Would not it be nice if we could add LinkedIn between social networks to share links Askubuntu? Especially focus on the labor side that this network continues to provide.
The LinkedIn button was removed when StackExchange added the Google+ share button.
As Jeff answered here those links were experimental. The LinkedIn one simply wasn't being used, not to nearly the volume of the others...so we removed the extra clutter from the UI.
It will likely be replaced with Google+, given they ever provide an officially supported link-only way to share.