Ideally, because they are supposed to represent all the people in the country and not the states, the President and Vice President should be elected by the entire country using direct election by popular vote. That's not going to happen anytime soon because the smaller states have too much clout in the current Electoral College setup to vote in favor of repealing it and replacing it with direct election.
So, instead, lets fix the Electoral College AND Gerrymandering
Here's an idea on how to at least partially fix the Electoral College (to help insure that the person who does win the popular vote does indeed also win the EC). And to make things better, I'll propose a second idea on how to fix gerrymandering.
(BTW, there's another proposal to fix the Electoral College problem without a constitutional amendment. It's called the National Popular Vote (https://www.nationalpopularvote.com/) and it requires states to pledge all their electoral votes to the candidate who wins the national popular vote. Great idea.)
SIZE OF THE HOUSE OF REPRESENTATIVES
First, the idea for the Electoral College. First of all, forget about ever amending the Constitution to eliminate the Electoral College and going for the direct election of the President. A Constitutional amendment needs a 2/3 majority in both houses of Congress, AND 3/4 of the states must approve of it. The smaller population states, particularly in the West, will NEVER go along with eliminating the EC. Along with the Senate, it's the thing that gives them clout far beyond what you'd expect from their population. Just forget about it.
Instead, what we need to do is to INCREASE THE SIZE OF THE HOUSE OF REPRESENTATIVES. The number of representatives in the House is NOT mandated by the Constitution, except to say in Section 2 of the 14th Amendment:
"Representatives shall be apportioned among the several States according to their respective numbers, counting the whole number of persons in each State, excluding Indians not taxed."
and in Article 1, Section 2, clause 3:
"The Number of Representatives shall not exceed one for every thirty Thousand, but each State shall have at least one Representative..."
The Permanent Apportionment Act of 1929 (https://en.wikipedia.org/wiki/Reapportionment_Act_of_1929) clarified when and how the size of the House of Representatives will be set. It set the number of representatives at 435 (which is where it had been since after the 1913 reapportionment as a result of the 1910 Census). (See also, Kromkowski & Kromkowski, "Why 435? A Question of Political Arithmetic", Polity, vol. 24, #1, Fall, 1991. http://www.thirty-thousand.org/documents/Kromkowski_Fall1991.pdf)
So it's been OVER 100 years since the size of the House of Representatives has changed. (https://en.wikipedia.org/wiki/United_States_congressional_apportionment)
This has lead to some anomolies in how many people are represented by a single representative in each of the states. Wyoming, with the smallest state population of just over 585,000 gets a single representative. Montana, with just over 1 million people, also gets just one representative. The most populous state, California, with nearly 36 million people, has 53 representatives, or one for about every 742,000 people. So the number of people each representative actually represents varies wildly across state boundaries.
If we increase the number of members of the House, then these anomolies can be evened out. This has been tried before (see Clemons vs Department of Commerce, 2009, https://en.wikipedia.org/wiki/Clemons_v._Department_of_Commerce), but not by trying an act of Congress.
If Congress enacts the so-called Wyoming rule (https://en.wikipedia.org/wiki/Wyoming_Rule) whereby each representative will represent a population roughly equal to the population of the smallest state, then the number of representatives will be increased from 435 to 537. California, Texas, and Florida will see the largest increases in representation (12, 10, and 7 seats respectively). Wyoming will still have a single representative.
This reapportionment will have the effect of giving voters in urban areas the clout that they do not have under the current numbers. It will also increase the number of Electoral votes to 637, with 319 needed to win the presidency.
(Another way to do this is to fix the number of people that a representative must represent, say at 600,000. Depending on how you count the remainders of state populations after you divide by 600,000 you'll get either 527 members of the House (if you use the floor function) or 576 (if you use the ceiling function). The effect will be the same as the current idea.)
GERRYMANDERING
Second, fixing gerrymandering (https://en.wikipedia.org/wiki/Gerrymandering and https://en.wikipedia.org/wiki/Gerrymandering_in_the_United_States). Gerrymandering occurs because in nearly all the states, the party that holds the majority of seats in the state legislature is the party that draws the boundaries for re-districting Congressional districts after each decennial census. This practice has gotten worse and worse over the decades, to the point where in several states, Wisconsin, Maryland, North Carolina, and Pennsylvania being the worst examples, the party that wins the majority of votes in the general election wins less than one-third of the seats in the legislature or in Congress. Here's a way to fix that.
Proposal: After each census, each state creates a committee with an equal number of Republicans and Democrats (sorry independents, you're out of luck here; if you want to play, declare a party affiliation; or how about a party gets to play if it polls more than 25% of the vote in the last general election?). If this is a state that only gets one Congressional representative, then we're done. For all other states, the party that won the most votes in the last general election goes first. That party draws one (1) Congressional district. Naturally, they'll draw one that favors their party. Then the other party gets a turn and they also draw one (1) Congressional district. The parties then alternate until all the districts for that state are drawn. All districts must be of approximately the same population (if the Wyoming rule is being used, then that population is the size of the smallest U.S. state) and they must be compact and contiguous - no snakes, or anchors, etc. The chief justice of the state's supreme court is the arbiter of whether the district is compact. It's likely that the last district will have either more or less population than the smallest state. There can be simple rules that will take care of this case.
In the end, there will be some safe Democratic districts and some safe Republican districts, but because of the alternation, there should be a number of competitive districts as well, almost certainly more competitive districts than there are today. Because these districts will be in place for at least a decade, it will be to both party's advantage to try to create a large number of closely divided districts.
With these two rules in place, the House of Representatives will more closely represent the majority of voters in their respective states and overall the majority of voters in the country. The Electoral College will also more closely represent the will of the majority of voters in a state; and in particular, the larger states will not have their votes in the Electoral College diluted by smaller states.
For other proposals to eliminate gerrymandering see
https://en.wikipedia.org/wiki/Open_Our_Democracy_Act
https://en.wikipedia.org/wiki/Gerrymandering#Changes_to_achieve_competitive_elections
http://www.rangevoting.org/
https://www.nytimes.com/2017/08/29/magazine/the-new-front-in-the-gerrymandering-wars-democracy-vs-math.html?mcubz=3
See also this article that illustrates how hard this will be to change:
https://www.nytimes.com/1992/04/01/us/supreme-court-upholds-method-used-in-apportionment-of-house.html
