to arrange for elections, but it also states that the Senate is the judge of the elections and qualifications of senators. The Senate can just go ahead and seat Franken. Coleman can contest the election, but the Minnesota Supreme Court's decision should be enough for the Senate to go ahead. That's my view. The Supreme Court would most likely have to adhere to the intent of the authors of the Constitution and permit the Senate to be the ultimate judge of the election of a senator.
Article I, Section 4 - Elections, Meetings
The Times, Places and Manner of holding Elections for Senators and Representatives, shall be prescribed in each State by the Legislature thereof; but the Congress may at any time by Law make or alter such Regulations, except as to the Place of Chusing Senators.
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Section 5 - Membership, Rules, Journals, Adjournment
Each House shall be the Judge of the Elections, Returns and Qualifications of its own Members, and a Majority of each shall constitute a Quorum to do Business; but a smaller number may adjourn from day to day, and may be authorized to compel the Attendance of absent Members, in such Manner, and under such Penalties as each House may provide.
http://www.usconstitution.net/const.html#A4Sec4I would argue that the Constitution specifically grants the authority to the state of Minnesota to hold the election and then bypasses federal court review to grant the authority to judge the election to the Senate. As I read these provisions, the only branch of the federal government to have jurisdiction to judge the election of a senator would be the Senate.
This is strictly a matter for the state of Minnesota and the Senate.