Food Chemistry: How do people determine that an artificial sweetener is X times sweeter than sugar?

They make up solutions and feed them to people. Generally, what they're talking about here is a threshold test: they're looking for the minimum amount that people can distinguish from plain water. For sucrose, that's about 1 part in 200. For acesulfame, it requires only 1 part in 40,000. So they say that acesulfame K is 200 times sweeter than sugar. That's really only one aspect of sweetness. For example, the sweetness comes on and falls off differently for different sweeteners, and you get graphs that look like this: You generally don't notice the difference consciously, but it means that even two sweeteners with comparable sweetnesses at the threshold can produce different sensations. And the detection is not necessarily linear: twice as much sugar may not taste twice as sweet to you, and the same with acesufame K, but it won't necessarily follow the same proportion as sucrose. Still, if you're trying to develop a recipe for a sugarless product, you start with those formulas, then tweak from there. The sugarless product will generally require a lot of other alterations to the formula: addition of bitter blockers, adjusting the ratios of other flavors, reproducing the mouth-feel of the sugar, etc. It requires years of training to acquire the necessary expertise, and the process involve a lot of tasting and adjusting. Eventually, it all comes down to a consumer acceptance panel who tells you whether they like it or not, and the formulas are all completely subordinate to that.