White roofs reflect infrared both out of the house and into the house

After reading a lot of comments on various articles about white roofs, there is a LOT of confusion about what white roofs do. This is very counterintuitive. A reflecting surface such as aluminum foil in insulation behind walls, mylar emergency blankets, and titanium oxide elastomeric roofs (sometimes called "white roofs") reflects infrared in both directions.

Even though you cannot see the side that is facing the roof, a white roof coating is reflecting infrared coming out of the roof back into the roof.

If you have a mylar emergency blanket, which is just a thin sheet of mylar, and you put it between you and the Sun, you will not feel any heat from the Sun because all the infrared from the Sun will be reflected back toward the Sun, and the heat from your body will be reflected back to you. Because you emit so much less infrared than the Sun, you will perceive it as being cooler under the mylar. On the other hand, if it were a cold night and you were to wrap the mylar around yourself, the mylar would reflect most of the infrared escaping from your body back to your body, so you would feel warm. If you place the sheet of mylar on the ground on a cold night with no snow, the ground underneath the mylar will not freeze, but the ground around it will freeze. Why? Because the heat in the ground under the mylar will not be lost as infrared radiation because the mylar will reflect it back into the ground.

In brief, what this means is that a reflective roof will reflect heat away from the roof during the summer when the heat would be undesirable, and it would reflect heat back into the house during the winter when it would be desirable to keep the heat in the house.

You see this effect all the time but may not have noticed.
In the summer, it is hot on clear days and cooler on cloudy days because the direct sunlight is being reflected away by the clouds.
In winter, it is cooler on clear nights and warmer on cloudy nights because the clouds reflect infrared back down to the ground so it is not lost to space.
This is because the clouds reflect infrared in both directions.
Having a white roof is like having a permanent white cloud over your house.
If you live in a cold northerly climate, in the winter, the sunlight is not hitting your roof very much anyway, so more heat would be lost through a dark roof than a white roof, and what you want is a lot of southfacing windows.

As I said above, this is very counterintuitive.