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

2. 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.