diff --git a/eppo_client/bandit.py b/eppo_client/bandit.py
index 2d05e82..8f9be69 100644
--- a/eppo_client/bandit.py
+++ b/eppo_client/bandit.py
@@ -160,8 +160,12 @@ def weigh_actions(
         self, action_scores, gamma, probability_floor
     ) -> Dict[str, float]:
         number_of_actions = len(action_scores)
-        best_action = max(action_scores, key=action_scores.get)
-        best_score = action_scores[best_action]
+        # Find the max score
+        best_score = max(action_scores.values())
+        # Get all the keys that have the same best score (if there's more than one)
+        best_action_keys = [k for k, v in action_scores.items() if v == best_score]
+        # Get the lowest lexicographically ordered key.
+        best_action = min(best_action_keys)
 
         # adjust probability floor for number of actions to control the sum
         min_probability = probability_floor / number_of_actions