Clusterwise least squares partitions regression data into K groups with separate linear fits. We study an ensemble whose base learner is exact: solve the problem to global optimality on each of B random subsamples of size m << n, extend each solution by nearest-surface assignment, align the labels, and combine the replicates by vote or by selection. Each replicate is then an empirical K-quantizer on m points, and the ensemble admits an exact analysis. A vote is correct at a unit once the probability of a clean subsample times the clean-data replicate accuracy exceeds one half, whatever the contaminating values; iterating the ensemble on the units it has not flagged gives a variant that estimates the trimming level rather than requiring it. With up to 20% of gross outliers in the response its worst-case accuracy was 0.89, against 0.80 for trimmed alternation at the true contamination fraction and less at every fixed level tried. Conditionally on the data the replicates are i.i.d., so the vote converges exponentially fast in B to the plurality partition of the replicate law, agreeing with the criterion minimiser outside a boundary set whose size depends on m and the micro-solver, not on B. For the two-group location model, subsamples of order 1/pi_min make a replicate right more often than wrong above a separation threshold. An O(n^3) enumeration gives the exact minimiser for two groups and one covariate, against which the theory is checked. On clean data the ensemble loses to multistart alternation at equal cost.

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