I say 50%; you say 80%. We could both be right. Here's why:
The odds you would use in the grandparent post's calculation would be different from the average conviction rate, because you'd have knowledge of the specific facts of your particular case, which would affect your estimate.
Despite all the noise HN's made about this case, I actually believe that most of the people who are punished by our justice system (1) are actually guilty of the crime(s) they're accused of (Aaron probably was), and (2) don't have mitigating factors that might cause the case to be dismissed by the judge when he/she becomes aware of all the facts, acquitted by a sympathetic jury, given a small fine or other slap-on-the-wrist sentence, or successfully appealed (Aaron's case clearly did have such mitigating factors).
Let's say hypothetically that, of every 100 defendants who go before the court, W=70 of defendants are rightfully convicted, X=10 are wrongfully convicted, Y=10 are rightfully found innocent, Z=10 are wrongfully found innocent. I'm using the term "innocent" here to lump together category (1) above, "factually innocent" (he/she didn't do it) and category (2), "morally/technically innocent" (he/she did it, but it shouldn't be a crime / sentence is far too harsh / prosecutor/police tactics were unconstitutional / jury didn't believe the evidence was good enough / good defense attorney managed to inject reasonable doubt / jury nullification [1], etc.)
Let's say you're being prosecuted. You know the above numbers (or they're your best estimates based on the available data and reasonable modeling assumptions). You know you're in the "innocent" category, that is, that you'll either be in X (wrongfully convicted) or Y (rightfully found innocent). Your chance of being wrongfully convicted is thus X/(X+Y) = 50%, as I stated.
But from the point of view of all cases, the overall conviction rate is (W+X)/(W+X+Y+Z) = 80%, as the parent stated.
The above numbers aren't based on any actual facts; they're made up to agree with both the parent's stated 80% number for overall conviction rate, and the grandparent's stated odds of a particular defendant's chance of winning of 50%.
These computations are an example of Bayesian reasoning [2].
