You can't prove it's impossible!

[reddragdiva]

A common sophistry which really annoys me is the one that conflates an utterly negligible probability with a non-negligible one. The argument goes:

1. There is technically no such thing as certainty.
2. Therefore, [argument I don't like] is not absolutely certain.
3. Therefore, the uncertainty in [argument I don't like] is non-negligible.

Step 3 is the tricky one. Humans are, in general, really bad at feeling the difference between epsilon uncertainty and sufficient uncertainty to be worth taking notice of — they can't tell a nonzero chance from one that's worth paying attention to ever. (This is why people buy lottery tickets.)

It’s a terrible, terrible argument, and an unfortunately common one. It needs to be bludgeoned to death every time it’s brought up.

Comments

[vatine]

Part of the problem is that even low-probability events may be worth paying attention to.

High-probability, low-danger (or low-payout) scenarios are easy to reason about. Low-probability high-danger (or high-payout) scenarios are much harder to reason about.

Then there's the wonders of "how frequently are we testing this probability". If we test something once a second, you'd expect a once-in-a-million event to occur about once every two weeks. If we try it once a year, not so much.

On the gripping hand, when I get gut-feelings one way or another, I do tend to return to the whiteboard and start working from first principles, because I am (probably) over- or under-estimating badly. So, I guess, one can learn to live with one's cognitive limitations.

[reddragdiva]

I would boggle at anyone who raises this argument doing the actual numbers, ever.

[blue_cat]

This seems to me to be akin to the known issue of people failing to understand, or choosing not to understand, statistical likelyhood especially as associated to the level of control.

When a person is in control of the situation (e.g. driving a car) the perceived risk of an accident is low and the tolerance of risk is high.

When a person is not in control (e.g. flying) the perceived risk is high and tolerance of risk is low.

As for actual numbers, reminding myself that more people are killed in car accidents yearly than plane accidents does kinda work (your 'returning to numbers' idea) but still only partially works.

Regarding Reddragdiva's original issue, it is a bit difficult to identify the scenario's other than the above without an example?

[vatine]

To continue with the "frequency of trials", for a 1-in-14M repeated trial (1-in-14M every time), you have 50% chance to win after somewhere between 9.7M and 9.8M trials. For something repeating once a week, really not worth expecting to walk away with the price (that's, what, couple of hundred thousand years), but for something repeating once a second, that's about 100 days.

FWIW, the 1-in-1M "number of trials to make it 50% give or take" is on the order of ~700k trials, still not worth it for a once-in-a-week event, but for a once-in-a-second...

[tcpip]

Are you confusing a debate about certainty with debates about conceivability and possibility? They are very different epistemological issues.

[reddragdiva]

No, I'm talking about a really basic level terrible argument stemming from a cognitive bias, just as I wrote.

[tcpip]

Ahh, my bad. That's a third issue!

[reddragdiva]

This is a general human stupidity rant, not a philosophers' stupidity rant ;-)

[reddragdiva]

I need to find out what this fallacy is actually called. It's common enough that it's got to have a name.

[tcpip]

You can call it the fallacy of magnification, to adopt the word from cognitive psychology, or more specifically, a "fallacy of magnification arising from cognitive bias".

Essentially the person is turning negligible "corner cases" in a proposition into a central flaw, because they want the argument to be centrally flawed. They are also ignoring that any rational proposition must, by its very nature, have fallible components.

[reddragdiva]

I could go for a neologism if necessary (basically I'll make the above a RationalWiki article), but I'd rather have its proper name if it has one.

The essence of crankdom is turning a negligible probability into a non-negligible one. Look into any crank idea (9/11, birthers, cold fusion) and you'll find a step where a negligible probability is treated as non-negligible.

[tcpip]

The essence of crankdom is turning a negligible probability into a non-negligible one.

Nicely put.

[doug]

"can't tell a nonzero chance from one that's worth paying attention to ever. (This is why people buy lottery tickets.)"

Good point ... that isn't enhanced by choice of final throwaway example, I reckon.

You're skating close to a fallacy yourself there. Let's start with saying that a one in fourteen million chance (main game in the UK National Lottery) is effectively the same as no chance at all. (Which is almost what you were saying.) Let's imagine a slightly differently structured lottery to most, with fourteen million tickets numbered sequentially, all sold, and one of which is then drawn at random. Ticket number one has no chance. Ticket number two has no chance ... ticket number fourteen million has no chance. But one of them will win.

There can be a really significant difference between epsilon probability and no probability; and there can be a really significant difference between epsilon and a merely very unlikely probability like one in fourteen million chance.

Lotteries are (usually) a really bad example of low-probability events, because we can be extremely accurate with our estimates of how probable they are. What's the chance of you winning the lottery? Treating it as pretty likely is wrong. Treating it as zero is also wrong. Treating it as epsilon is also wrong. It should be treated it as 1 in 14 million (to 2 sig fig).

(... you've almost triggered my rant about how it can be entirely rational to play the lottery, but this margin of my time is too small to contain it. Hint to part of it: People's utility function is not linear with money. If I find time I'll post it on my own journal and post a link here.)

[reddragdiva]

Treating it as one in fourteen million is, I suspect, perceptually impossible for humans without training. I suspect that without practice people don't have a feel for less than ten percent. (I sure don't and I've actually tried to, therefore everyone else has the same problem ... but they do in fact seem to.) But people observably just don't shut up and calculate even as they concede the lottery is way below their perceptual level.

I wonder if work's been done to measure just how good humans are at feeling probability, with or without practice.

[reddragdiva]

No, people's utility function with money appears to be logarithmic. (No link to hand, I think I can find one if needed.)