A better runoff election

BACKGROUND:
Instant Runoff Voting (IRV) is a term used in the United States for a single-winner voting system where ballots allow candidates to be ranked in order of preference, and counted in a runoff process, where everyone's top choice is counted each round, and the least supported candidates are eliminated, and votes for such candidates are transfered to the next choice. It's also called "Ranked Choice voting", "Contingency vote", "Supplementary vote", and "Single transferable vote".

IRV is a simple reform over plurality system where there's no runoff process because there's no spoiler effect. It is better than a regular runoff because voters only need to vote once. But it can be considered inferior to a regular runoff because it takes more work to rank choice, and voters don't know how deep they need to rank to make sure their vote counts. In comparison a regular runoff, voters have another chance to evaluate the remaining competition.

PROBLEM
The primary problem with IRV exists also in any runoff process - cases where you have 3 strong candidates. In any runoff process, candidates advance by having "core appeal" - support by people who consider such candidates better than all others. But to win majority support in the final round, a candidate must also have "compromise appeal". The FLAW of a forced-elimination runoff is somtimes a candidate will rise to second place to make the final round, but not have the compromise appeal to win. Such supporters can't move their vote back to a compromise candidate.

ONE SOLUTION
A solution to this problem is obtained in an election method called Condorcet, named after a French Mathematician. He proposed the "true majority opinion" among 3 or more choices be obtained by performing head-to-head competition. If any choice has majority support head-to-head over every other choice, that choice is called the "Condorcet winner". An ambiguity of this approach is that there may be no such winner. Like the "Rock, Paper, Scissors" game, it's possible in every pair competition to have a different winner.

It can be seen that "Plurality" is a pure "core appeal" method. It uses the "spoiler effect" to get coalitions of voters to "agree to agree" before the election to improve their chances to win. "Condorcet" is a pure "compromise appeal" method. A candidate can theoretically win by being no one's favorite but everyone's second choice.

RUNOFFS AS A COMPROMISE
Runoffs actually represent a simple hybrid of these two extremes. Runoff reward "core appeal" in the early rounds, and require "compromise appeal" in the final round.

A BETTER COMPROMISE THAN IRV
I believe two rounds of voting is good because it allows voters a chance in the second round to evaluate the remaining candidates. The first round is best seen as a "Primary" or "elimination round". Rank preference ballots can be used like IRV, but no winner is chosen. Instead the weakest candidates are eliminated one-by-one until all the remaining candidates exceed some predetermined level of support, like 20 or 25% perhaps.

Candidates who survive the elimination are all treated as equals in a Condorcet process. Voters again rank their choices, and the ballots are tallied with head-to-head competition to find a Condorcet winner.

In the rare case that no candidate passes as the Condorcet winner, then we must consider what to do, and there's no right answer. A revote might be done. My thought is that if no candidate can beat all competitors head-to-head that you have a "virtual tie", just like you could have an exact tie in a plurality system. In this case, if a single winner must be made, and the people can't decide, then there's no fair way to break the tie except by a random determination.

My reasoning for this compromise is:
1. Candidates require "core appeal" to pass the first round. These candidates have been "vetted" by a strong fraction of the voters and deserve consideration by the whole.
2. Candidates in the second round are never eliminated and voters are encouraged to look at all of them carefully to rank their choices.

The first round reduced the number of candidates to a number voters are willing to evaluate, and the second round picks the strongest majority winner (OR determines there is no majority winner in a virtual tie.)

FINAL NOTES:
Election theorists generally dislike runoffs, and IRV specifically, saying it contains a property call "Nonmonotonicity" which basically means sometimes voting against your favorite can help him win. This can be understood in a runoff process. Let's say your candidate polls around 40% against two competitors near 30%. If you believe one of your competitors has "compromise appeal" to beat your choice, you might consider voting against your 40% favorite, in favor of the weaker competitor to help eliminate your stronger competitor. This strategy is more powerful in sequential voting runoffs, while dangerous in IRV since you can't move your vote back to your real favorite there.

The compromise above retains a "spoiler effect" in that good compromise candidates can get eliminated in the first round, AND it retains a monotonicity failure potential. But at least it has a clear "threshold for viability". Candidates are encouraged to gain the threshold percentage, and like-minded voters are encouraged to work together on one strong candidate who can make the threshold.

I don't know of any weaknesses of this system. All election methods are somewhat "subjective", containing rules that encourage voters to compromise, and finding the balance between "having choices" and "having knowledge to make good choices" can never be solved absolutely. Different elections may choose different solutions. This solution is just one solution of many that tried to balance these issues.