I think it’s really important to get the idea of a sliding scale of evidentiary strength across to people. (This is something that has occurred to me from some of my recent attempts to explain the Knox case to people without training in Bayesianism.) One’s level of confidence that something is true varies continuously with the strength of the evidence. It’s like a “score” that you’re keeping, with information you hear about moving the score up and down.
The abstract structure of the prosecutor’s fallacy is misjudging the prior probability. People forget that you start with a handicap—and that handicap may be quite substantial. Thus, if a piece of evidence (like a test result) is worth, say “10 points” toward guilt, hearing about that piece of evidence doesn’t necessarily make the score +10 in favor of guilt; if the handicap was, say, −7, then the score is only +3. If, say, a score of +15 is needed for conviction, the prosecution still has a long way to go.
(By the way, did you see my reply to your comment about psychological evidence?)
I take it you’ve already looked at Eliezer’s “Intuitive Explanation”?
I think it’s really important to get the idea of a sliding scale of evidentiary strength across to people. (This is something that has occurred to me from some of my recent attempts to explain the Knox case to people without training in Bayesianism.) One’s level of confidence that something is true varies continuously with the strength of the evidence. It’s like a “score” that you’re keeping, with information you hear about moving the score up and down.
The abstract structure of the prosecutor’s fallacy is misjudging the prior probability. People forget that you start with a handicap—and that handicap may be quite substantial. Thus, if a piece of evidence (like a test result) is worth, say “10 points” toward guilt, hearing about that piece of evidence doesn’t necessarily make the score +10 in favor of guilt; if the handicap was, say, −7, then the score is only +3. If, say, a score of +15 is needed for conviction, the prosecution still has a long way to go.
(By the way, did you see my reply to your comment about psychological evidence?)