Change the spring election to a unified open primary, with all candidates on one ballot, and the favorite four will advance. Each voter may choose two from the primary field. Parties are limited to having one candidate advance in the top four.
The fall ballot will have two separate parts:
1. Voters may choose as many of the four as they wish. (Approval vote.)
2. Voters are also presented with the six possible head-to-head pairings, and may choose their preferred candidate of each pair.
The primary determines the top four.
Part 1 in the fall narrows the field to two.
Part 2 is a real runoff between the top two. (Only one of the six pairings comes into play.)
The statehood bonus, and state-by-state tabulation could still be used, with a point system instead of electors. One option would be 300 points minimum (instead of 3 electors) per state for national tallies for the top four and top two, and 300 minimum for the final, with the winner of each state taking 100 points, and the remainder allocated proportionally to the top two per state.
Instant Runoff?
The term "Instant Runoff" is usually used interchangeably, and erroneously, with "Ranked Choice," a voting system that many people are suddenly excited about.
I have been aware of ranked choice since the 2000 election. I have done a lot of looking at it, and I can confidently say that the concept is very flawed. Ranked choice creates the illusion of a majority, when the actual majority might prefer another candidate. The 3rd choices of fringe voters are considered, while the 2nd choices of many mainstream voters are ignored; this is unequal voting power, in favor of weirdos. The complexity of shifting votes between candidates requires computer tabulation, and hand recounts have been called off due to difficulty. Ranked choice is not worth using. There are multiple superior alternatives.
1st and 2nd choices are apples and oranges. Ranked choice only counts some people's oranges as being worth apples. Approval voting makes it clear to all that all votes will count the same.
Ranked choice is not even an accurate "instant runoff", it is only approximate. While some people will vote strategically in a ranked choice, the only possible strategy in a top-two is to vote for the better one.
Top 4, Top 2, Head-to-Head
This system takes the primary out of the polarizing hands of the parties. Candidates who advance can be selected by a majority of all of the voters, not just a majority of the 1/3 who are party members.
The top four concept should result in a redistribution of power to at least four major parties, which would provide more options, and would make it less believable for one partisan to say "You have to support me, because the other three are all the devil!"
Limiting the field to four candidates also makes possible a real, "instant," head-to-head runoff, as a safeguard against possible strategic voting or spoiler effect. (Six pairs is doable, but six or seven candidates would make 15 or 21 pairs, which would dazzle voters.)
The fall election produces the actual top two with an approval vote that decides which two are acceptable to the most voters. Approval voting allows people to not have to choose between their favorite and one "who can win;" they can choose both. Or negative voters can choose the three opponents of the one they hate most, instead of giving the lesser of two evils disproportionate support just to keep the other one out.
The pairs section allows ALL voters to give input as to which of the top two is better. This is like insurance against a weird situation such as one liberal vs three conservatives who might split some votes, or a virtual 4-way tie. Although no one voting will know who the top two will be, it should still work for people to vote on each of the six possible pairs, or on as many pairs as they care to.
Why use Approval instead of only head-to-head pairs? It is important to have two sections because this allows voters to precisely answer two different questions. The first question is "Which of these would you want to win vs the others," and the second is "Which in each pair is better." If the fall ballot was head-to-head only, voting for a poor candidate over a terrible one could cause the poor one to beat the best one! With two separate sections, we are free to choose one per pair, without fear of putting a poor one over the best one.
[UPDATE 1/22/2020: I did another blog post featuring this plan, complete with PICTURES!
https://americarepair.home.blog/2020/01/17/head-to-head-matches-make-a-better-instant-runoff/ ]