simont | A thing I keep feeling there ought to be a word for

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.

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I'd probably say "better in several ways and in no ways worse" or just "in no ways worse" if its betterness has already been established in the current context.

Pareto superior seems about right.

So it does, after a quick check with the Big W. Shame it isn't widely understood enough for my needs, though; I for one would have had to look it up if anyone had used it to me!

Use it, explain it as necessary?

If people want concise terminology, they have to learn it. If they only want to use simple terms, they're going to have to put up with more verbose chains of them to explain anything accurately.

And between that and "in the product order" you've covered _several_ classes of people :)

Existentially superior semi-definite? Or not.

I would probably say "at worst, no worse than" but that is quite clumsy.

I like "pareto superior" as a phrase and will try to popularise it! If we all do the same, it might catch on...

"at least as good as"

That doesn't rule out the possibility that it might be only as good, which makes it sound less compelling as an argument for throwing away what you were previously using. I do need to emphasise that it's actually better in at least one aspect.

Indeed, although I would point out that's _normally_ clear from context.

Seconded. If you want to be explicit about the fact that you're covering multiple criteria, you want "at least as good as X in all ways / all areas"

I heard somebody using "strictly better than" recently for this purpose.

That's rather good. No implication of perfection, but definite information that it's the thing you want.

That's the exact phrase I was about to suggest.

So was I. I most often use it in board games, e.g. if some card/building/etc will let you do A and B and another will let you do A, B and C. The post seemed to be describing the phrase perfectly.

Simon: And in particular in Magic: The Gathering, where it comes up a lot. Because printing card A strictly better than card B makes card B not much use, and annoys people, but making it better in _almost_ every way is ok.

Also because the dividing line is often interestingly contentious: eg. a creature card is normally strictly worse than the same creature card with the flying ability. However, if the metagame has many people playings card that damage flying creatures but not non-flying creatures, you may sometimes prefer the other card.

I'm not quite sure how to parse "strictly better", but I think it is both clear, accurate and unambiguous (if you assume you can compare each aspect of the things).

I was expecting to be able to apply notions of orderings, specifically that if the object is better in some ways and worse in others, then as a whole they're incomparable (unless you define specific weightings), giving a description like "comparable and better". But that doesn't sound very good, and is likely to be misunderstood, even where people might understand that you meant "incomparable" in that sense.

Roughly comparable and mostly better is wordy but effective. Other adverbs may improve it; but the adjective 'comparable' has exactly the ambiguity you seem to need.

'Dominates' means exactly this in game theory.

(Er, I have just somehow discovered your very entertaining lj and been reading back entries this far. Hmm, I think it's time for bed now)

A thing I keep feeling there ought to be a word for

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