The basic sources on right of succession to public office are Rambam, Hilchos Melachim 1:7, and Rema, Yoreh Deah 245:22. For additional references, including citations from the Israeli courts, see the article on "Public Authority" in the Encyclopedia Judaica, vol.13, cols. 1355-6. But a son who isn't qualified doesn't automatically succeed his father.
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