I think your hearts in the right place, but the logistics of your plan won't work. There is an existing method used in a variety of places called
Instant Runoff Voting that allows people to vote, and ensures that a candidate has majority of votes. In a nutshell, you vote by ranking the candidates 1st, 2nd, 3rd, etc in order of preference. Then all the 1st place votes are tallied. If one candidate has a majority vote (50%+1) it ends there, and that candidate is declared the winner. If no candidate recieves a majority, the candidate with the fewest number of first place votes is eliminated, and the seocnd place candiate on those ballots is moved to first place. Votes are then recounted, and when majority is reached, the winner is declared.
Here's an example with 4 candidates and 100 voters:
The first round votes are:
Anne - 45
Bob - 45
Carol - 7
David - 3.
No one has a majority, so David is eliminated and those who voted for him have their 2nd choice candidate counted in the next round. All three have Anne as their 2nd choice, so the votes in round 2 are:
Anne - 48
Bob - 45
David - 7
Still no majority, so the 7 David voters move to their second candidate. 6 vote for Bob, and 1 votes for Anne. The third round votes are now:
Anne - 48
Bob - 52
Bob has the majority of votes, and is declared the winner.