How would you describe someone that continues to perform and action solely because they have observed someone else performing that same action, but do not know the reason. Or, they perform an action in a certain way and do not change to a better method, only because they believe the current method must be the best way to do it because it has been done that way previously.
What word/phrase/expression would you use to describe this scenario?
These are two different things. You should not conflate them.
How would you describe someone that continues to perform and action solely because they have observed someone else performing that same action, but do not know the reason.
The colloquial expression that comes to mind here is "monkey see, monkey do."
Or, they perform an action in a certain way and do not change to a better method, only because they believe the current method must be the best way to do it because it has been done that way previously.
You could say they are set in their ways or hidebound.
The term Cargo Cult could fit this situation. See the Wikipedia page http://en.wikipedia.org/wiki/Cargo_cult and scroll down to 'Other uses of the term'.
In a commercial environment, especially at a large company (although small ones are by no means immune to this effect), one might say that such people are suffering from "institutional inertia".
At one extreme, sheeple can be used to describe people who follow the masses and act without thinking for themselves.
they perform an action in a certain way and do not change to a better method, only because they believe the current method must be the best way to do it because it has been done that way previously.
Traditionalist.
One could say they are "set in their ways". But that's more the latter scenario. For the first... well, sheeple (which is a portmanteau of "sheep" and "people", btw) doesn't quite cut the mustard here, but it's not far from it, as it is "doing something without thinking".
There's a slightly obscure word that means something very close to this: perseverate. The word comes from the medical context (discussing mental illness), and means to continue doing something after the reason has disappeared.
Slightly different shade of meaning: do it by rote, that is, you've learnt it by repetition and do it without knowing why.
Some previously-mentioned words (eg hidebound, traditionalist, perseverate) seem good. Reactionary (“Opposed to change; urging a return to a previous state” or “Very conservative”), conservative (“A person who favors maintenance of the status quo or reversion to some earlier status”), and stick in the mud (""one who is slow, old-fashioned, or unprogressive; an old fogey) must also be mentioned. Stick in the mud dates from the late 1500's, according to phrases.org.uk, which also says
figurative phrase 'stick in the mud' ... was preceded in the language by earlier versions, for example 'stick in the briers, clay, mire' etc. These were usually applied to people who remained in a difficult situation, either by choice or because they were stuck.
