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That still doesn't give us a reason why customers have this special calculated value. You could just multiply the volume by this percentage to get the absolute value. Why is the percentage preferred over the volume? I see no reason for either side.
Like I said, because the percent doesn't change with the volume served. If you are an 1800s brewer you can calculate the ABV from samples, and subsequently sell kegs of various sizes, bottles, which in turn can be served in various amounts and the percent doesn't change. And the industry never changed, nor the laws written. So it's the way it is because that is how they used to do it and how laws were written and there hadn't been a motivation for people to change that.
In a word - tradition.
Yup.
We do lots of things as a society because we've always done them that way, or it's good enough, and not enough reason to go through the effort of changing everything including legal language, etc.
Happily, in this case I think ABV is about the best way we could have inherited, maybe only second to alcohol by weight in terms of consistency across temperature.
Also, it's practical. If you know something is twice as concentrated (12% instead of 6%) you know to drink it more carefully, rather than if you get a jug of something and it just says how much alcohol is in there, then you have to mentally calibrate how strong it is by considering the volume of the jug vs. how much alcohol there is.
You have to print a separate label for each bottle size then. Much easier to print something like '10% strength' and slap the same label on all of your barrels and bottles regardless of their volume.
You still have to show total volume on each bottle. So the label is different anyway. Plus, it could have been done as they do to show singer content - amount per serving size and servings per container.
Present age does nearly the same thing though. 20% simply means 20ml in serving size of 100ml.