[ismaildonmez]

You should have quoted the sentence just before:

> I agree that blind auditions can make sense—even if they do not have the large effects claimed in that 2000 paper, or indeed even if they have no aggregate relative effects on men and women at all.

so, what the OP said

> Many orchestras switched to blind auditions, and it drastically increased the number of female musicians.

is incorrect because quoting again from the article:

> or indeed even if they have no aggregate relative effects on men and women at all.

[lolinder]

A clause that begins with "even if" is a hypothetical and should not be taken as declarative. The author is saying that they don't know whether the number in question is correct, they're not saying that they believe it to be incorrect. Hence "I’ll reserve judgment".

The bit starting with "even if" is just saying that it doesn't matter to them: either way they're still in favor of blind auditions.