Least squares has no defence against a single bad point — RANSAC just lets the outliers fail to vote

Fit a line with ordinary least squares and one bad measurement can wreck it. Because OLS minimises the sum of squared residuals, a lone far-off point — whose squared error is enormous — pivots the whole line toward itself. Its breakdown point is zero: corrupt one observation and the estimate is arbitrarily wrong. RANSAC throws that whole approach away and does something almost cheeky instead. I built it from scratch in the browser; here's the idea. Guess from the smallest possible sample…