diff --git a/deap/base.py b/deap/base.py
index f9d84ba6..3fd2a518 100644
--- a/deap/base.py
+++ b/deap/base.py
@@ -232,10 +232,10 @@ def __hash__(self):
         return hash(self.wvalues)
 
     def __gt__(self, other):
-        return not self.__le__(other)
+        return self.wvalues > other.wvalues
 
     def __ge__(self, other):
-        return not self.__lt__(other)
+        return self.wvalues >= other.wvalues
 
     def __le__(self, other):
         return self.wvalues <= other.wvalues
diff --git a/deap/tools/support.py b/deap/tools/support.py
index 2f7433bd..95948f70 100644
--- a/deap/tools/support.py
+++ b/deap/tools/support.py
@@ -522,10 +522,12 @@ def update(self, population):
                            update the hall of fame with.
         """
         for ind in population:
+            if ind.fitness.values[0] != ind.fitness.values[0]:
+                continue
             if len(self) == 0 and self.maxsize != 0:
                 # Working on an empty hall of fame is problematic for the
                 # "for else"
-                self.insert(population[0])
+                self.insert(ind)
                 continue
             if ind.fitness > self[-1].fitness or len(self) < self.maxsize:
                 for hofer in self: