The Extra Choice principle is straightforwardly incompatible with agent-relative duties or prerogatives, right? You don't need the 100 rings to show this. Just consider any case where the "extra choice" bestowed has two features: (i) it better satisfies the other agent's agent-relative duties, but (ii) it is impartially (or agent-neutrally) worse.

E.g. imagine giving a parent an option to save their child from a fire, at the cost of flooding a basement and accidentally killing two other children. Suppose it's permissible (or even ideal, due to special obligations) for the parent to save their child. Still, others probably shouldn't give them this option!

Seems closely related to the 'Hope Objection': https://www.utilitarianism.net/arguments-for-utilitarianism#the-hope-objection

That said, I don't know that deontologists would be that bothered by rejecting the Extra Choice principle. You write, "If the extra option is worse than the existing options then they won’t take it." But this just assumes agent-neutral consequentialism. It could result in a worse outcome, yet be better *as an option for that agent*. (As in the parenting case.)

Returning to 100 rings: I'd expect the deontologist to respond as follows. First, work out the threshold for moderate deontology, beyond which one should just save more lives. Let's say >20 lives warrants killing one. Then, by backwards induction, work out which ring corresponds to passing this threshold. E.g. the last ring of deontologists should choose (2), letting five be killed by others rather than killing 1 themselves. But the prior ring (and all others before them) should be disposed to choose (1), each killing 1 rather than letting 25 (or more) be killed by others.

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The Scenario is logically incoherent (just like utilitarianism)

Mainly because the argument relies on this line:

"The 100th circle is comprised of psycho murderers who will take option one if the buck doesn’t stop reaching them."

but what you are attempting to prove is this line

"a cluster of perfectly moral people would bring about 1.5777218 x 10^69 murders"

when you have JUST stated (in a poor attempt to get out of the objection I articulated on your third blog post). that the majority of this circle, is in fact not composed of perfectly moral people...

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