Which action is recommended when 80% of the bagged trees' first splits are by the same dummy variable?

Running a random forest is recommended in this scenario due to the behavior of the bagging technique you are utilizing. When a high proportion, such as 80%, of the first splits in a bagged tree model are influenced by the same dummy variable, it indicates that this variable is dominating the splits. This can lead to overfitting, where the model is too closely tailored to the training data and may not perform well on unseen data.

A random forest, which is an ensemble of decision trees that inherently incorporates randomness in selecting predictors for each tree, helps mitigate this issue. It averages the results over multiple trees to reduce variance and gives more balanced predictions. By allowing the random forest to randomly sample features, the influence of any single dummy variable will be diminished, leading to a more robust model that generalizes better to new data.

Thus, opting for a random forest alleviates the risks associated with having a dominant predictor, ultimately enhancing the model's performance.