In electricity, the ballast would be considered the source of the power. The bulb is the load. The load draws current from the source. It will draw as much current it needs to opperate. So if the source can not supply enough current, the bulb will not opperate or draw so much current that the source would over load.
Also, MH bulbs are not like normal incandecent bulbs. They dont have a metal filiment. They are considered a gas discharge light. The gas gets energized and becomes the path for the electricity. Thus giving off light in the process. If the ballast cant supply enough current to get the initial spark to ignite the gas, it wont operate.
Metal halide lamp - Wikipedia, the free encyclopedia
Here is a nice little article on MH
Now the case that you gave me, you are probably refering to the voltage rating of the bulb. A 12V bulb on a 6V supply would be half as bright and would burn out on a 24V system. This is because the current being drawn by the bulb decreases on the 6v system and increases on the 24v system.
The equation you use to show this is Volts / Resistance = Current
Say the bulb has a resistance of 1 Ohm
In the 12v system, the bulb would draw 12 Amps
12V/1 Ohm = 12 A
In the 6v system, it would draw 6A
6V/1 Ohm = 6 A
In the 24v system, it would draw 24A
24V/1 Ohm = 24 A
Since the bulb was only designed to be on a 12V system, it is only designed to draw 12 amps. So when 24 amps are going through it, it will burn out.
Hope I didnt confuse you
Brian