So why can Paul Ryan run in two elections at the same time? Well, it goes back to LBJ!
In 1959, fresh off a string of Democratic victories in the 1958 midterms, then-Senate majority leader Johnson was eyeing the presidency in 1960. But he was also up for re-election in the Senate and, for obvious reasons, did not wish to relinquish his seat. Texas law forbid a candidate from appearing twice on the ballot -- which was supremely ironic, considering that Texas Democrat and Speaker of the House John Nance Garner ran as FDR's running mate in 1932 while conducting a simultaneous campaign for his House seat (Garner got off on a technicality -- prior to 1945, ballots in Texas listed the names of the parties fielding presidential tickets, not the names of the candidates themselves). Johnson, using his numerous allies in the Texas statehouse, persuaded the state legislature to change the law in order to allow for his name to appear on the presidential ticket and the Senate simultaneously.
When Johnson got the consolation prize of the vice-presidency in 1960, the so-called "LBJ Law" allowed him to thrash Republican challenger John Tower (who campaigned on the cheeky slogan "Double your pleasure, double your fun -- vote against Johnson two times, not one"). Subsequently, many states -- including Wisconsin -- then passed their own LBJ laws allowing for exceptions for presidential candidates. (Still other states, like Pennsylvania, allow for a candidate to for two state offices simultaneously). Lloyd Bentsen, himself a Democratic senator from Texas, took advantage of the law in 1976 and 1988, as did Joe Lieberman with a similar Connecticut law in 2000 and Joe Biden with Delaware's LBJ law in 2008.