diff --git a/owners.py b/owners.py
index 7fa69e365..1a2a1ab73 100644
--- a/owners.py
+++ b/owners.py
@@ -2,7 +2,7 @@
 # Use of this source code is governed by a BSD-style license that can be
 # found in the LICENSE file.
 
-"""A database of OWNERS files.
+r"""A database of OWNERS files.
 
 OWNERS files indicate who is allowed to approve changes in a specific directory
 (or who is allowed to make changes without needing approval of another OWNER).
@@ -62,6 +62,12 @@ import fnmatch
 import random
 import re
 
+try:
+  # This fallback applies for all versions of Python before 3.3
+  import collections.abc as collections_abc
+except ImportError:
+  import collections as collections_abc
+
 
 # If this is present by itself on a line, this means that everyone can review.
 EVERYONE = '*'
@@ -80,9 +86,9 @@ def _assert_is_collection(obj):
   assert not isinstance(obj, str)
   # Module 'collections' has no 'Iterable' member
   # pylint: disable=no-member
-  if hasattr(collections, 'Iterable') and hasattr(collections, 'Sized'):
-    assert (isinstance(obj, collections.Iterable) and
-            isinstance(obj, collections.Sized))
+  if hasattr(collections_abc, 'Iterable') and hasattr(collections_abc, 'Sized'):
+    assert (isinstance(obj, collections_abc.Iterable) and
+            isinstance(obj, collections_abc.Sized))
 
 
 class SyntaxErrorInOwnersFile(Exception):
diff --git a/owners_finder.py b/owners_finder.py
index 61869347e..62fe355a8 100644
--- a/owners_finder.py
+++ b/owners_finder.py
@@ -9,6 +9,7 @@ from __future__ import print_function
 import os
 import copy
 import owners as owners_module
+import random
 
 
 def first(iterable):
@@ -161,10 +162,12 @@ class OwnersFinder(object):
     self.selected_owners = set()
     self.deselected_owners = set()
 
-    # Initialize owners queue, sort it by the score and name
-    self.owners_queue = sorted(
-        self.owners_to_files.keys(),
-        key=lambda owner: (self.owners_score[owner], owner))
+    # Randomize owners' names so that if many reviewers have identical scores
+    # they will be randomly ordered to avoid bias.
+    owners = list(self.owners_to_files.keys())
+    random.shuffle(owners)
+    self.owners_queue = sorted(owners,
+                               key=lambda owner: self.owners_score[owner])
     self.find_mandatory_owners()
 
   def select_owner(self, owner, findMandatoryOwners=True):
diff --git a/tests/owners_finder_test.py b/tests/owners_finder_test.py
index a520d9a2d..126cc3a2e 100755
--- a/tests/owners_finder_test.py
+++ b/tests/owners_finder_test.py
@@ -153,8 +153,12 @@ class OwnersFinderTests(_BaseTestCase):
   def test_reset(self):
     finder = self.defaultFinder()
     for _ in range(2):
-      self.assertEqual(finder.owners_queue,
-                       [brett, darin, john, peter, ken, ben, tom])
+      expected = [brett, darin, john, peter, ken, ben, tom]
+      # darin and john have equal cost, the others have distinct costs.
+      # If the owners_queue has those two swapped then swap them in expected.
+      if finder.owners_queue[1] != expected[1]:
+        expected[1], expected[2] = expected[2], expected[1]
+      self.assertEqual(finder.owners_queue, expected)
       self.assertEqual(finder.unreviewed_files, {
           'base/vlog.h',
           'chrome/browser/defaults.h',
@@ -202,7 +206,13 @@ class OwnersFinderTests(_BaseTestCase):
 
     finder = self.defaultFinder()
     finder.select_owner(brett)
-    self.assertEqual(finder.owners_queue, [darin, john, peter, ken, tom])
+    expected = [darin, john, peter, ken, tom]
+    # darin and john have equal cost, the others have distinct costs.
+    # If the owners_queue has those two swapped then swap them in expected.
+    if finder.owners_queue[0] == john:
+      expected[0], expected[1] = expected[1], expected[0]
+
+    self.assertEqual(finder.owners_queue, expected)
     self.assertEqual(finder.selected_owners, {brett})
     self.assertEqual(finder.deselected_owners, {ben})
     self.assertEqual(finder.reviewed_by,