Argument 2 is correct. There are lots of ways to show this, since it has a numeric conclusion, and there are lots of correct ways to arrive at that number.
Where precisely does Argument 1 fail?
Argument 1 says “which is just the same state of knowledge...” but it is flat-out lying. One direction is fine: if you answer “yes, yes” to Scenario 3, then you would answer “yes” in Scenario 1. But if you would answer “yes” to Scenario 1, then you would not answer “yes, yes” to Scenario 3. This is not the same state of knowledge so we cannot conclude the answer is the same.
(Or different, for that matter, just from knowing the knowledge is different—maybe the knowledge differences are only in irrelevant details by some happy coincidence. Like the differences between Scenario 3 and Scenario 2.)
Argument 2 is correct. There are lots of ways to show this, since it has a numeric conclusion, and there are lots of correct ways to arrive at that number.
Where precisely does Argument 1 fail?
Argument 1 says “which is just the same state of knowledge...” but it is flat-out lying. One direction is fine: if you answer “yes, yes” to Scenario 3, then you would answer “yes” in Scenario 1. But if you would answer “yes” to Scenario 1, then you would not answer “yes, yes” to Scenario 3. This is not the same state of knowledge so we cannot conclude the answer is the same.
(Or different, for that matter, just from knowing the knowledge is different—maybe the knowledge differences are only in irrelevant details by some happy coincidence. Like the differences between Scenario 3 and Scenario 2.)