I am not familiar with the rabbinic group named "Chotem". and a brief online search only found a few other publicized halachic decisions but nothing about the organization itself. They recently issued a psak halacha about the Bet Shemesh elections.

Before mentioning the psak, I find the very nature of the psak being decided and publicized to be interesting on its own. This is a situation in which one might ask - who would listen to such a psak? The case is in the hands of the police and the courts. It is in nobody else's hands to decide, so for whom is the psak being issued? As well, with the matter being handled by the police and the courts, I would presume that much of the information discovered is kept out of the public eye - if that is true, they are issuing a psak for a situation in which there is no way they can possibly have all the information.

With that introduction, here is the psak.

According to NRG, the psak issued is that even if there was some fraud, and there was some fraud in some ballot boxes, new elections should not be held. If a certain ballot box was tainted, that ballot box alone should be invalidated. Even if someone thinks there is a beneficial purpose to overturning the elections, it should not be done. However, if the election board decides to invalidate the entire election, than it too has halachic standing.

Rav Brali's, on behalf of Chotem, main point seems to be that there is a strong necessity for participating in elections and being involved in the election of leaders in israel, and a persons sole concern should be for the good of the public. Every person should have his or her say in the matter and then go after the majority decision. This is true, he says, for leaders, for chazzan, for gabbai, for tzedaka officials, etc.

Regarding the fraud, the election board must check the level of fraud and determine how much it influenced the overall election, and their decision will have halachic standing.

The psak seems to be more focused on the mitzva of participating in elections for leaders and respecting the decision of the majority, and less focused on what did or did not happen in Bet Shemesh elections and what should be done. And, as mentioned above, I am not quite sure who is supposed to do what with this psak.