The Relativity of Wrong

Recent political comment brings me back to a point I'd written about before, under the label of Successive Approximation.  The better title, unsurprisingly, is Isaac Asimov's The Relativity of Wrong. 

I first became aware of Paul Ryan's lie when my wife asked me, having mentioned nothing about context, whether a runner could conceivably mis-remember his marathon of somewhat over 4 hours as having been somewhat under 3 hours.  As has been reported in many places, and some reporters having done some experiments, the answer is no.  It is completely implausible that someone, especially someone with only one marathon, could make that mistake as an honest mistake.  Confusing a little over 4 for a little under ... maybe.  You would likely have trained for some time under 4 and that number could have stayed with you longer than your disappointment in not making your goal. 

But confusing your over-4 hours, a perfectly respectable time to cover a marathon if nothing to brag about for an open class man, for sub-3 -- a time that entitles you to some bragging (as a friend worked to earn the right to) and is achievable only with some serious training and talent -- is not an accident.

The political side of this, well, not so very interesting.  Except for the fact, perhaps, that Ryan is supposed to be a leading light for Republican number-crunching.  Number types are even less likely to make a mistake like that.  At least as a mistake. 

More interesting, and perhaps useful, to the local purpose is to look some at how to assess the relativity of wrong.  The route I took in the successive approximation post was quantitative.  Some articles have taken something like that, observing that his claimed time was about 70% of his actual time, or, conversely, that he lied by about 30%.  That's actually much too generous to his lie.  The problem with that is that if he had claimed the world record time (a bit less than 2 hours faster than he ran, as opposed to the somewhat more than 1 hour of his actual lie), it would only be scored as 50% wrong.  You can't run faster than the world record, or you'd be the record holder, which even Ryan didn't claim.  So, the most he could have lied by is about 2 hours (iirc his actual time was 4:01, and the world record back then was about 2:07, so 114 minutes).  His actual lie is about 65 minutes (taking 2:50-something as 2:56) wrong, so 57%, more than half, of the span that he could possibly have lied by.  That could be refined some by comparison against, say, the race winner's time, or the Olympic qualifying time.  But you get the idea.  And the 57% is about double what the other approach shows.  Compare how wrong something is with how wrong it could be.

But some things, and this is where I'll especially invite comments, don't lend themselves to that kind of quantification.  For instance, I'm comfortable with saying that it is more wrong to say that the earth has no greenhouse effect than it is to say that CO2 is not a greenhouse gas.  But how can we assess this comparative wrongness with the error in saying that CO2 levels have not risen over the past 200 years?

So I'll invite description of approaches to assessing relative errors, preferably with examples.  Note, too, that it's best to have them be objective examples -- so which candidate is better kinds of things are not going to work.  Marathon times and the radiative properties of the earth's atmosphere aren't partisan matters.