I remember a story where public offices were filled not by candidates running, but by selection, similar to jury duty. Does this ring any bells?
There is a short story by Asimov, called "Franchise".
But it's the voter, not the candidates, that is drafted. Since computers have become better at predicting the outcome of elections, only a single voter is drafted.
The man presented credentials, stepped into the house, closed the door behind him and said ritualistically, "Mr. Norman Muller, it is necessary for me to inform you on the behalf of the President of the United States that you have been chosen to represent the American electorate on Tuesday, November 4, 2008."
He is then interviewed by the computer, MultiVac, about all kinds of seemingly unrelated issues.
"Now let me explain, Mr. Muller," Paulson went on. "Multivac already has most of the information it needs to decide all the elections, national, state and local. It needs only to check certain imponderable attitudes of mind and it will use you for that. We can't predict what questions it will ask, but they may not make much sense to you, or even to us. It may ask you how you feel about garbage disposal in your town; whether you favor central incinerators. It might ask you whether you have a doctor of your own or whether you make use of National Medicine, Inc. Do you understand?"
From this, the computer decides the outcome of the election.
In this imperfect world, the sovereign citizens of the first and greatest Electronic Democracy had, through Norman Muller (through him!) exercised once again its free, untrammeled franchise.
Perhaps the novel version of Clarke's The Songs of Distant Earth? My recollection is that public officials were chosen at random; as long as they weren't criminals or insane, they were compelled to serve a term in whatever job they had been selected for.