When chopped vegetables are measured by the glass, what is being measured is the space between the pieces, not the vegetables themselves. Coarsely chopped pieces sit at angles in the glass and leave large gaps; the same vegetable, chopped finely, fits noticeably more tightly in the same glass. If a recipe gives a glass measure, it should also specify how coarsely the vegetables are chopped.
The amount of chopped vegetables that fits in a glass depends on more than the vegetables themselves; the air between the pieces also takes up part of the volume. As the pieces get larger, they cross over one another, lean against one another, and leave larger gaps. The same vegetable, chopped finely, settles together and leaves fewer gaps. As a result, the same glass holds noticeably less coarsely chopped vegetables. What is actually being measured in the glass is the way the vegetables are cut.
This is the vegetable equivalent of the principle the corpus shows for salt. The weight of 1 spoon of salt varies with its crystal shape: fine table salt packs tightly in the spoon, while flaky salt leaves a lot of air between the flakes, so the same spoon holds roughly half as much salt. With vegetables, the thing that changes is the knife, not the crystals, but the physics is the same. Diced carrots and julienned carrots do not weigh the same in the same glass, and if a recipe does not distinguish between these two, the measurement is ambiguous from the start. Even a dull knife plays a role, because crushed vegetables release their juices and lose volume.
The difference is even greater with some vegetables because their structure also matters. Leafy vegetables have the most empty space; one glass measure of chopped spinach is reduced by half when pressed lightly. With layered vegetables such as onions and leeks, the layers separate during chopping and increase the volume. Dense vegetables such as potatoes and carrots show the smallest difference because their pieces are solid. That is why there is no single correction factor, and it is not right to look for one.
The best practice is to try three methods in order. First is a scale, which settles the question: when chopped vegetables are weighed, the coarseness of the cut makes no difference because weight is not affected by empty space. Second is counting: if a recipe calls for one medium onion, the amount was determined before chopping, which is more reliable than a glass measure. Third, if you have to use a glass measure, look for the cut size in the recipe; if it does not say, use the medium cut customary in your kitchen. A scale also accounts for any loss during chopping, because it weighs what remains.
The rule is clearer for anyone writing their own recipe. Specify vegetables either by weight in grams or by quantity and size; if you use a glass measure, state the cut in the same line. “One 200 ml measure of finely chopped onion” is a clear measurement; “one 200 ml measure of onion” is not. Give the same care to the order: unless you say whether the amount is measured before or after chopping, the reader faces two different quantities, and both quantities are defensible. A recipe written this way produces the same result in another kitchen.