Take measures based as though the complaints are made in good faith.
If you assume them true then you would act as if the investigation has already taken place, and determined that they are true. If you're going to act like that why would you need an investigation?
If complaints or concerns are raised in good faith then you have no need to mistrust the representation and instead can look to the facts and context of the situation.
Believing someone is not important, understanding the sequence of events that led to them speaking up is.
Responding as if someone is acting in good faith means that
- you believe that
- they believe that
- they are true
On the other hand, if you believe someone it means that
- you believe that
- they are true
Using "believe" to mean the first situation only makes everyone's meaning less clear.
That should give you pause when you claim (incorrectly) that a such a narrow usage of language is correct.
All three points lead to different actions and the one in the middle seems to be the most appropriate.
Which is to say, do more than just investigate. Take action as though the complaints are true, although not necessarily all the action you would take if you knew the complaint to be exactly factual.
You should always investigate, even if (to borrow your formatting)
you believe that they believe that their statements are false
and are making a bad faith accusation. It would still be correct to investigate if that was your belief. If you believed that the accusations were entirely factual, then perhaps the immediate step would be to fire someone. But if instead you simply believe that the person is accusing someone of something in good faith, something has already gone wrong and there is a problem. Even if no one did anything wrong.
To put it in terms that might be more familiar, every complaint is an incident and should involve a (blameless) postmortem that asks how the system failed such that someone felt the need to complain. And action should be taken in response. Sometimes, the system failed in such a way that it allowed a malicious actor to do a bad thing, and that malicious actor should be reprimanded, independent of the postmortem.
Believe the accuser when writing the postmortem, and begin incident response as soon as possible. Investigate fully before reprimanding a potential malicious actor.
What's that supposed to mean?
Do not believe every word anyone says as the absolute truth of an event. Evidence, corroboration, attempts to be objective -- these are all the rights of the accused.
Believe the complainant but do not assume they are correct. Our memories are the movies based on real events.
That's sounds like giving accusers too much power, especially if it leads to firing. It's not as if people don't lie.
He says on the same line.