# Pas­cal’s Mugging

TagLast edit: 23 Sep 2020 18:49 UTC by

Pascal’s mugging refers to a thought experiment in decision theory, a finite analogue of Pascal’s wager.

Suppose someone comes to me and says, “Give me five dollars, or I’ll use my magic powers from outside the Matrix to run a Turing machine that simulates and kills 3^^^^3 people. Pascal’s Mugging: Tiny Probabilities of Vast Utilities

Unpacking the theory behind Pascal’s Mugging:

A rational agent chooses those actions with outcomes that, after being weighted by their probabilities, have a greater utility—in other words, those actions with greater expected utility. If an agent’s utilities over outcomes can potentially grow much faster than the probability of those outcomes diminishes, then it will be dominated by tiny probabilities of hugely important outcomes; speculations about low-probability-high-stakes scenarios will come to dominate its moral decision making.

A common method an agent could use to assign prior probabilities to outcomes is Solomonoff induction, which gives a prior inversely proportional to the length of the outcome’s description. Some outcomes can have a very short description but correspond to an event with enormous utility (i.e.: saving 3^^^^3 lives), hence they would have non-negligible prior probabilities but a huge utility. The agent would always have to take those kinds of actions with far-fetched results, that have low but non-negligible probabilities but extremely high returns.

This is seen as an unreasonable result. Intuitively, one is not inclined to acquiesce to the mugger’s demands—or even pay all that much attention one way or another—but what kind of prior does this imply?

Robin Hanson has suggested penalizing the prior probability of hypotheses which argue that we are in a surprisingly unique position to affect large numbers of other people who cannot symmetrically affect us. Since only one in 3^^^^3 people can be in a unique position to ordain the existence of at least 3^^^^3 other people who can’t have a symmetrical effect on this one person, the prior probability would be penalized by a factor on the same order as the utility.

Peter de Blanc has proven [1] that if an agent assigns a finite probability to all computable hypotheses and assigns unboundedly large finite utilities over certain environment inputs, then the expected utility of any outcome is undefined. Peter de Blanc’s paper, and the Pascal’s Mugging argument, are sometimes misinterpreted as showing that any agent with an unbounded finite utility function over outcomes is not consistent, but this has yet to be demonstrated. The unreasonable result can also be seen as an argument against the use of Solomonoff induction for weighting prior probabilities.

If an outcome with infinite utility is presented, then it doesn’t matter how small its probability is: all actions which lead to that outcome will have to dominate the agent’s behavior. This infinite case was stated by 17th century philosopher Blaise Pascal and named Pascal’s wager. Many other abnormalities arise when dealing with infinities in ethics.

## References

1. Peter de Blanc (2007). Convergence of Expected Utilities with Algorithmic Probability Distributions.

2. Nick Bostrom (2009). “Pascal’s Mugging”. Analysis 69 (3): 443-445. (PDF)

# Pas­cal’s Mug­ging: Tiny Prob­a­bil­ities of Vast Utilities

19 Oct 2007 23:37 UTC
90 points

# Pas­cal’s Mug­gle: In­finites­i­mal Pri­ors and Strong Evidence

8 May 2013 0:43 UTC
70 points

# [Question] Has there been any work on at­tempt­ing to use Pas­cal’s Mug­ging to make an AGI be­have?

15 Jun 2022 8:33 UTC
7 points

# Against the Lin­ear Utility Hy­poth­e­sis and the Lev­er­age Penalty

14 Dec 2017 18:38 UTC
39 points

# The Lifes­pan Dilemma

10 Sep 2009 18:45 UTC
55 points

# More on the Lin­ear Utility Hy­poth­e­sis and the Lev­er­age Prior

26 Feb 2018 23:53 UTC
16 points

# Pas­cal’s Mug­gle (short ver­sion)

5 May 2013 23:36 UTC
46 points

# Ob­served Pas­cal’s Mugging

28 Jun 2011 15:53 UTC
36 points

# Prob­a­bil­ities Small Enough To Ig­nore: An at­tack on Pas­cal’s Mugging

16 Sep 2015 10:45 UTC
27 points

# Pas­cal’s mug­ging in re­ward learning

5 Nov 2017 19:44 UTC
9 points

# Ex­pected util­ity, un­los­ing agents, and Pas­cal’s mugging

28 Jul 2014 18:05 UTC
32 points

# Tac­tics against Pas­cal’s Mugging

25 Apr 2013 0:07 UTC
26 points

# Con­sider Re­con­sid­er­ing Pas­cal’s Mugging

3 Jan 2018 0:03 UTC
5 points

# A Thought on Pas­cal’s Mugging

10 Dec 2010 6:08 UTC
15 points

# Pas­cal’s Mug­ging for bounded util­ity functions

6 Dec 2012 22:28 UTC
18 points

# Com­ments on Pas­cal’s Mugging

3 May 2012 21:23 UTC
15 points

# No, I won’t go there, it feels like you’re try­ing to Pas­cal-mug me

11 Jul 2018 1:37 UTC
9 points

# Pas­cal’s Mug­ging—Pe­nal­iz­ing the prior prob­a­bil­ity?

17 May 2011 14:44 UTC
12 points

25 Dec 2010 19:42 UTC
13 points

# What do you mean by Pas­cal’s mug­ging?

20 Nov 2014 16:38 UTC
10 points

# An in­vest­ment anal­ogy for Pas­cal’s Mugging

9 Dec 2014 7:50 UTC
9 points

# Strong­man­ning Pas­cal’s Mugging

20 Feb 2013 12:36 UTC
4 points

# Pas­cal’s Mug­gle Pays

16 Dec 2017 20:40 UTC
25 points
(thezvi.wordpress.com)

# Model Uncer­tainty, Pas­calian Rea­son­ing and Utilitarianism

14 Jun 2011 3:19 UTC
34 points