The likes used to show with the newest like on the left, and the oldest on the right.
They now seem to show in a random order.
See:

(I was the second like)
Then the 3rd like:

Right, so that looks like the reverse order, but no…
Users have reported that likes on posts are no longer displayed in the order they were awarded. Instead, they appear in a random order. loopback0 provided screenshots showing this issue, and abarker and ChaosTheEternal confirmed the problem. anon25879736 inquired about progress on the issue, and codinghorror requested that it be added to the list of issues to be fixed. sam has proposed a fix, which can be found in this commit.
The likes used to show with the newest like on the left, and the oldest on the right.
They now seem to show in a random order.
See:

(I was the second like)
Then the 3rd like:

Right, so that looks like the reverse order, but no…
We should maintain ordering and not ship the likers avatar from right to left on reload.
Some oddness is here.
I never actually thought about order here, but any order is better than random!
Any progress on this? Just confirmed today that it is still happening.
Can you add this to your list @eviltrout, I dislike random orders.
This should fix it:
https://github.com/discourse/discourse/commit/bddbf7069728ddc3d8bc6376d872fb693c2a77a5