Under the Constitution,  the candidate with the most electoral votes became President, and the runner-up became Vice President.   This is why the Vice-President has almost no power under the

Constitution. - he was the one who ran against the President.  At the death of the President, the Vice-President (the next-best candidate) would become president (not some unknown as in the case of  Johnson, Truman,  Ford, etc.

           In 1804, the 12th amendment to the constitution changed the electoral process of choosing Presidents and Vice Presidents.   After 1804, Presidents and Vice Presidents ran as a "ticket". The problem is that when the President dies or resigns the next man in line is usually someone the people never would have voted for. 

 

THE SOLUTION

  Let us return to the original system of selecting the vice-president. Let him be the runner-up - the one next in line in the minds of the voters..  To some extent, this would limit the power of Party Politics ( which is just another phrase for legalized corruption)