Borrowing from the health communication field, there are elements of
Kim Witte’s research on fear appeals (also known as “scare tactics”)
and her health risk message model, the Extended Parallel Process
Model, that can be applied to this discussion.

For those of you unfamiliar with her work or this theory, in a nutshell:

People who are threatened will take one of two courses of action:
danger control or fear control. Danger control seeks to reduce the
risk. Fear control seeks to reduce the perception of the risk. Danger
control is outer-focused and towards a solution. Fear control is
inner-focused and away from a solution.

– For
danger control to be selected, a person needs to perceive that an
effective response is available (response efficacy) and that they are
capable of utilizing this response to reduce the risk (self efficacy).
If danger control is not selected, then action defaults to fear control.
So what?

If you want a person to take an action, show them the threat, but also
ensure they can see that there is a solution which they can use.

However, the critical point is when percieved threat slips above
perceived efficacy, meaning that people no longer think they can do
something to effectively avert the threat. The minute that perceived
threat exceeds perceived efficacy, then people begin to control their
fear instead of the danger and they reject the message.

Here’s a link that might be helpful.

It also has a lot to do with “issue involvement” level. People who are
more involved will react differently to negative and positive messaging
than those who are not as involved.
Check scholarly research on
“valence-framing”, “gain-framed vs. Loss-framed”, “risky choice
framing”, “attribute framing”, “issue involvement”, and “goal framing”.

Authors to check on these subjects include:

P. Salovey, A. J. Rothman, Millar & Millar, X. Nan, and Tsai & Ts