Suppose you have a thing which you're comparing to another thing. (Whatever they might be. Consumer products, pieces of software, business models, algorithms, I don't care.) Suppose there are a number of criteria on which you might compare the two things, so that there are two ways in which the comparison might be inconclusive: as well as ‘they're both the same’ the answer might be ‘better in some ways, worse in others’.

The thing I keep finding I need a word for is the situation where neither of these is the case: where one of the things is better in at least some ways, and although they might be exactly tied in other ways there is no way in which it is worse. This is the point at which it typically becomes a no-brainer to throw away the other thing and adopt the better one, whereas in any other situation you might hesitate for fear that one of the ways in which the new thing is worse might turn out to be the most important criterion.

I've heard people use – and found myself unconsciously using – a lot of different words for this, but none ever seems quite right. ‘Uniformly superior’ isn't right, because often it's not actually superior in every single way: merely superior in some and equivalent in others. ‘Linearly superior’ is one I've heard a surprising number of times, and it always seems to make sense in context, but when you look at it more carefully there isn't the remotest connection between this concept and any of the usual meanings of ‘linear’. ‘Unconditionally superior’ is one of the better ones, suggesting that its superiority is not conditional on the relative importance to you of the various criteria, but again it has a bit of the ‘uniformly’ problem, in that if one doesn't pay attention it's easy to read it as suggesting that the thing is actually better in all ways.

In mathematics, there is a precise term which means what I want: ‘greater in the product order’. (A product order is one possible way of combining many individually comparable quantities to produce an overall comparison of the lot, and it states that one list of quantities is greater or equal to another list if and only if each individual quantity in the first list is greater or equal than its counterpart in the second. So, ‘greater or equal in the product order’ means that the thing is at least as good on every criterion, and ruling out the ‘or equal’ clause means that there's at least one criterion on which it's actually better.) However, on the rare occasions that I've tried using this phrase for this purpose it has confused even other mathematically trained people.

I'm sure there ought to be a sensible and widely understood phrase for this concept, because I find myself needing to use it so often.