Some estimators have arbitrary ways to break ties:

• k-nearest neighbors with data points lying on a uniform 1d grid (see BallTree.query returns inconsistent indices between scikit-learn versions 0.24.1 and 1.1.1 #23667 for the BallTree for instance);
• tied splits on different features in histogram gradient boosted trees with redundant features.
• decision tree splits on the same feature with equivalent threshods: X = [[0], [1], [2], [3]] and y = [0, 1, 1, 0]: X > 0.5 and X > 2.5 are tied splits but only X > 0.5 is considered;
• possibly other models (please feel free to edit this list or suggest missing estimators in the comments).

If the tie breaking logic is deterministic, then it might introduce a non-controllable bias in a datascience pipeline. For instance when analyzing the feature importance of an histogram gradient boosting model (via permutations or SHAP values), the first feature of a group of redundant features would always deterministically be picked up by the model and could lead a naive datascientist to believe that the other features of the group are not as predictive.

Note that this is not the case for our traditional DecisionTreeClassifier/Regressor / RandomForestClassifier/Regressor and extra trees because they all do feature shuffling (controllable by random_state) by default even when max_features == 1.0. This makes it easy to conduct the same study many times with different seeds to see if the results are an artifact of an arbitrary tie breaking or not.