The elections held Tuesday in Beit Shemesh and Nazareth prove an important victory for the rule of law over its political offenders. The High Court of Justice ordered the new elections, contrary to interest groups who thought the results of October's municipal elections would stand despite the uproar. But the judges listened carefully and ruled differently. Whether the fradulent votes cast in the previous election cycle cover the difference between winners and losers has no significance. If the difference in Beit Shemesh was 900 votes and 100 impostors were discovered, then that is a worthy reason to reopen the voting booths. Because it would be reasonable to say the police did not discover all voting irregularities. The question is not how many votes were fraudulent, but what the method was. There was great concern in Beit Shemesh that the fraud was systemic, rather than a private scheme by individuals. This doesn't mean that incumbent mayor Moshe Abutbul knew about these acts, but in hindsight, he benefited from them. So it is appropriate for the mayor to subject himself to the test of the public once again- The wholesale filling of ballot boxes with fraudulent votes or removing legitimate voters should interest the Interior Ministry for the future. Former minister Ophir Pines-Paz drew Interior Minister Gideon Sa'ar's attention this weekend, to the widespread failure to count soldiers' votes in a number of communities. This is part of the failure of the system that needs repair. The battle in Beit Shemesh is significant to the image of the State of Israel. No one is trying to bar the ultra-Orthodox community from settling in the ever-expanding city, yet it is very worrying that community leaders are not getting rid of posters and signs excluding women from street and markets -- in contrast to the court's direct orders. The two camps are large and expanding. The Zionist parties, both secular and religious, support Eli Cohen, while Abutbul sees support from the ultra-Orthodox community and Shas party followers, and it seems this time they convinced the extremists not to boycott the election but come to the voting booths for the first time in their lives. That is also a welcome change. In think that for the sake of Israel's enlightened image it is better if Cohen wins the mayoral election. It is possible that his opponent Abutbul is also worthy, but his large base of supporters favor laws and norms that are not accepted by Israeli society as a whole. The same goes for Nazareth. Choosing Ali Salem is preferable to voting for Ramiz Jaraisy. The results of the previous elections hung on one vote, and the decision now rests on the efforts of both candidates to bring their supporters to the voting booths. However, even if Abutbul and Jaraisy win the elections, Israeli democracy benefits when the rule of law proves to party officials that the mantra "the strength of power wins" is not suitable in a modern state.