Pulldown resistors and multiple switches
Call the resistors R1 and R2, the negative terminal Ground, and the positive terminal V+.  The junction of R1 and R2 is connected to Ground.  This holds the resistor ends at the junction to zero volts relative to ground.  Ignoring P2 for the moment, the other end of R2 is open circuit to V+ when S2 is open.  Applying Ohm's law, we have a finite resistance in series with an infinite resistance, so zero volts across R2 when S2 is open.  Thus one sees that voltage across R2 is not affected by voltage changes across R1.

P2 as an input is not completely an open circuit; typically its effect is similar to a multi-gigaohms resistor to some voltage between Ground and V+.

Edit: 
More directly, observe that the voltage at the Ground ends of R1 and R2 is zero and remains at zero no matter what S1 and S2 do.  Thus, operation of S1 does not affect voltage at P2, and operation of S2 does not affect voltage at P1.