# People neglect small probability events

Over at overcomingbias Robin Hanson wrote:

> On September 9, 1713, so the story goes, Nicholas Bernoulli proposed the following problem in the theory of games of chance, after 1768 known as the St Petersburg paradox …:
> 
> Peter tosses a coin and continues to do so until it should land heads when it comes to the ground. He agrees to give Paul one ducat if he gets heads on the very first throw, two ducats if he gets it on the second, four if on the third, eight if on the fourth, and so on, so that with each additional throw the number of ducats he must pay is doubled.
> 
> Nicholas Bernoulli … suggested that more than five tosses of heads are morally impossible \[and so ignored\]. This proposition is experimentally tested through the elicitation of subjects‘ willingness-to-pay for various truncated versions of the Petersburg gamble that differ in the maximum payoff. … All gambles that involved probability levels smaller than 1/16 and maximum payoffs greater than 16 Euro elicited the same distribution of valuations. … The payoffs were as described …. but in Euros rather than in ducats. … The more senior students seemed to have a higher willingness-to-pay. … Offers increase significantly with income. ([more](http://d.repec.org/n?u=RePEc:crf:wpaper:10-14&r=exp))
> 
> This isn’t plausibly explained by risk aversion, nor by a general neglect of possibilities with a <5% chance. I suspect this is more about analysis complexity, about limiting the number of possibilities we’ll consider at any one time.  I also suspect this bodes ill for existential risk mitigation.

The title of the paper is _'Moral Impossibility in the Petersburg Paradox : A Literature Survey and Experimental Evidence'_ ([PDF](http://d.repec.org/n?u=RePEc:crf:wpaper:10-14&r=exp)):

> The Petersburg paradox has led to much thought for three centuries. This  
> paper describes the paradox, discusses its resolutions advanced in the  
> literature while alluding to the historical context, and presents experimental  
> data. In particular, Bernoulli’s search for the level of moral impossibility in  
> the Petersburg problem is stressed; beyond this level small probabilities are  
> considered too unlikely to be relevant for judgment and decision making. In  
> the experiment, the level of moral impossibility is elicited through variations  
> of the gamble-length in the Petersburg gamble. Bernoulli’s conjecture that  
> people neglect small probability events is supported by a statistical power  
> analysis.

I think that people who are interested to raise the awareness of _risks from AI_ need to focus more strongly on this problem. Most discussions about how likely _risks from AI_ are, or how seriously they should be taken, won't lead anywhere if the underlying reason for most of the superficial disagreement about _risks from AI_ is that people discount anything under a certain threshold. There seems to be a point where things become vague enough that they get discounted completely.

The problem often doesn't seem to be that people doubt the possibility of artificial general intelligence. But most people would _sooner question their grasp of “rationality” than give five dollars to a charity that tries to mitigate risks from AI because their calculations claim it was “rational”_ (those who have read the article by Eliezer Yudkowsky on _'[Pascal's Mugging](/lw/5qi/pascals_mugging_penalizing_the_prior_probability/)'_ know that I used a statement from that post and slightly rephrased it). The disagreement all comes down to a general averseness to options that have a low probability of being factual, even given that the stakes are high.

Nobody is so far able to beat arguments that bear resemblance to [Pascal’s Mugging](/lw/5qi/pascals_mugging_penalizing_the_prior_probability/). At least not by showing that it is irrational to give in from the perspective of a utility maximizer. One can only reject it based on a strong gut feeling that something is wrong. And I think that is what many people are unknowingly doing when they argue against the SIAI or _risks from AI_. They are signaling that they are unable to take such risks into account. What most people mean when they doubt the reputation of people who claim that _risks from AI_ need to be taken seriously, or who say that AGI might be far off, what those people mean is that _risks from AI_ are too vague to be taken into account at this point, that nobody knows enough to make predictions about the topic right now.

