Inverse gambler's fallacy

Inverse gambler's fallacy

The inverse gambler's fallacy is a term coined by philosopher Ian Hacking to refer to a formal fallacy of Bayesian inference which is similar to the better known gambler's fallacy. It is the fallacy of concluding, on the basis of an unlikely outcome of a random process, that the process is likely to have occurred many times before. For example, if one observes a pair of fair dice being rolled and turning up double sixes, it is wrong to suppose that this lends any support to the hypothesis that the dice have been rolled before. We can see this from the Bayesian update rule: letting "U" denote the unlikely outcome of the random process and "M" the proposition that the process has occurred before, we have

:P(M|U) = P(M) frac{P(U|M)}{P(U)}

and since "P"("U"|"M") = "P"("U") (the outcome of the process is unaffected by previous occurrences), it follows that "P"("M"|"U") = "P"("M"); that is, our confidence in "M" should be unchanged when we learn "U".

Real-world examples

The inverse gambler's fallacy is unquestionably a fallacy, but there is disagreement over whether and where it has been committed in practice. In his original paper, [Ian Hacking, "The Inverse Gambler's Fallacy: The Argument from Design. The Anthropic Principle Applied to Wheeler Universes". "Mind" 96:383 (July 1987), pp. 331–340.] Hacking takes as his main example a certain response to the argument from design. The argument from design asserts, first, that the universe is fine tuned to support life, and second, that this fine tuning points to the existence of an intelligent designer. The rebuttal attacked by Hacking consists of accepting the first premise, but rejecting the second on the grounds that our (big bang) universe is just one in a long "sequence" of universes, and that the fine tuning merely shows that there have been many other (badly tuned) universes preceding this one. Hacking draws a sharp distinction between this argument and the argument that all possible worlds coexist in some non-temporal sense. He proposes that these arguments, often treated as minor variations of one another, should be considered fundamentally different because one is formally invalid while the other is not.

A rebuttal paper [John Leslie, "No Inverse Gambler's Fallacy in Cosmology." "Mind" 97:386 (April 1988), pp. 269–272.] by John Leslie points out a difference between the observation of double sixes and the observation of fine tuning, namely that the former is not necessary (the roll could have come out differently) while the latter is necessary (our universe must support life, which means "ex hypothesi" that we must see fine tuning). He suggests the following analogy: instead of being summoned into a room to observe a particular roll of the dice, we are told that we will be summoned into the room immediately after a roll of double sixes. In this situation it may be quite reasonable, upon being summoned, to conclude with high confidence that we are not seeing the first roll. In particular, if we know that the dice are fair and that the rolling would not have been stopped before double sixes turned up, then the probability that we are seeing the first roll is at most 1/36. (It may be smaller because we have not assumed that the roller is obliged to summon us the first time double sixes come up.)


Wikimedia Foundation. 2010.

Look at other dictionaries:

  • Gambler's fallacy — The Gambler s fallacy, also known as the Monte Carlo fallacy (because its most famous example happened in a Monte Carlo Casino in 1913)[1], and also referred to as the fallacy of the maturity of chances, is the belief that if deviations from… …   Wikipedia

  • Gambler's conceit — is defined by economist David Ewing as the mistaken belief that one will be able to stop performing a risky action while one continues to succeed or win at it. This belief frequently arises during games of chance, such as casino games, or stock… …   Wikipedia

  • Fallacy — In logic and rhetoric, a fallacy is usually incorrect argumentation in reasoning resulting in a misconception or presumption. By accident or design, fallacies may exploit emotional triggers in the listener or interlocutor (appeal to emotion), or… …   Wikipedia

  • Fallacy of composition — The fallacy of composition arises when one infers that something is true of the whole from the fact that it is true of some part of the whole (or even of every proper part). For example: This fragment of metal cannot be broken with a hammer,… …   Wikipedia

  • Fallacy of division — A fallacy of division occurs when one reasons logically that something true of a thing must also be true of all or some of its parts. An example: A Boeing 747 can fly unaided across the ocean. A Boeing 747 has jet engines. Therefore, one of its… …   Wikipedia

  • Fallacy of quoting out of context — The practice of quoting out of context, sometimes referred to as contextomy or quote mining , is a logical fallacy and a type of false attribution in which a passage is removed from its surrounding matter in such a way as to distort its intended… …   Wikipedia

  • Fallacy of the single cause — The fallacy of the single cause, also known as causal oversimplification, is a fallacy of questionable cause that occurs when it is assumed that there is a single, simple cause of an outcome when in reality it may have been caused by a number of… …   Wikipedia

  • Reification (fallacy) — Contents 1 Etymology 2 Theory 3 Difference between reification and hypostatisation …   Wikipedia

  • Deductive fallacy — A deductive fallacy is defined as a deductive argument that is invalid. The argument itself could have true premises, but still have a false conclusion.[1] Thus, a deductive fallacy is a fallacy where deduction goes wrong, and is no longer a… …   Wikipedia

  • Nirvana fallacy — The nirvana fallacy is the logical error of comparing actual things with unrealistic, idealized alternatives. It can also refer to the tendency to assume that there is a perfect solution to a particular problem. A closely related concept is the… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”

We are using cookies for the best presentation of our site. Continuing to use this site, you agree with this.