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As the RailsCast #147 on Sortable Lists is somewhat outdated, I’ve created an own short demo on how to implement dynamically sortable lists in an Rails Application. It can be found here: https://github.com/drblinken/sortable-list-demo - the README contains a list of the steps I’ve taken.
The main part can be found in https://github.com/drblinken/sortable-list-demo/blob/master/app/views/lists/show.html.erb, and all other steps can be seen in the commits.