Is there a difference between "less ambiguous" and "more unambiguous"?

Solution 1:

Less ambiguous is easier to understand because ambiguity can vary. By saying 'more unambiguous', the speaker or writer is saying that the sentence is not ambiguous but it could still use improvement. It could be that the speaker or writer is a polite person, and didn't want to suggest that your sentence had ambiguity.

UPDATE: Maybe the British English speakers are more polite! LINK

In actual usage 'more unambiguous' shows up 10% as often as 'less ambiguous' (warning: N-gram link), and it's pretty constant usage since 1950.

Despite the absolute nature of unambiguous, common usage doesn't strictly follow that definition. If one thing can be less ambiguous than another, then another thing can be more unambiguous than another.

In case you are curious, more unambiguous is most commonly followed by 'than' (link), and 'more unambiguous than' is most often followed by 'the' (link).

Solution 2:

Unambiguous is an absolute state. Hence, you can't be more unambiguous.

Whether or not you can be less ambiguous is difficult to say. Ambiguity may or may not be an absolute state. For example, if the majority of a text is unambiguous but one point is ambiguous (such as my answer here!) does it make the whole text ambiguous? Or, is it slightly ambiguous? It seems more natural to be slightly ambiguous than say slightly unambiguous, though.

As the two expressions are commonly used, they are equivalent, though.

There are plenty of examples of this type of incorrect usage in English that have become completely acceptable.

Consider the words right and wrong. Technically you are either right or wrong. They are both absolute states. Regardless of how many points you are wrong about, you are still wrong.

But, we all accept terms like more wrong and more right because they are intellectual expediences that allow for nuances to be explained more easily.

Great example from The Big Bang Theory:

It's a little wrong to call a tomato a vegetable. It's very wrong to call it a suspension bridge.

Update I've spent quite a few hours thinking this over, and I think I have a better answer:

When we describe absolute states yet use a modifier in front of them, we are actually just employing a linguistic shorthand.

When we say less ambiguous or more unambiguous we mean:

Contains less ambiguous content than ...
Contains more unambiguous content than ...

In both cases it is the content that is being modified and not the ambiguity itself.

As neither of those rolls of the tongue (or pen, or keyboard), we say less ambiguous, etc.

Solution 3:

The difference is immense:
Less ambiguous is negative: your text was ambiguous, which is bad, and after the the change it will be less bad.
More unambiguous is a compliment: your text already was unambiguous and the change will make it even better.

This is a general phenomenon which I, as a mathematician, find quite amusing: logically equivalent sentences are perceived as quite different emotionally according to the formulation used.

You don't believe me? Tell your friend the boxer that he is more intelligent than your neighbour and then that he is less stupid (which is logically equivalent) than his cousin and see (feel?) his different reactions...

Remark
It is true that unambiguous is essentially absolute (in which case the phrase more unambiguous doesn't make sense) but for the sake of argument one could claim that the answer I don't think so to the statement "2+2=5" is unambiguous but that the answer No! is more unambiguous.