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Musings about the environment and all it touches, from education to city planning

Logical fallacies and the environment: the gambler and the sharp-shooter

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2014-04-07-Gamblers-Fallacy

You’re playing dice, and you’ve rolled four ones in a row.  On your next throw, you’re going to be thinking “there’s no way I’ll roll a one again, the odds are against it”.  If you think your odds are less that one in six, you’re committing a gambler’s fallacy.  Likewise, the odds of getting heads on a coin toss are one out of two – regardless of what has been tossed before.  Committing a gambler’s fallacy is assuming that independent events are linked; one coin toss, one dice toss are independent of the previous ones.

The problem has to do with true independence.  In games of chance, coins and dice are supposed to be fair.  But are they?  When there is a long and improbable run, the suspicion may be that coin or the dice is loaded.  If that is the case, the improbable event (yet another four, or another head) is actually the one more likely to happen.

The psychology behind it is complex, and leads us to assume that selecting the numbers “1,2,3,4,5” for a lottery ticket is a poorer choice than “11, 13, 21, 30, 33”.  We like patterns and seek them unconsciously; therefore, accepting true randomness is difficult.

We can also be fooled into thinking that something is “due”.  For instance, after dealing a number of cards, you may say that an ace is due to come up if you’ve been drawing twenty cards before (the chance of drawing an ace increases as the rest of the pack gets smaller).  This reasoning is correct, because there are only a 52 cards – and we’re not replenishing the pack and reshuffling after each draw.

Gambler's fallacy in reverse: the odds are not independant

Gambler’s fallacy in reverse: the odds are not independant

Compare this with a game of rock-paper-scissors.  This is an instance where the outcome of one draw is quite dependant on the previous ones; a skilled player tries to outsmart his opponent’s guess, but there is no randomness in the decision.

A form of gambler’s fallacy can be seen in our response to natural events.  For instance, consider the odds of getting flooded.  You are told that “This was the storm of the century.  In fact, our statistical analysis shows that the odds of a storm of such intensity and duration is actually of happening only once in 230 years”.  The natural reaction is to rebuild: another storm like this just can’t happen in your lifetime, can it? The odds are so low.  But there are at least two problems with that reasoning.

The first problem is a gambler’s fallacy reasoning.  Whatever the odds of that storm were, the fact that you just got flooded has no impact on the odds of another storm just as bad occuring again next year.

The second problem has to do with our estimate of the odds.  It’s not like a coin toss; the odds are approximated based on what we have observed historically.  But, specially in places where weather data has not been collected for a long time (as in BC), these may be poor estimates, specially when it comes to rare events.  Further, using odds assumes that the conditions – the coin, so to speak – are constant; but we now know that climate is changing.  In a constant climate, each new storm adds to the data, giving us more accurate odds; but in a changing climate, the conditions for which these odds have been calculated may no longer apply.

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Another fallacy, related to the gambler’s fallacy, is the Texas sharp-shooter fallacy.  The name comes from the image of a person shooting at random inside a barn.  The shooter looks at the wall filled with bullet holes and draws a target around where some of the holes are grouped, to show how precise his shooting is.

The sharp-shooter fallacy can occur in cases where clusters of rare diseases are found and an environmental pollution cause is suspected.  For instance, clusters of rare cancers have formed the basis for the popular movies Erin Brockovich and A Civil Action, both based on true legal cases against alleged polluters.  But the problem with clusters is that they can also occur at random; as with a bunch of random shots, some are bound to be closer together.  A statistical test must be done to test the possibility that the appearance of a cluster is due to mere randomness.

In these celebrated court cases, it is usually relatively easy to demonstrate that pollution has taken place; it is much harder is to show that the pollution is likely to be the cause of the disease cluster.  Questions such as “if this groundwater was tainted so badly, why didn’t everyone who drank from it get sick?” must be addressed on a probabilistic basis.

This has been a problem for the cases of bile duct cancer exposed by Dr John O’Connor in Fort Chipewyan, for instance.  The six cases reported in the town of 1200 had very low odds of occuring.  Was pollution from the tar sands the cause?  This remains an open question, because the low numbers make it very difficult to determine the odds conclusively.  Clustering, in this case, may be random, but may also be due to an unknown genetic factor.  Critics have said that the level of statistical confidence used in such cases (99% confident) is unnecessarily high. (See http://oilsandstruth.org/rare-cancer-strikes)

The best description of the cluster problem I’ve encountered in a popular book is in Dan Fagin’s Toms River (2013, Bantam Books) about the cluster in the New Jersey town of the same name (See http://danfagin.com/).

Also see ludic fallacy http://fallacyaday.com/2011/09/ludic-fallacy/ about the coin example.

Note: As instructors we’re expected to instill in our students critical thinking abilities. So this semester I included in my Environmental Issues class a review of some common logical fallacies with examples taken from the environmental scene. Much to my surprise, I couldn’t find such a collection through a Google search. So I started crafting my own by collecting examples of logical fallacies that occur in environmental news and discussions. Previous post in the series: appeal to tradition.

 

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Written by enviropaul

March 26, 2016 at 11:59 am

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  1. […] Note: As instructors we’re expected to instill in our students critical thinking abilities. So this semester I included in my Environmental Issues class a review of some common logical fallacies with examples taken from the environmental scene. Much to my surprise, I couldn’t find such a collection through a Google search. So I started crafting my own by collecting examples of logical fallacies that occur in environmental news and discussions. Previous post in the series: the gambler and the sharp-shooter. […]


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