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I'm using in hopes that in the following sentence. However, it does not seems to be formal and appropriate for a scientific paper. Is there any similar phrase that has the same meaning but more formal ? Thanks.

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 in hopes that the aggregated result is actually the correct one.

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    How about 'under the auspices of'? – Elberich Schneider Aug 3 '14 at 22:58
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    Might one ask why you are looking for a more formal equivalent? Will you be addressing the Pope or the Queen of England, for instance? – Drew Aug 3 '14 at 23:51
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    I don't see anything "more formal" about expecting, anticipating, expecting that, in expectation that, with expectation that (or similar expressions using belief), compared with in hopes that. The verb to hope is not particularly informal, and none of the proposals are particularly formal. – Drew Aug 4 '14 at 2:11
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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.)

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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.

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