But this is more like a procedure that will let you guess the number that will land > 50% of the time.

That's orthoganal the math at play here.

The point of that analogy was to create a situation in which someone is right 55% of the time and see how the language "prudent and cautious" feels in those circumstances.

Whether that means rolling over a certian number on a die, or rolling a specific number on a very strange weighted die is irrelevant.

The "someone is right 55% of the time" scenario is meaningless without considering the base rate. A 100-sided dice has a 55% chance of landing on a number greater than 45. That's the implicit base rate in the hypothetical.

Consider, instead, something like guessing whether someone has had cancer. Only 8.5% of the population has ever had it. If you can guess randomly, you'll be right about 8.5% of the time. If you can guess correctly 55% of the time, you're doing far better than random guessing.

The implicit assumption of the "probable cause" concept is that the base rate is low. I.e. only a small percentage of people have illegal contraband. If a police officer is able to guess that someone is more likely than not to have contraband (i.e. more than 50% correct), then he must be acting on some concrete clues, because he's doing far better than if he just searched people randomly.

But... you are missing the point yet again. The officer's own judgement is not probable cause without specific indicators (e.g. visual evidence).

"The problem here is that invasive searches based on no more than a government official’s hunch is precisely what the Fourth Amendment is supposed to guard against."

Due to the high alert rate, we actually have a pretty good idea of the base rate of drugs in the situations that this dog is being used in (~50-60%).

The question is whether the dog is actually providing probable cause when the dog has such a high false positive rate.

The assertion of the article is specifically that drug dogs are being used and trained by police in ways that allow them to be be used as "a probable cause generator".

"The Supreme Court originally gave its imprimatur to drug dog sniffs because when used properly, the dog’s finely tuned sense of smell can detect drugs and their absence with incredible precision. But that caveat — when used properly — is critical. If a drug dog isn’t eliminating any innocent people, if it’s validating the suspicions of the police nine out of ten times resulting in searches for which up to half or more of the suspects are innocent, then descriptors such as finely tuned and incredible precision no longer apply."

Thus the base rate that we should be judging the dog against is not the base rate in the general population, but the base rate in the dog's tested sample. We need to incentivize the cultivation of higher levels of accuracy that the dogs are capable of providing.

A correction for your cancer example.

Now if you take the 50% of people you guessed to be positive for test, only 4.25% will be true positives, indicating 8.5% accuracy rate; if you take the 50% people you guessed to be negative for test, 45.75% will be true negatives, indicating a 91.5% accuracy rate.

But your overall accuracy rate is 50%.

Um... not at all. That procedure has 100 different possible guesses. A drug dog only has 2 possible guesses.

edit: Seriously? A downvote for this comment?

Yes, this comment makes no sense. Your selection of a 100 sided dice was obviously just a method to discuss probability. But then you randomly jump to a statement about having 100 possible outcomes? This doesn't have anything to do with the original topic at hand.

I downvoted your comment because the argument you are attempting to make is incoherent. I'm sure that you understand what you are trying to say, but as written your comment does a poor job of expressing that point of view.

> But this is more like a procedure that will let you guess the number that will land > 50% of the time.

If have a procedure for guessing the number rolled on a 100 sided die, you are choosing between 100 different possible guesses. That is nothing like a dog guessing if a person has, or does have drugs (two possible guesses). Attempting to compare the accuracy rates between those two cases is major statistical error.

I thought this difference would be obvious to most readers of HN and was thus surprised to see such a simple statistical error being made. I did not think that verbose explanation would be needed once the error was pointed out.

I agree with you.

But I don't think "prudent and cautious" can quite be boiled down to just a certainty of outcome. Risk/reward plays in a lot. If we take "cautious" to mean a medium degree of risk aversion, then I don't think a cautious person would risk their year's wage on the chance to double it, even with a 55% certainty of success. However, I think they would risk $10 for a 55% chance of getting $20.

So what is at stake? What's the cost of an invasion of privacy?

Because of civil asset forfeiture, the base value is however much cash happens to be in the car, assuming it's enough to be "suspicious" (how just having cash is suspicious, I don't know). Most people don't have large amounts of cash in their car, but those who do have, well, a large amount.

The other quantifiable loss to a car search is time. Based on a quick search, it seems the average hourly wage of americans is $25. Wage isn't really the best evaluation of time, but it's easy. That covers the time wasted, but not the losses due to being late to something. A car search could make someone miss an appointment, or even get fired — or nothing.

I'm going to estimate that the sum of how much the average person stands to lose to asset forfeiture and time is about $100. That's of course not even considering the emotional impact of having your privacy violated, or the potential non-legal consequences of having a car search, say having an affair exposed. I'll try to give a personal answer to that question. How much would someone have to pay me for me to be okay with them tipping of the police that I have drugs in my car? Well since I'd be able to plan for it, missing appointments and asset forfeiture are hardly a concern, but time is. I suppose someone could hire me to stand around and be bored for an hour for $40. I'd let them tip off the cops for say, $600. Since that's how much it would take to make it worth my while and not really just meet the baseline of acceptable, I'll cut off a bit from that, say $60. And then subtract the $40 for my time. Adding in the estimated tangible cost, and that's $600 again.

So let's go with $600 as the cost of an erroneous search. Now we need the value of a successful search.

It's hard to quantify (I'd argue the value is negative because of the questionable value of the war on drugs and the cost of incarceration), but for this purpose, I'll use bounties. A quick search turned up a really bullshit looking page that mentions a county police department offering $1000 cash to anyone who turns in a heroin dealer. While the value to the county is going to be higher than the bounty they offer, I'm going to assume that since this county is offering a bounty in the first place, they value it slightly higher than other municipalities. So let's go with $1000 as the value of catching a drug dealer.

Risking $600 for a 55% chance of $1000 isn't just not cautious, it's a losing game.

*

So what would I consider cautious? Risking $1000 for a 60% chance of doubling it? I'd characterize that as "cautiously optimistic". 65%? Same. 70%? Sure I'll call that "cautious". Obviously different people will have different ideas of what "cautious" means.

But by my definition, and my value estimates, I'll say the certainty required for probable cause for searching a car with drugs is 85%.

This link was posted: https://news.ycombinator.com/item?id=10024503

The main gist of which is the difference between 'concrete' and 'statistical', which seems to be very different from the way many of use think about 'reasonable'.

The article certainly indicates that you don't need 85% certainty to have probable cause. While officers can have pretty high accuracy rates to their guesses, they need a 'concrete' piece of evidence to point to so they can have probably cause. Drug dogs are being used to create this concrete reason, but this has more to do with their perceived reliability than their actual effectiveness reliability.

My biggest concern with the points that this article raises is that it seems like the dogs are being trained to reliably provide probable cause rather than being trained to provide reliable probable cause.