Interesting historical footnote in this Slate Explainer.
Can Rod Blagojevich still appoint a replacement senator?
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Even if Blagojevich makes his pick before any state-level action can be taken, the buck stops with the U.S. Constitution, which states: “Each House shall be the judge of the elections, returns and qualifications of its own members.” That leaves the final say up to the discretion of the U.S. Senate in Washington. There have been five cases in which the Senate has refused to recognize an appointee (although all but one occurred before the 17th Amendment and the direct election of senators). In 1912, the Senate concluded that a 33-year-old businessman named William Lorimer had obtained his seat (three years earlier) through bribery and corruption. The would-be lawmaker hailed from the great state of Illinois.