Cold, it gives the inside more time to come up to the same temperature with the outside, for more even cooking.
cooking.stackexchange.com/users/1393/Michael Natkin
According to McGee "On food and cooking: the science and lore of the kitchen" P.283 potatoes have an enzyme that firms the cell walls at 55ºC-60ºC (130ºF-140ºF).
Starting cooking from cold can make the potatoes firm.
Starting cooking from hot will make a more granular potato.
That's also the reason that you shouldn't add cold water to cooking potatoes if you don't want them to be firm.
cooking.stackexchange.com/users/641/BaffledCook
If you want to make potato salad, you definitely want to start with the potatoes in cold water so that the potato cooks through evenly and won't fall apart or dissolve when making the salad.
Also helps to choose the correct potato for what you want.
The Yukon Gold is a good all around boiling potato but also try the 'blue' - there are about 5000 varieties of potato.
I like using different colored potatoes in salads.
cooking.stackexchange.com/users/None/
I have done it both ways, depending on whether I'm in a hurry.
Ideally, you will fill the pot with your spuds and then add cold water to that pot and then add to heat.
As Michael describes above, this will give more even cooking and you can avoid the outer surface "splitting" and other wise breaking apart with this technique.
cooking.stackexchange.com/users/215/nicorellius
If your house heating system is the kind that gives you a tank of pre-heated hot water, it makes sense to use this water.
Boil your potatoes using water from your hot tap.
This way, you will save time and money and your boiled potatoes will taste just as good.
cooking.stackexchange.com/users/21270/user21270
I've heard both. What's the correct way to boil a potato? Why?
When boiling potatoes, should I put them in with the cold water or in to the hot?
cooking.stackexchange.com
<potatoes><boiling>
cooking.stackexchange.com/questions/6007
cooking.stackexchange.com/users/1259/yossarian
Cold water allows the inside to come up to the same temperature as the outside, and provides a firmer and less granular result. Cold water will give a firmer potato.
Cooking from cold water will give a firmer potato.