How to represent the sentence "If everyone votes then the motion passes" with FOL

Question

Should it be ∀x Votes(x) ⟹ Passes(Motion)?

Probably not, because if none but 'John' votes, then using extended interpretation, Votes(John) ⟹ Passes(Motion) implies that Passes(Motion) is true.

Answer 1

You need to distinguish between $$\bigl[\forall x\;V(x)\bigr]\Rightarrow P(M) $$ and $$ \forall x\bigl[V(x)\Rightarrow P(M)\bigr] $$

The first one is what captures the sense of the English sentence; the second one is what you need for your John counterexample to work.

Unfortunately there's no really strong consensus about how far to the right a quantifier applies when there are no brackets, so there's a real potential for confusion here. One just has to be very careful about checking which convention each particular author uses.