Actually, the current ruling political party (LDP) is the same political party (LDP) whose leaders approved those nuclear power plants in the first place. They've ruled the nation of Japan for most of the past five decades, with only two (very brief) interludes when they didn't control it all. The immediately previous political administration (DPJ) tried to shut down the power stations permanently; then they got pushed out of power by scandals of rather tenuous, oddly convenient timing. The DPJ's leader, Ozawa, was kept out of the political theatre for nearly two years by accusations and investigation of corruption - all of which in court cases were later proven unfounded and spurious. The DPJ went through multiple prime ministers and cabinet ministers, with none lasting more than a few months, each time due to scandals that might not have been based on real evidence. The common public had originally elected the DPJ into power in a landslide result, then despaired over the DPJ's inability to take on the bureaucrats, big corporations, and the USA's bullying antics. So, now we have the LDP back again, with another figurehead "Abe", who does nothing but repeat the same old lies and toady up to the same old lobby groups. He's doing an astounding job of destroying the country's economy regardless of the funny rubbery statistics that they keep producing trying to claim otherwise; Japanese GDP and consumer confidence has plummeted even more so.
Japanese elections are easily rigged, of course. The public apathy about voting - especially the apathy of young people - allows elections to be biased by the simple trick of a minority number being able to swing the votes. Less than 40% of those who are eligible to vote will do so, and so religious groups such as Soka Gakkai which have a political party (New Komeito) use a long term deal with the LDP to bloc-vote and put the LDP into power repeatedly. Not enough young people vote, yet they'll complain about the governments they get. Apathy kills democracy, so the LDP and general political establishment encourage such apathy.