Given the current state of the country in which a President can be elected without winning the popular vote, I would change the U.S. Constitution to abolish the electoral college. States would no longer get a set number of electoral votes, and each person's votes would be directly applied toward a candidate. This would better reflect the will of the country in a democratic society as it would be more democratic than the current system.
I would also add an amendment to strictly regulate the drawing of Congressional districts so that they could not be drawn to the advantage of whatever party happens to be in power. I would insist on a bipartisan commission to devise districts based on strict guidelines that would, say, mandate that districts be drawn as close to geographic squares as possible, not wiggling here, there, and everywhere to suit the party in power. This would more fully allow the will of the people in this country to be accurately reflected in their representatives. For example, Austin, Texas, a liberal enclave in a conservative state, has been chopped into a a series of "flower petals" that extend into more conservative suburbs, where the suburban voters swamp the urban voters, making it nearly impossible for Austin residents to elect a congressperson who reflects their political positions.
Another amendment would mandate that all party primaries be open to all voters, regardless of party affiliation.
Finally, the Constitution must mandate that all elections be publicly financed.
These changes, seemingly small, I believe would have a profound effect on our society. Right now our national politics are highly, and some would say dangerously, polarized because parties and politicians know they only have to earn the vote of a certain portion of the population to be elected. Often the rewards go to those who take extreme positions popular only to a minority of voters who decide which candidate wins the primary. In a gerrymandered system, that candidate is often virtually guaranteed the seat in the general election, meaning that an individual not at all representative of the will of the people is helping to create the legislation that influences their lives. In a system in which one person or small group of people can write million dollar checks to a candidate, that kind of money forces candidates to attend to the will of a very small group rather than the larger public they are sworn to serve.
A more fair and democratic electoral system would force politicians to attend to the will of all the people, not just small segments in "swing states" who decide elections or decide who wins a primary. Politicians would have no reason to allow the very wealthy a disproportionate influence on policy. (The wealthy would still have ways to "buy in," but the government would no longer be for sale to the highest bidder.) This would force parties from extreme positions to a more centrist point of view and encourage the kind of compromises that have been largely missing in recent governance, allowing us to move forward with repairing the country in ways that reflect the will of the governed.