Mad Men
There are few characters that have displayed overt political philosophies, and a number of them which I assume may be a political. Given their residence in New York, their vote narrows it down. Went with '64, and pointless not to include primaries--though that does mean there'd be an NY primary, and I don't believe there was. 
1960 would be interesting as well.
Don Draper: Didn't vote. Seems to be a political.
Bertram Cooper: Goldwater - Ayn Rand fan!
Roger Sterling: Rockefeller - When he hears about Rocky's divorce, he's pretty upset that all they have left is Goldwater.
Peter Campbell: Rockefeller - Comes from money. Only clue.
Peggy Olson: Goldwater - Only one clue with this one, where she says in Season 4 that she'd like to have worked for the Goldwater campaign.
Paul Kinsey: Johnson - Got all "New Left" on us in Season 2 and went to register African-American voters in Mississippi with his African-American girlfriend.
Betty Draper/Francis: Rockefeller - Indicated a preference for Nixon in 1960, plus by Season 4 she's seeing someone working for Rockefeller. Best guess here.
Henry Francis: Rockefeller - Duh! Works for Governor Rockefeller and later "the Congressman", John Lindsay running for Mayor.
Stan Rizzo: Johnson - He worked for the Johnson campaign, of course.
I should do 1960... Also, apparently the most recent season goes up to '68, so maybe we'll see that.
Peggy had a JFK picture in her apartment. Pretty sure she was a Democrat, she just said that in regard to business.
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