I haven't actually done the math yet, but I don't believe you. I think that if your terms are "per interview" then the more recent chunk of 100% even will overpower all the older stuff because there are so many of them, and the series of averages will oscillate.
I take it that my approach was not discussed in the heated debate you had? Because it seems a good exercise for grad students.
Also, I don't understand why you think a per interview series would net fundamentally different results than a per coin toss series. I'd be interested in your reports after you (or your colleagues) have done the math.
I got into a heated debate a couple days ago with some of my (math grad student) colleagues about the Sleeping Beauty Problem. Out of this discussion came the following thought experiment:
Sleeping Beauty volunteers to undergo the following experiment and is told all of the following details: She will be put to sleep. During the experiment, Beauty will be wakened, interviewed, and put back to sleep with an amnesia-inducing anti-aging drug that makes her forget that awakening. A fair coin will be tossed until it comes up heads to determine which experimental procedure to undertake: if the coin takes n flips to come up heads, Beauty will be wakened and interviewed exactly 3^n times. Any time Sleeping Beauty is wakened and interviewed, she is asked, "What is your subjective probability now that the coin was flipped an even number of times?"
I will defer my analysis to the comments.