In RambaM's Hilkhot Melakhim u'Milhamot chapter 6, we read (halakhah 2): ולא יתמנו על ישראל, לשום דבר בעולם "They [viz. gentiles] may never be appointed over a Jew, regardless of the position."
Apparently, then, non-Jews may not hold any position of authority at all. But 1:4 and 1:5 respectively forbid converts and women to be kings of Israel, and yet we know that if the people accept their rule, this law does not apply; as Rabbi Benzion Uziel shows (in his teshuva on women's suffrage, here, the prohibition for a convert or women to be king applies only when the beit din must undemocratically select a king itself, but when the people themselves choose, they may choose whomsoever they desire. According to Rabbi Uziel, the people's democratic choice obviates any prohibition for women and converts to wield serarah (authority). Apparently, there is nothing wrong with a woman or convert, but since Judaism is fundamentally democratic in its essence, a woman or convert cannot rule if this is unacceptable to the people. If the people are sexist or racist, then this is unjust and unfair, but nevertheless, if the people, due to their unlawful and unjust sexism and racism, choose to reject the woman or convert as ruler, then democratic Judaism cannot but forbid the woman's or the convert's appointment. But if the people freely choose the women or convert, then there is no problem, ipso facto. The people's very choosing the convert or the woman is itself a sign that the woman's or the convert's rulership is permissible according to the Torah.
The question is, does this ability of the people apply even regarding the prohibition for a non-Jew? Somehow, I suspect not. With a non-Jew, the fear is presumably that his entire outlook and direction and intent will not be in keeping with Torah Judaism, and that his rule will be simply totally improper. For this reason, the Torah explicitly mandates that a king of Israel must be Jewish, whereas there is no express prohibition for a convert or woman to a king. Furthermore, there is an explicit Gemara showing that the people's acceptance of Aggripas as king (saying "You are our brother, you are our brother!") was of no avail, and that he was nevertheless an improper king. On the other hand, Hazal seem to have liked Queen Shlomtzion just fine. We see from history itself that Hazal approved of female Jewish queens but not of non-Jewish male kings.
Nevertheless, it appears to me personally that as long as the ruler is ruling according to a contract, covenant, or constitution written by the corporate Jewish people (`am yisrael), that this itself is a form of subservience to Jews. The government is by the people and for the people, and its officers are servants of the of the people, and thus, government workers are called "public servants". Any Arab - or Jew, for that matter - who holds office in the Knesset or the like is halakhically a slave, an עבד, as long as the constitution is suitably Jewish in character, or at least specifies that the Jewish people is sovereign even if it fails to specify that Judaism as such also is.
Therefore, even according to a Kahanist adherence to the pesaq of RambaM that a non-Jew may not wield serarah (authority) over Jews in Israel, even according to this notion, one may circumvent it by having an explicitly Jewish constitution that, as per authentic federal democracy, stipulates that the country is Jewish and that the government exists only for the good of the people. By this manner, the government's officials and employees would all be public servants, contractually obligated ("social contract") and responsible and accountable to the people and to Judaism, subservient alike to the people and to either the corporate Jewish people (`am yisrael) and/or to Judaism (however that constitution chooses to define something as nebulous and hotly debated as "Judaism"), and so halakhically, any Arab - or Jewish - members of the government would not be wielding serarah (authority), for they would be nothing more than proxies, shelihim, chosen to execute those powers and only those powers granted the government by the people, which the people may enlarge or diminish as they freely choose, the people being the rulers of the land with the government merely the people's proxy by contract. ("Federal" means "covenant" and "democracy" means "rule of the people", and thus, a federal democracy is any government in which the people rule by making a covenant with the government, i.e. electing it their proxy via a contract. In Biblical Israel and in Calvinist societies like Puritan America, for example, the Torah was the constitution which the king or government ruled by, and he or it had no powers save those which the Torah granted him, and he had no power to pass any laws except that somehow served to do nothing more than to enshrine in civil law that which the Torah already mandated anyway. Biblical Israel and Puritan America were - at least, when they lived up to their ideals - were perfect exemplars of constitutional (federal) government.) Thus, even according to RambaM's pesaq forbidding a non-Jew to wield serarah (authority) over Jews in Israel, even according to this pesaq, nothing would be violating halakhah even were Arabs to wield power. Legally and halakhically, the government would be the subordinate to the people - as indeed authentic federal democracy declares - and so even RambaM and Kahanism would be satisfied.
Conversely, however, if one holds by undemocratic absolutist statism in Israel, in which the government has absolute and unlimited undemocratic authority which the people are obligated to obey without right of dispute or disobedience or dissent - this philosophy being held by Israel leftists (Labor, Kadima, etc.) as well as many left-wing Religious-Zionists (such as the sort who opposed the Gaza Expulsion and yet nevertheless counseled soldiers to obey their illegal orders) - according to this undemocratic absolutist philosophy, any government official is a lord, an אדון, with free reign to trample the people without limitation or compunction, and according to this, it would still be prohibited for an Arab to wield authority, as per the plain sense of the RambaM. My proposal only works if the government is liberal and libertarian, if the government is contractually-bound and accountable to the people and subservient to them, as per authentic liberal federal democracy, in which the government is subordinate to the people. But where there is an illiberal statist government, such as in Israel, where democracy is scoffed at and flouted, in such a place, the plain sense of the RambaM stands as it is.
As an aside, Tzipi Hotovely has an interesting suggestion, viz. to grant all Arabs citizenship. She has not yet explained why she advocates such, but as I understand her proposal, based on my own personal thought, her suggestion is this: Making the Arabs into Israeli citizens will allow Israel to use its police and intelligence forces to prosecute terrorist Arabs while neglecting to harm or infringe on peaceful Arabs. If the Arabs are foreigners, then Israel has no choice but to invade with the IDF and unfortunately kill innocents unintentionally. But if the Arabs are made citizens, then Israel can discriminate and precisely target only those specific and peculiar offenders of the law, while keeping the law-abiding and peaceful Arabs safe from any harm.
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