In the electoral college, members vote for a president and vice president in order to get both positions. Could they just vote for the same man twice for president (thus giving up the vice presidency chances) and double their chances of getting a president in office?
That isn't quite how the system works. You seem to be confusing and combining the current electoral system with the old one.
As originally conceived by the Framers, each elector only cast one vote. The candidate with a majority of the votes would become President, while the candidate with the second-most votes became Vice President. This system became unworkable with the formation of political parties, as the runner-up would typically be from another party. The real impetus for change was in the 1800 election, in which the Democratic-Republicans won enough electors to secure the presidency AND the vice presidency. However, the electors didn't properly work out who would vote for who, and Thomas Jefferson and Aaron Burr recieved the same number of votes, throwing the election to the House of Representatives.
Under the 12th Amendment to the Constitution, electors now cast two ballots for president and vice president, but the ballots specifically designate what post they're voting for:
The Electors shall meet in their respective states, and vote by ballot for President and Vice-President, one of whom, at least, shall not be an inhabitant of the same state with themselves; they shall name in their ballots the person voted for as President, and in distinct ballots the person voted for as Vice-President, and they shall make distinct lists of all persons voted for as President, and all persons voted for as Vice-President and of the number of votes for each, which lists they shall sign and certify, and transmit sealed to the seat of the government of the United States, directed to the President of the Senate.
So it is possible for an elector vote for a presidential candidate twice. But the second vote would be for vice president.