> Is that why LEDs display a non-linear brightness response too?

Non-linear with respect to what?  The brightness response is pretty linear 
with respect to current, double the current you get double the brightness to 
within a few %.

> I presume you mean you can "ignore" them for the purposes of figuring out 
> the total current flowing through the system. Clearly the current flowing 
> through each path only depends on the resistence of that path and the 
> potential difference...

I meant if you have a point of unknown voltage connected to two (or more) 
other known voltages via resistors.  If one of the resistors is drastically 
lower than all the others, then you can just assume the unknown point is 
directly connected through the lowest resistance and treat all the other 
resistors as essentially not connected.

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