Original:  The conversations suggest that RAI (Italian state television) and private rival Mediaset ( owned by Silvio Berlusconi ) made arrangements to favour Berlusconi himself when he was Prime Minister of Italy.
Revised:  The conversations suggest that RAI (Italian state television) and private rival Mediaset , which is owned by Silvio Berlusconi ) made arrangements to favour Berlusconi himself when he was Prime Minister of Italy.
Edit intent: coherence