Prognosticate 'as to' ...
 

What is the difference between these two sentences if any?

prognosticate as to this election's outcome.
prognosticate this election's outcome.

Re: Prognosticate 'as to' ...
 

No difference. try searching on Google. "prognosticate" can be used either just with a direct object, or with a prepostion like "on" or "about" or - as here - "as to".

More interesting to me is "this election's outcome" rather than "the outcome of this election". What's the explanation of the possibility of using the 's possessive there ?

election's outcome
 

Well I think theoretically it must not (or at least ought not) be used that way, but I see that people are using this form, widely.

An article in NY Times that uses this phrase. <---