Note: If serialize returns an empty string, make sure the id attributes include an underscore. They must be in the form: "set_number" For example, a 3 element list with id attributes "foo_1", "foo_5", "foo_2" will serialize to "foo[]=1&foo[]=5&foo[]=2". You can use an underscore, equal sign or hyphen to separate the set and number. For example "foo=1", "foo-1", and "foo_1" all serialize to "foo[]=1".
So add a underscore to the id like
<ul id="sort">
<li id="li_1">one</li>
<li id="li_2">two</li>
<li id="li_3">three</li>
<li id="li_4">four</li>
</ul>
Demo: Fiddle