slim chance of guessing right first time. The only permissible action within the game is to open the box and look inside, this effectively forces you to privilege a hypothesis: to choose a box you think the top prize is in and not pick it. This continues in a fashion until you prove yourself wrong (or walk away with the cash and a smug grin). Because the appearance of the top prize is randomised out of the 22 boxes and because of the game mechanic, on average it will be 11 boxes before a player opens the box with this highest prize value inside.

You may as well start somewhere...

In this simple game, the "may as well start somewhere" gambit is actually enforced as part of the rules. You can only open one box at a time, and as far as evidence suggests (if you're just searching out this one prize value) you may as well do this in any order, your odds don't change. But out of n boxes, you average n/2 turns to locate it this way. It might seem okay with 22 boxes, it only takes 20 minutes and that's mostly Noel Edmonds chatting away. Consider, then, if n was much higher. 100 boxes? 1000 boxes? A million boxes?

In a one million box game of Deal or No Deal? you would expect, on average, to locate that one top prize after half a million boxes. Even assuming you can get Noel Edmonds to shut up and you take only a few seconds on each box, that's over two weeks straight opening boxes. Hardly efficient. This is why privileging the hypothesis is a problem just from a purely mathematical prospective: as the number of potential hypotheses increases, the time taken to examine each one in turn via the "you may as well start somewhere..." gambit increases as n/2. And to make matters worse, we might not be restricted to a mere million hypotheses nor will we have the good fortune to discriminate them in a few seconds.

Also, remember that this is currently just the basic mathematical treatment. The emotional attachment to a pet theory, or confirmation bias that results is another angle entirely, and is arguably the more powerful reason for why to avoid it in the first place.

Gaining meaningful information

So we need to refine our system a little. Instead of hunting for our prize box by individual box in our cosmic-scale million box game of Deal, we refine our rules to be far more useful. In this case, we're allowed to separate our boxes into two groups (A and B) and ask the yes/no question of "is it in group A?" How we separate them is up to the player; in the original rules, it's the same thing but we're forced to make group A consist of only one box. This leads us to the efficient information theory way to track down the right box - and this is what guides how we go about gaining the right evidence. So we play the game like this instead:

• Is the prize in boxes 1-11? - Yes
• Is the prize in boxes 1-5? - No
• Is the prize in boxes 6-8? - Yes
• Is the prize in boxes 6-7? - Yes
• Is the prize in box 7? - Yes

So in stead of an average of 11 turns, it takes us a maximum of 5 questions (in actual information theory terms it's an average between 4 and 5 bits). The fact is, we could split them less evenly and get lucky, like "is it in boxes 12-14? - Yes" and get it in two, but the methodological way puts a maximum number of turns on our game, limited by the information it takes to narrow our hypotheses down efficiently and correctly. For the sake of round numbers, if we had 1024 boxes we'd take a maximum of 10 turns - a vast improvement on the average of 512 we'd expect from the "you may as well start somewhere" problem. What about a million boxes? Well, that's actually around 20 bits, or 20 turns if you use the methodological root rather than the 500,000 you'd expect the other way. That's compressing a 2 week game of Deal down into a more manageable chunk just by being smart, rather than simplistic.

This is precisely why detectives don't pull random people off the street just as somewhere to start their investigations: it would be the most feckless approach possible.

Real world considerations

That's just basic information theory, which demonstrates that the "you may as well start somewhere" objection is just plain inefficient. I briefly mentioned confirmation bias and a few other problems with privileging the hypothesis. Plugging in the numbers above is nice for idealised systems, but this is where the meat of the fallacy comes in because while privileging the hypothesis is bad from the above, this only makes it considerably worse. In fact, a lot of these factors make it so bad that they can cripple critical thinking immediately.

Usually, privileging the hypothesis occurs only because someone suggests something randomly. They take a hypothesis and raise it up for examination based on no prior evidence that would give a logical or rational reason to do so - it is purely random chance. Yet once this hypothesis is there, we are compelled to make a decision on it. The degree to which this decision is informed will vary, but it comes under consideration and therefore comes to the foreground for no reason at all. The detective is forced to accuse John Q Cloggs for no reason other than a random person mentioned the name and said "you may as well start somewhere", and thus is immediately biased to ignore that their confidence is literally as low as 1-in-billions. When you isolate a single hypothesis, you isolate it from the context of competing hypotheses, and this is where the illusion of higher confidence comes in. If you unfairly privilege 10 hypotheses out of 100, you overestimate your initial confidence as 1-in-10, rather than 1-in-100, and at the very worst you explicitly discount the remaining 90 from any consideration.

The basic drawback given this "you may as well start somewhere" approach is that once committed you must thoroughly disprove the hypothesis before moving onto the next. This can often be considerably more complicated than merely opening a box, and so the detective analogy is better. The detective must first check out John Q Clogg's alibi, genetics, fingerprints, and other evidence before being confident of dismissing him as a suspect, then move on. The trouble is, how can we be sure we've thoroughly debunked the hypothesis in the real world? Particularly with so much focus levied onto this one individual circumstance, it can be difficult to let go. Considering confirmation bias at work and we quickly see that we run a very high risk of fixating on and accepting the first hypothesis we test: for no other reason than we've chosen it arbitrarily. Without critical evaluation of the alternative competing hypotheses, and without a smarter method for narrowing them down and increasing our actual confidence (rather than an illusion of confidence caused by confirmation bias) we have effectively settled on a solution that still has considerable odds stacked against it.

It's easy enough to apply this to religion. We constantly see people of particular religions focused exclusively on proving their own religion versus complete non-existence of any particular deity or any other supernatural network underpinning the belief. Rarely, however, do we see anyone run the same question in the context of proving it against the myriad alternatives. The reality is that there are infinite potential gods to worship and religious frameworks to follow, yet believers always have this strange tendency to be focused on the ones that their background culture (family or country, for instance) endorses already. This is also an apt demonstration of how attached someone can get to an idea just because it is presented to them. Along similar, but broader lines, anyone declaring themselves agnostic is almost certainly guilty of privileging the hypothesis of "does God exist?". While there is the infinite set of potential gods and religious frameworks, there is also a larger infinite set of "general things" to believe in or not believe in - and no one explicitly states that they're agnostic about invisible dragons or invisible unicorns, and no one disparages those who outright state such things do not exist for not being open minded.

The moral is that you need a smart methodology to refine hypotheses. Simply picking one and testing it is a flippant and risky attitude. It only works when the most you have to do is open a box and read the number inside. And even then it's only a workable approach if you don't have too many boxes.