diff --git a/lib/matplotlib/backends/backend_pdf.py b/lib/matplotlib/backends/backend_pdf.py
index 8bbe991bd1a1..c73f0e867101 100644
--- a/lib/matplotlib/backends/backend_pdf.py
+++ b/lib/matplotlib/backends/backend_pdf.py
@@ -18,6 +18,7 @@
 import warnings
 import zlib
 from io import BytesIO
+from functools import total_ordering
 
 import numpy as np
 from matplotlib.externals.six import unichr
@@ -182,8 +183,8 @@ def pdfRepr(obj):
     # represented as Name objects.
     elif isinstance(obj, dict):
         r = [b"<<"]
-        r.extend([Name(key).pdfRepr() + b" " + pdfRepr(val)
-                  for key, val in six.iteritems(obj)])
+        r.extend([Name(key).pdfRepr() + b" " + pdfRepr(obj[key])
+                  for key in sorted(obj)])
         r.append(b">>")
         return fill(r)
 
@@ -243,6 +244,7 @@ def write(self, contents, file):
         write(b"\nendobj\n")
 
 
+@total_ordering
 class Name(object):
     """PDF name object."""
     __slots__ = ('name',)
@@ -262,6 +264,15 @@ def __repr__(self):
     def __str__(self):
         return '/' + six.text_type(self.name)
 
+    def __eq__(self, other):
+        return isinstance(other, Name) and self.name == other.name
+
+    def __lt__(self, other):
+        return isinstance(other, Name) and self.name < other.name
+
+    def __hash__(self):
+        return hash(self.name)
+
     @staticmethod
     def hexify(match):
         return '#%02x' % ord(match.group())