Formal phrase for "in hopes that"

Could you try expecting or anticipating?

But in seriousness, in hopes that doesn't strike me as very colloquial, though it would seem in the context presented in this question that want of something to happen might be considered more non-scientific than something that has reason or justification to be correct.

In context:

To overcome this crucial issue, a popular solution has been used where a task is assigned to many workers and the results for this task are aggregated expecting that the aggregated result is actually the correct one.

(I thought "that" was allowed to be optional, but since "the aggregated result is actually the correct one." is a complete sentence, "that" is a conjunction and necessary.)

Instead of in hopes that, you could use phrases including expectation or belief, as in expecting that, in expectation that, with expectation that, or similarly with belief.

Your problem isn't formality, it's confidence. "In the hopes that" implies you want something, but aren't sure at all that you'll get it; since this is a scientific paper, you probably want to sound a bit more confident than that! "In the expectation that" works well.