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DanielLC comments on Thinking Bayesianically, with Lojban - Less Wrong Discussion
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75% is beyond a reasonable doubt? I always thought that would be more like 99%. At the very least, 95%.
Some time ago, I went looking for numbers, and the best I found was a specialized survey which asked how certain people would have to be in order to convict someone as being guilty 'beyond a reasonable doubt'. The answers varied depending on the crime, from 75% for petty larceny to 95% for murder; so I assumed that the higher numbers were because of the significant punishments involved, and that people wanted to be extra sure that if they voted to convict, that the person really deserved it; and thus that the 'real' meaning of 'beyond a reasonable doubt' was the lower number, 75%.
A bit of Googling turns up http://www.law.northwestern.edu/faculty/fulltime/diamond/papers/conflictBetweenPrecisionAndFlexibility.pdf , which appears to be what I was looking at.
"Beyond a reasonable doubt" seems to suggest that the chance of being wrong is small enough to be safely ignored unless the utilities involved are enormous, a standard that I would expect to require at least around 98% confidence. If people noticed that you were wrong 1 in 4 times that you say there is no reasonable doubt, they would think of you as severely overconfident. The numbers you assign to "preponderance of the evidence" and "clear and convincing evidence" also seem badly skewed, though less so.
As a lawyer, I want to say that "preponderance of the evidence" is satisfied by the theory that is most likely given the evidence presented. It's fancy talk for "we can't both lose."
Edit: 50% plus epsilon satisfies the legal standard "preponderance of the evidence"
One theory I've come up with is that the true value of the term 'beyond a reasonable doubt' is less in the specific percentage value, and more in that it makes for a significant difference in the evidence required to convict someone of a civil tort (in which they are merely required to compensate the harmed party) and the evidence required to predict that someone is likely to commit further criminal actions in the future (and thus it would be reasonable to take additional measures, beyond simple harm-compensation, to deal with the expected future threat); and that the 'reasonable doubt' standard is simply what happens to result in the right rate of convictions. (I wrote this idea up in more detail at http://www.ncc-1776.org/tle2011/tle639-20111002-05.html .)
'Preponderance of the evidence' simply means more likely than not - 50%+1. (As I see TimS posted.) 'Clear and convincing evidence' is a level between 'preponderance' and 'beyond reasonable doubt', so without having found any particular surveys or statistics, I put it midway between the two.