The Top Level of Government

​The recent turmoil in the process of selecting a replacement for John Boehner as Speaker of the House of Representatives drove home to me the chaos at the top level of our government. In the end, a competent man, Paul Ryan, was selected, which is fortunate since the Speaker of the House is third in the line of succession to the presidency. There were other possibilities that were pretty frightening. I started thinking there must be a better way to do this.
Here is the idea I came up with:

1. The top three positions in the government should all be elected through nationwide elections. The three positions would stand separately. In other words, no party ticket.
2. The president’s role would not change except that candidates would run without a running mate.
3. The President of the Senate (currently the vice president) would be elected separate from the president and would be first in line for succession.  The President of the Senate would preside over senate business, but would not vote on legislation (under any circumstances). To insure against tie votes, the District of Columbia would get one senator.
4. The Speaker of the House would also be elected nationally and would be second in line for succession. The role of the speaker would be essentially the same as the role of the President of the Senate. DC would get two representatives.

What do you think?