The following are two simple results that constraint the number of liars, and the number of truth-tellers, in any such group (I’ll provide proofs of these results in the comments after a few days).
“Accusations of untrustworthiness tend to decrease the overall level of trust we place in those involved”
Result 1: If, for some numberm, each person in the group accuses at leastmother people in the group of lying (and there is no paradox) then there are at leastmliars in the group.
Result 2: If, for any two people in the groupp1andp2, eitherp1accusesp2of lying, orp2accusesp1of lying (and there is no paradox), then exactly one person in the group is telling the truth, and everyone else is lying.
These results support an affirmative answer to our…
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