When GiveWell, a charity evaluation service, interviewed the SIAI ([PDF](http://commonsenseatheism.com/wp-content/uploads/2011/05/siai-2011-02-III.pdf)), they hinted at the possibility that one could consider the SIAI to be a sort of Pascal’s Mugging:

> **GiveWell:** OK. Well that’s where I stand – I accept a lot of the controversial premises of your mission, but I’m a pretty long way from sold that you have the right team or the right approach. Now some have argued to me that I don’t need to be sold – that even at an infinitesimal probability of success, your project is worthwhile. I see that as a Pascal’s Mugging and don’t accept it; I wouldn’t endorse your project unless it passed the basic hurdles of credibility and workable approach as well as potentially astronomically beneficial goal.

This shows that lot of people do not doubt the possibility of _risks from AI_ but are simply not sure if they should really concentrate their efforts on such vague possibilities.

Technically, from the standpoint of maximizing expected utility, given the absence of other existential risks, the answer might very well be yes. But even though we believe to understand this technical viewpoint of rationality very well in principle, it does also lead to problems such as Pascal’s Mugging. But it doesn’t need a true Pascal’s Mugging scenario to make people feel deeply uncomfortable with what Bayes’ Theorem, the expected utility formula, and Solomonoff induction seem to suggest one should do.

Again, we currently have no rational way to reject arguments that are framed as predictions of worst case scenarios that need to be taken seriously even given a low probability of their occurrence due to the scale of negative consequences associated with them. Many people are nonetheless reluctant to accept this line of reasoning without further evidence supporting the strong claims and request for money made by organisations such as the SIAI.

Here is for example what mathematician and climate activist [John Baez](http://johncarlosbaez.wordpress.com/2011/02/28/this-weeks-finds-week-310/#comment-4496) has to say:

> Of course, anyone associated with Less Wrong would ask if I’m really maximizing expected utility. Couldn’t a contribution to some place like the Singularity Institute of Artificial Intelligence, despite a lower chance of doing good, actually have a chance to do so much more good that it’d pay to send the cash there instead?  
>   
> And I’d have to say:  
>   
> 1) Yes, there probably are such places, but it would take me a while to find the one that I trusted, and I haven’t put in the work. When you’re risk-averse and limited in the time you have to make decisions, you tend to put off weighing options that have a very low chance of success but a very high return if they succeed. This is sensible so I don’t feel bad about it.  
>   
> 2) Just to amplify point 1) a bit: you shouldn’t always maximize expected utility if you only live once. Expected values — in other words, averages — are very important when you make the same small bet over and over again. When the stakes get higher and you aren’t in a position to repeat the bet over and over, it may be wise to be risk averse.  
>   
> 3) If you let me put the $100,000 into my retirement account instead of a charity, that’s what I’d do, and I wouldn’t even feel guilty about it. I actually think that the increased security would free me up to do more risky but potentially very good things!

All this shows that there seems to be a fundamental problem with the formalized version of rationality. The problem might be human nature itself, that some people are unable to accept what they should do if they want to maximize their expected utility. Or we are missing something else and our theories are flawed. Either way, to solve this problem we need to research those issues and thereby increase the confidence in the very methods used to decide what to do about _risks from AI_, or to increase the confidence in _risks from AI_ directly, enough to make it look like a sensible option, a concrete and discernable problem that needs to be solved.

Many people perceive the whole world to be at stake, either due to climate change, war or engineered pathogens. Telling them about something like _risks from AI_, even though nobody seems to have any idea about the nature of intelligence, let alone general intelligence or the possibility of recursive self-improvement, seems like just another problem, one that is too vague to outweigh all the other risks. Most people feel like having a gun pointed to their heads, telling them about superhuman monsters that might turn them into paperclips then needs some really good arguments to outweigh the combined risk of all other problems.

(Note: I am not making claim about  the possibility of _risks from AI_ in and of itself but rather put forth some ideas about the underyling reasons for why some people seem to neglect existential risks even though they know all the arguments.)