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## Fine-Tuning and the Sharp-Shooter Fallacy

(This is a repurposed Facebook comment.)

The Fine-Tuning Argument (FLA) is accused of committing the Texas sharpshooter fallacy. Sam the shooter wants to hit a bullseye, but isn’t having much luck. They can barely hit the side of a barn. Having sprayed bullets at the barn all day, they devise a plan: pick an arbitrary bullet hole, paint a bullseye around it, ignore the rest of the bullet holes, and announce themselves to be a sharpshooter.

The moral of this story can be stated in a few ways. Don’t ignore data. Keep in mind the number of failed attempts when you go looking for (and set a criterion for) successful attempts. You can avoid these problems if you specify your hypothesis before you collect your data. Drawing conclusions from a sub-sample is dangerous – if you must, try to choose a random sub-sample.

### A Bayesian Sharpshooter

Let’s put the tale of Sam in Bayesian terms, and then see if it applies to the FTA. Suppose,

• $S$ = Sam is a sharpshooter
• $\bar{S}$ = Sam is not a sharpshooter.
• $T$ = Sam said “I’m going to hit that painted bullseye with this shot”, and then he did.
• $P$ = Sam shot at a wall, and then painted a bullseye around his shot.
• $B$ = background information about guns and bullets and such.

In both cases $T$ and $P$, we observe a bullet at the centre of a bullseye. The difference between the cases is as follows. Sharpshooters are much more likely to hit a given target than non-sharpshooters, thus: (more…)