Ok, I did the maths.

Voltage at A0 depends on which switch is pressed. Say R1 is the sum of all resistors above the switch that is pressed and R2 the sum of all resistors below the switch that is pressed.

Then Voltage at A0 = 5 * R2 / (R1 - R2).

Everyting is fine, and the setup behaves just like an ordinary potentiometer. But...

Now we can have the possibility that no switch is pressed. To avoid having A0 to "float", let's link it to ground via a resistor (R3).

Now R3 is parallel to R2 and old R2 becomes (R2*R3)/(R2+R3). To keep the new R2 as close to the original R2, we need (ideally) to have R3 = to be infinite.

So, here is where 470K comes from. 100 times 4.7K looks cool and is high enough to keep new R2 close enough to old R2 so that the system still behaves like a potentiometer with 0V when no switch is pressed.