Is IPE equivalent to Baldwin's method?

[Baldwin's method](https://electowiki.org/wiki/Baldwin%27s_method) is an elimination method that eliminates the Borda loser.

[Instant Pairwise Elimination](https://electowiki.org/wiki/Instant_Pairwise_Elimination) is an elimination method that eliminates the Condorcet loser, or (if none exists) the Borda loser.

In all my sim work, I've run somewhere on the order of a million simulated electorates--normal, polarized, 2D, 3D, cycles, cycles-within-cycles, 6+ candidates, whatever. I've never ***once*** had IPE return a result different than Baldwin's. They might eliminate candidates in a different order, but the winner is always the same, both natural and for any strategy. Their entry heatmaps are pixel-for-pixel identical.

Baldwin's method is Smith-compliant in that a Condorcet winner, *which can never be the Borda loser*, can never be eliminated. IPE is Smith-compliant too by the same logic: neither of its elimination options can eliminate a Condorcet winner aka the last member of the Smith set. (The electro-wiki notes suggest this is only true for strict orderings outside the Smith set, failing to take into account the former Borda/Condorcet guarantee. I assert IPE is always Smith-compliant.)

I've been trying to deliberately construct a counter-example that distinguishes the two, both in curated simulations or by hand, for about two weeks now to no avail. I've also failed to produce a mathematical proof.

[Your turn!](https://www.chocolatepi.net/voteapp/?election=F0.6188738776897205&candidates=133,233,4,273,455,4,396,291,6,385,218,6,318,464,6) Enjoy the puzzle.