Allais Paradox II : Do Two Wrongs Make a Right?

I have begun a possibly long series on people’s heuristics and biases when we try to think about probability. I posted one explanation of the Allais Paradox. Click on the link for definitions as I go on assuming earlier posts have been read (this will create problems but I can’t avoid it). Briefly the Allais Paradox is that we care too much about the difference between 99% and 100%. The rationale I mentioned is that the difference matters a lot if we suspect we might be dealing with crooks and care if we would then find proof beyond reasonable doubt,

Another explanation is that normal people use the phrase “90% chance” or “99 percent chance” differently than mathematicians do and that we can communicate with each other even if we don’t understand what psychologists are telling use during experiments.

Do two wrongs make a right? When people are asked for a 90% interval (on say how much tea there is in China) they give intervals half of which include the correct number. So when asked for a 90% probability, they give a 50% probability. Cumulative prospect theory says when people are told a 99% interval they act as if they were told a 90% interval. With the errors in stating intervals and in interpreting stated intervals cancel. When normal people talk to normal people about probabilities communication is achieved. It is as if there were 2 different languages / probability as formally defined and probability as discussed in ordinary language.