If an officer offers to release a female prisoner as long as she has sex with him, that's rape, extortion, and abuse of power.
This is the same situation, just with Marion "paying the fine on the behalf" of Robin.
That
can be rape and extortion, and it almost certainly is abuse of power, but I definitely wouldn't say it is the former two in all cases. If the prisoner's term is somehow special cased (longer time/worse conditions than others who have been sentenced for the same crime) and the officer is the cause of that, it's
definitely extortion. If the prisoner has no other choice (such as the obvious one of finishing the mandated prison time), then I'd pretty comfortably call that rape.
But the prisoner (serving a standard sentence and in appropriate conditions) going up to the officer and saying, "I'll do anything if you let me go." and the response being sex? That's not something I'd call rape or extortion if the prisoner accepts. Prostitution, abuse of power, corruption,
yes. But not rape or extortion. There's clear consent with acceptable alternatives to declining the offer and the party who has created the situation and is seeking to gain something is the
prisoner (having broken the law and seeking illegal release), not the officer (who is approached and sets and accepts sex as payment.).
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It's kind of an interesting nuance to most of the scenarios that have been presented so far, honestly. The person in the position to free the imprisoned has generally been presented as the
passive party (at least if you ignore the literary burden caused by using Robin Hood characters). The imprisoned caused their imprisonment by breaking the law and the one seeking their illegal release is the one approaching the releaser, who doesn't really have anything to do with the shit the other three have found themselves in. While the releaser
is the one that sets the cost to the illegal release, it's the one seeking the release that initiates the interaction and attempts to seek a notable gain.
Basically, the sheriff-equivalents aren't really
doing anything in these scenarios, they're having things done
to them (either the responsibilities of their position forcing their action or the one seeking illegal release opening negotiations. To the degree the one in power expresses agency, it's to set and accept the price and release the prisoners.). It's an unusual thing to have the one in the position of power be the passive party in these kinds of scenarios.