diff --git a/doc/whats_new/v0.20.rst b/doc/whats_new/v0.20.rst
index 38bd521412926..e857c7811c845 100644
--- a/doc/whats_new/v0.20.rst
+++ b/doc/whats_new/v0.20.rst
@@ -129,3 +129,10 @@ Linear, kernelized and related models
 - Deprecate ``random_state`` parameter in :class:`svm.OneClassSVM` as the
   underlying implementation is not random.
   :issue:`9497` by :user:`Albert Thomas <albertcthomas>`.
+
+Metrics
+
+- Deprecate ``reorder`` parameter in :func:`metrics.auc` as it's no longer required
+  for :func:`metrics.roc_auc_score`. Moreover using ``reorder=True`` can hide bugs
+  due to floating point error in the input.
+  :issue:`9851` by :user:`Hanmin Qin <qinhanmin2014>`.
diff --git a/sklearn/metrics/ranking.py b/sklearn/metrics/ranking.py
index 01e71a8514ce5..bc18b248cadfe 100644
--- a/sklearn/metrics/ranking.py
+++ b/sklearn/metrics/ranking.py
@@ -36,7 +36,7 @@
 from .base import _average_binary_score
 
 
-def auc(x, y, reorder=False):
+def auc(x, y, reorder='deprecated'):
     """Compute Area Under the Curve (AUC) using the trapezoidal rule
 
     This is a general function, given points on a curve.  For computing the
@@ -47,12 +47,23 @@ def auc(x, y, reorder=False):
     Parameters
     ----------
     x : array, shape = [n]
-        x coordinates.
+        x coordinates. These must be either monotonic increasing or monotonic
+        decreasing.
     y : array, shape = [n]
         y coordinates.
-    reorder : boolean, optional (default=False)
-        If True, assume that the curve is ascending in the case of ties, as for
-        an ROC curve. If the curve is non-ascending, the result will be wrong.
+    reorder : boolean, optional (default='deprecated')
+        Whether to sort x before computing. If False, assume that x must be
+        either monotonic increasing or monotonic decreasing. If True, y is
+        used to break ties when sorting x. Make sure that y has a monotonic
+        relation to x when setting reorder to True.
+
+        .. deprecated:: 0.20
+           Parameter ``reorder`` has been deprecated in version 0.20 and will
+           be removed in 0.22. It's introduced for roc_auc_score (not for
+           general use) and is no longer used there. What's more, the result
+           from auc will be significantly influenced if x is sorted
+           unexpectedly due to slight floating point error (See issue #9786).
+           Future (and default) behavior is equivalent to ``reorder=False``.
 
     Returns
     -------
@@ -83,8 +94,15 @@ def auc(x, y, reorder=False):
         raise ValueError('At least 2 points are needed to compute'
                          ' area under curve, but x.shape = %s' % x.shape)
 
+    if reorder != 'deprecated':
+        warnings.warn("The 'reorder' parameter has been deprecated in "
+                      "version 0.20 and will be removed in 0.22. It is "
+                      "recommended not to set 'reorder' and ensure that x "
+                      "is monotonic increasing or monotonic decreasing.",
+                      DeprecationWarning)
+
     direction = 1
-    if reorder:
+    if reorder is True:
         # reorder the data points according to the x axis and using y to
         # break ties
         order = np.lexsort((y, x))
@@ -95,8 +113,8 @@ def auc(x, y, reorder=False):
             if np.all(dx <= 0):
                 direction = -1
             else:
-                raise ValueError("Reordering is not turned on, and "
-                                 "the x array is not increasing: %s" % x)
+                raise ValueError("x is neither increasing nor decreasing "
+                                 ": {}.".format(x))
 
     area = direction * np.trapz(y, x)
     if isinstance(area, np.memmap):
diff --git a/sklearn/metrics/tests/test_ranking.py b/sklearn/metrics/tests/test_ranking.py
index 34973f138514e..acdec8932211c 100644
--- a/sklearn/metrics/tests/test_ranking.py
+++ b/sklearn/metrics/tests/test_ranking.py
@@ -20,6 +20,7 @@
 from sklearn.utils.testing import assert_array_equal
 from sklearn.utils.testing import assert_array_almost_equal
 from sklearn.utils.testing import assert_warns
+from sklearn.utils.testing import assert_warns_message
 
 from sklearn.metrics import auc
 from sklearn.metrics import average_precision_score
@@ -425,7 +426,20 @@ def test_auc_errors():
     assert_raises(ValueError, auc, [0.0], [0.1])
 
     # x is not in order
-    assert_raises(ValueError, auc, [1.0, 0.0, 0.5], [0.0, 0.0, 0.0])
+    x = [2, 1, 3, 4]
+    y = [5, 6, 7, 8]
+    error_message = ("x is neither increasing nor decreasing : "
+                     "{}".format(np.array(x)))
+    assert_raise_message(ValueError, error_message, auc, x, y)
+
+
+def test_deprecated_auc_reorder():
+    depr_message = ("The 'reorder' parameter has been deprecated in version "
+                    "0.20 and will be removed in 0.22. It is recommended not "
+                    "to set 'reorder' and ensure that x is monotonic "
+                    "increasing or monotonic decreasing.")
+    assert_warns_message(DeprecationWarning, depr_message, auc,
+                         [1, 2], [2, 3], reorder=True)
 
 
 def test_auc_score_non_binary_class():