An issue I haven’t seen addressed in any of these discussions is the choice between a large, partially-filled refrigerator and a compact, mostly-filled refrigerator, each containing the same amount of food. Defining efficiency loosely as the ratio of “what you get” to “what it’ll cost you”, unchanged from one fridge to the other in this thought experiment is the numerator (amount of food kept cold), so we only need to consider the energy costs associated with each fridge.
The large fridge would suffer greater exchange of warm air for cold whenever the door is opened, but the second thread linked to above suggests a variation on Uncle Cecil’s proposed remedy: plastic bags filled with air to occupy the empty space. If both fridges are given the same treatment, energy losses from door openings might be rendered insignificant. However, the amount of thermal mass trapped inside each fridge (whether in the food or the air-filled plastic bags) is now slightly different.
Using the numbers from the second thread, if the difference between the two fridges’ air volumes is 100 L, then an extra 0.13 kilojoules needs to be produced by the larger fridge for every 1-degree C rise in temperature. How frequently the temperature rises by 1 degree C depends on door opening habits and other usage patterns, of course, but also on the heat transfer through the walls that occurs constantly despite our best choice of insulating materials.
So how does the ongoing heat transfer depend on the size of the fridge? Some sources apply the square-cube law and conclude that the smaller object spends more energy maintaining its temperature, because of a greater surface-area-to-volume ratio. But in the case of our small fridge, most of that volume has a high specific heat, whereas in the larger fridge the extra volume is mostly air. Therefore the square-cube law can’t be applied blindly, because the relevant property of thermal mass doesn’t scale in the same way that volume does. Instead we might compute the ratio of surface area to thermal mass directly, at which point the energy costs associated with the smaller fridge come out lower. If you want to improve the comparison, the two fridges’ surface areas can be weighted according to the U-factors of the walls.
Although his discussion didn’t consider the fridge size as variable, I’ll give Uncle Cecil the last word.