The elements of the rule of law include “no one is above the law”, “everyone is equal before the law”, “judicial independence” and “protection of human rights”.
The elements of the rule of law include “no one above the law”, “everyone equal before the law”, “judicial independence” and “protection of human rights”.
In each example, as the elements in the list are quoted, they need not be independent clauses. In fact, the 3rd and 4th elements are not independent clauses.
The 2 examples are hence similar and fine except for a missing comma before the coordinating conjunction.
Following rjpond's comments on quotation signs, I amended the affected paragraph and the final one. I retain the comma placement concept used in the original examples.)
On quotation signs and comma placement, starting off with double quotes does not mean it must be the American system. In this context, the commas need not be placed within quotes.
Jeko suggested using a colon to start the list. To do that, an independent clause is needed before the colon. I suggest an additional 'these'.
For the colon option, my suggestion is as follows:
The elements of the rule of law include these: "No one is above the law", "Everyone is equal before the law", "Judicial independence", and "Protection of human rights".