They have removed it for quite some time now, but I made a script that restores that function back. If you want to give it a try you can find it here: http://openuserjs.org/scripts/ParticleCore/Playlist_Autoplay_Control_for_YouTube
You will need an addon/extension to install it, like Greasemonkey for Firefox or Tampermonkey for Chrome.
I've created an userscript that controls autoplay, if you want to give it a try: http://openuserjs.org/scripts/ParticleCore/Playlist_Autoplay_Control_for_YouTube
A play button should show up in any playlist you watch which will give you control over the playlist autoplay.
One way is to save the watch later playlist as a new playlist and then change the order in that playlist or you can try using my userscript that adds a reverse playlist button to all playlists, this way whenever you want you just have to click on that button while you are watching your playlist and it will play in reverse order.
You will need a userscript manager like Greasemonkey or Tampermonkey and then install my script which can be found here: http://openuserjs.org/scripts/ParticleCore/Reverse_Playlist_Order_for_YouTube
I can help you with the later, if you want to give it a try, but you will need Greasemonkey (if you use Firefox) or Tampermonkey (if you use Chrome) to install it.
After that you can try my userscript which can be found here: http://openuserjs.org/scripts/ParticleCore/Playlist_Autoplay_Control_for_YouTube
Let me know how it went if you try it.
The playlist autoplay option was already removed quite some time ago and replaced with the repeat playlist option.
If you want the autoplay option again you can use the script I created just for that purpose, you can find it here: http://openuserjs.org/scripts/ParticleCore/Playlist_Autoplay_Control_for_YouTube
This is a userscript, which requires an addon/extension to run it such as Tampermonkey for Chrome or Greasemonkey for Firefox.
Simply put: they want to see how many will leave the playlist going and compare to how many won't. If they see that a big number does leave the playlist going then they will most likely make the change permanent since they will assume that most YT users "prefer" not having autoplay.
They are basically trying to find more ways for users to watch ads and forcing playlists has been their recent goal. Last test they did was to force playlist to any video you clicked in a user's channel, which backfired and they have since reverted that feature. They are also testing the Autoplay suggested videos (http://techcrunch.com/2014/12/11/youtube-is-testing-an-autoplay-feature-that-streams-suggested-videos-automatically/) as well which in the begining would not stay off, something that also backfired and they have fixed it eventually.
Also, in case anyone wants, I created autoplay control and reverse playlist userscripts which can be found here:
http://openuserjs.org/scripts/ParticleCore/Playlist_Autoplay_Control_for_YouTube
http://openuserjs.org/scripts/ParticleCore/Reverse_Playlist_Order_for_YouTube
It has come to my attention that the site I was using to host the script, Open User JS, has been offline for at least 24 hours. The Party is investigating if there was any capitalist influence that led to this event.
In any case, I have mirrored the script on Gist, so that the word of our Party may live on.
I don't know if you can change others' playlist order by a specific attribute unless you clone it yourself (basically create a manual copy of someone's playlist instead of saving the original playlist) or via third party software, but I know I can help you reverse the order of any playlist you want.
If no one can help you with what you want and you have any interest in trying my userscript you can find it here: http://openuserjs.org/scripts/ParticleCore/Reverse_Playlist_Order_for_YouTube
You will need a userscript addon/extension to install it though, like Greasemonkey for Firefox or Tampermonkey for Chrome.
You can use my reverse playlist order userscript if you want to give it a try, but you will need Tampermonkey if you are using Chrome or Greasemonkey for Firefox to install it, after that all you need is to get my script which can be found here: http://openuserjs.org/scripts/ParticleCore/Reverse_Playlist_Order_for_YouTube
Let me know how it went.
That playlist button has been changed to Repeat Playlist which is why it only works on the last video of a playlist.
I have created a script that restores the playlist autoplay functionality if you want to try it out: http://openuserjs.org/scripts/ParticleCore/Playlist_Autoplay_Control_for_YouTube