in steps 6 and 7 of the switching argument, the writer imagines that that envelope a contains a certain amount "a", and then seems to believe that given that information, the other envelope would be equally likely to contain twice or half that amount. that assumption can only be correct, if prior to knowing what was in envelope a, the writer would have considered the following two pairs of values for both envelopes equally likely: the amounts "a"/2 and "a"; and the amounts "a" and 2"a". (this follows from bayes' rule in odds form: posterior odds equal prior odds times likelihood ratio). but now we can apply the same reasoning, imagining not "a" but "a/2" in envelope a. and similarly, for 2"a". and similarly, ad infinitum, repeatedly halving or repeatedly doubling as many times as you like. (falk and konold, 1992).