[QUOTE=John Mace]
I honestly don’t know. I don’t know how to calculate the mathematical probability that Jack is lying based on no data points about Jack. Because, remember, that’s the key issue. We’re not talking about “what is the probablity of X happening”, we’re talking about “what is the probablity that Jack is lying about X.”
But why is the original scenario only less cridible by a “razor thin” margin? Can you put some mathematical bounds on the thinness? If not, how do you know it’s not non-existent rather than “razor thin”?
[/QUOTE]
Because it’s the only thing that’s different between the two stories.
Picture each story on a balance scale. We know nothing about Jack or Jill - if one were a known liar, the balance scale would tip strongly in one direction, for instance. But the chances of that are equal for them both. Everything is exactly even on both sides… EXCEPT for the likelihood of the event they are describing. Jakc describes an event that’s perfectly plausible, but less likely to occur than Jill’s story. So the balance scale is tipped, ever so slightly, ever so razor-thinly, towards Jill telling the truth. The more unlikely the event Jack describes, the more the scale tips. At some point, if his story becomes implausible, it tips far over. But even the first scenario tips the scale slightly towards Jill.
Now, I can’t tell exactly what has people up in arms here. In the case of ywtf, it seems to be the idea that that scale tip would someho translate into any sort of action as far as the handling of the case.
Let’s think a bit about standards of proof. We might run the scale from “Utter certainty,” through “beyond a reasonable doubt,” to “preponderance of the evidence,” to “probable cause,” through “reasonable suspicion.”
The slight, razor-thin nudge I’m talking about here wouldn’t satisfy any standard of proof, even “reasonable suspicion.” It’s not something that alone would sway any fact-finder. No one could reasonably accuse Jack of being a liar if he told his story.
But that wasn’t ever the question. The question was, IN THE ABSENCE OF ALL OTHER INFORMATION, what do the stats tell us?
Now, you may rightly protest that we’re not in a IN THE ABSENCE OF ALL OTHER INFORMATION scenario. That’s certainly a valid observation. But the thing to do then is not simply declare that stats irrelevant. It’s to point out that their tiny, near-zero, epsilon value is massively overshadowed by other, specific evidence.
Zero does not mean “almost zero.”