On the results of the survey depend the extent and the type of campaign, we shall wage.
In the above sentence, is we shall wage a reduced version of the relative clause which we shall wage?
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On the results of the survey depends the extent and the type of campaign [we shall wage].
Yes, it's a relative clause. Since it's an integrated (defining) one, no comma is required, as shown.
It's not a 'reduced' relative as you put it, but a 'bare' relative, the kind where the subordinator "that" is omitted.
A wh relative is also possible, as you mention.