Is it the threat of not being re-elected that keeps politicians honest?

A lot of academics treat politicians like they treat firms in that it is the treat of re-election that they say keeps politicians from deviating from their constituents' interests.  But there is a problem with that.  Politicians don't have any chance of living forever, and we often know in advance of their last election when an election will be their last.  The problem is that this threat of non-election can't work if everyone knows at what point the politician won't be running for re-election again.  


From the WSJ.com's Political Diary:

The 78-year old Mr. Hatch is a lock to win reelection in November in this heavily Republican state. He will be the longest serving Republican in the Senate and says he will serve one last term.

Other such cases involve term limits.  As I have argued in my past work, such as my book Freedomnomics, the solution is to rely on a politician's preferences.  If you can put into office a politician who values the same thing as his constituents, you can solve the "last period" problem.  If the politician then deviates from his constituents interests, he will lower his own level of utility.  In my book, I apply this point to a lot of examples such as friendships and Supreme Court appointments.