Wednesday, September 25, 2013

Honest manipulation

Suppose I know for sure whether p is true, and you know for sure that I know, and you completely trust me. Moreover, suppose your credence in p is neither 0 nor 1. Then I can slightly manipulate your credence in p, in either direction, with great reliability, and without any dishonesty. Suppose I want to slightly raise your credence. Then I uniformly randomly pick a number N between one and a billion, and inform you whether

  1. p is true or N>1
is true. All but certainly, N won't be 1, so I will end up announcing that (1) is true. But then you will ever so slightly raise your credence in p. For if q is the proposition expressed by (1), then P(q|p)=1 and P(q|~p)=1−10−9, so learning q will slightly raise your credence in p. And if I want to slightly lower your credence, I instead inform you whether
  1. p is false or N>1
is true.

The above manipulation observation weakens the manipulation argument I used in this paper, though the manipulation in the paper is much more radical.


Dagmara Lizlovs said...

"Honest manipulation"?

There I go misusing "quotation marks". Your argument sounds like something a politician does.

Alexander R Pruss said...

Politicians won't be satisfied with a one in a billion shift in credences.

Dagmara Lizlovs said...


I initially misread your response earlier today while standing in line at the Subway during lunch, I misread "shift" by leaving the "f" out. I blame low blood sugar for that; however, it seemed more applicable to politicians that way. :-)