The fallacy in the argument is that, first choice only, NO candidate has even a slim majority, let alone a strong one. If you decay the hypothetical 3 party se

The fallacy in the argument is that, first choice only, NO candidate has even a slim majority, let alone a strong one. If you decay the hypothetical 3 party set of options by eliminating the least popular candidate then you're back to first past the post which is the current status quo in the US. Schulze and similar methods use the ranked lists to evaluate pairs of candidates and eliminate the candidates that are universally the worst first / retain candidates that rank well in isolation. This is more likely to result in a compromise that works best for the most people.