That's where our study comes in. It shows that for at least some populations, asking "is the statute ambiguous?" isn't the same as asking "would ordinary speakers of English agree probably about the meaning of the statute?" Judicial opinions often argue about ambiguity without making clear which of those two questions they mean to be answering. Perhaps judges assume that they really are the same question. But they needn't be. To say a text is "unambiguous" could be a statement that the judge (or whoever is talking) is very sure how best to read the text. Or it could be sort-of empirical claim that most people would agree about what the text means. Sometimes judges seem to argue with each because some of them are coming at the question the first way and others are coming at it the second way. (This is one of the "ambiguities about ambiguity" we refer to in the title of our paper.)
Our study suggests that there is an important difference between these two ways of thinking about ambiguity. The point isn't quite that people sometimes think a text is unambiguous when in fact there is lots of disagreement about its meaning—though of course that's true. The point, rather, is that thinking about those two questions produces different likelihoods that the answers will be entwined with (probably "influenced by") the policy preferences of the reader. Those who consider whether ordinary readers would agree about the meaning of a text—which is a question some judges fuss about more than others—are more likely to be able to give answers that are independent of their own policy judgments. This may not achieve true "neutrality" (which for these purposes might just mean an answer uninfected by policy preferences), but it does better than other questions we have researched.
Of course some might say that they want policy judgments to play a part in interpretation. That's fine, but we still think that most judges like the idea of being able to think separately about questions of ambiguity and meaning on the one hand and about their own policy preferences on the other, even if they go on to weigh those considerations differently when they decide who wins the case. (Another objection is that we didn't experiment with judges; we experimented with law students. Fair enough.)