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"The winner is preferred to each other candidate, by the majority of voters" seems pretty straightforward to me. The problem with Approval is that we're right back at the Faustian bargain of needing to fully support the lesser evil at the expense of your preferred option. And the only thing Range adds is allowing you to moderate the amount of that bargain.

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> "The winner is preferred to each other candidate, by the majority of voters" seems pretty straightforward to me.

It is, but 1) the public needs to be sufficiently convinced that all of the bookkeeping reliably determines which candidate that applies to in the face of possible error or malfeasance, and 2) sometimes there is no such candidate (cycles are possible) and what happens then can be complicated.

(And sure, ties are possible in ~any system, but if we treat cycles as ties we've made ties much more likely.)

If you have a Condorcet winner, sure. In fact, approval voting with "honest" ballots always yields the Condorcet winner if one is expressed†.

Where you get into trouble is that not all elections have a Condorcet winner. In particular:

> The problem with Approval is that we're right back at the Faustian bargain of needing to fully support the lesser evil at the expense of your preferred option.

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