Does Improved Critical with a Double Weapon apply to both sides of the weapon?

[AwesomenessDog]

Some Double weapons (like a double sword, Darth Maul style) make sense as to why if you take the feat, you get the effect to both sides, because it's the same weapon on both ends. But others, like the Urgosh and "sickle and chain" are realistically two different weapons on either end of the proverbial stick.

In both cases, just taking the feat would allow you to do what you need two keen weapon abilities to do.

[Cavall]

Yes.

Just like if you had weapon focus short sword and two weapon fought.

[Syries]

It counts as one weapon for all purposes except for enchantments and TWFing. So yes, improved critical (much like weapon focus and weapon specialization, or any other feat that requires choosing one weapon) does apply to both ends of a double weapon.