Top Law Schools

'They' include those top 14 schools, especially for the lower 14.
I checked GULC's website, they say that they might consider the average score if you take LSAT over 3 times.
And Cornell says that they won't take the higher score unless it is 3 points higher than the last one.
UMich says that the average score becomes less useful, though, as the disparity between two scores increases; And they consider a 6 points or higher as a significant disparity.
I know a lot of people on the forum say that a higher score is always better. But does a 1 or 2 points improvement really make a big difference for lower 14?

There's no way to definitively prove it, but admissions results say that any school claiming to ignore scores that aren't enough of a jump up or claiming to average your scores is lying. They only report the high score in their 509s, so they have no motivation to play number games.

As for how much of a difference one or two points makes: it depends. If you're talking about the difference between 169 and 171, it's hugely increased chances at T6 admissions and likely tens of thousands of dollars of scholarship money on the table. If you're talking about the difference between 155 and 157, then not so much.