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Can you use first person plural (we) in objective essays?
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It depends on the context. An objective essay is intended to convey unbiassed information, so you probably would not be writing 'we feel that the speaker was an idiot'. On the other hand, you could easily write 'and so we can see that the statistics indicate that a majority of speakers are idiots'.

It is probably unlikely that you would be using the first personal pronouns much, as the main point in any formal essay writing is to keep the viewpoint consistent.