KP Voting

Why Voting Reform Matters
The people who run large businesses undergo training via the carrot and the stick. Those who fall short when it comes to taking care of the bottom line strike out. The ones who remain are the ones who take care of the bottom line. Darwinian selection applies; we can guess what the orientation will be of most of these managers and directors in the course of their work. And purchasing political power is a straightforward business expense with a good expected value toward the bottom line. People and systems that take care of the bottom line have no incentive to care about survival of our families, nor about morality in foreign policy, nor about decolonization of people of African descent or other outgroups. These are the considerations that should drive evaluation of voting systems. The selective pressure I mentioned above, in combination with the monetary system, creates a kind of AI that is not implemented on a computer as we would usually think of AI, but is rather, implemented on a crowd of humans. Even if some of the participating humans are kind toward their spouses or dogs, any streak of morality or compassion or forwardthought that may assert itself in these individuals does not affect the AI as a whole. The thoughts of a bee colony are not the thoughts of an individual bee. This AI has control of the US government (USG) via the "Cash3" mechanism. As a result, humankind is in a death trap. There probably isn't any escape. But I say that the most promising escape route I can think of involves voting systems that defeat the absolute and total control of the USG by the AI, by removing the "Cash3" mechanism of control.
The Two Main Candidates Today
A few people passionately advocate for Condorcetcompliant ranking systems or so on, but if there is any contest today in interest in the alternatives, it is between IRV and Approval Voting. IRV is by far the best known, and then most of the time when anyone criticizes it, they are advocating Approval.
Feelings on both sides are pretty sharp.
Why Hybridize
A hybrid system could settle the IRVApproval debate by offering a solution both camps could embrace. It would allow each to vote in their preferred way and decide the election fairly.
My Current Proposal
The ballot is a table with rows and columns. Each candidate has two columns. The candidate's name is printed on a diagonal at the top, and the two columns for that candidate are sublabeled K and P. The ballot can provide room for say 10 rows, and they are simply numbered, 1 for the top row, 2 for the next one, and so on. In any given cell of the table, the voter can black in a circle or leave it blank.
At any given round of the tally, the procedure examines the ballots and finds from each ballot the row to take effect for that round. It is the first row, reading down from the top, in which the K cell for any candidate still in the running is marked. Once having determined that row, the tally uses the P marks as that voter's Approval contribution to the round.
Each round eliminates the worst candidate. When only one candidate remains, she wins.
Analysis
By way of analysis of this system, the first thing to check is can it do IRV. Yes. To do IRV, you map each IRV rank to a row in this system, in order, and you mark both K and P for your candidate.
Can it do Approval? Yes. You fill in all K cells on the first row and mark the P cells for your Approval vote.
Can you cancel my vote with yours? Yes. You mimic my K entries and invert my P entries.
Here is an example of hybrid use, and it illustrates my hope for how clearly this system can express the will of a voter who wants survival and freedom from the AI. Suppose there are five candidates and this voter sees two of them as evil (Hitler and Mussolini), two as highly desirable (Gandhi and King) and about equal in value, and the remaining one is the compromise candidate (Gore). She votes:
 Gandhi P, King P, Gore P, Hitler K, Mussolini K.
 Gandhi PK, King PK
End of screed.
Update 20210403 UCT
Originally, I titled this topic "IRV 3.0." Now I rename it "KP Voting".

Someone asked me how I thought the following factions would vote in this system and how it would respond:
20 = A:5, B:2, C:2, D:0 20 = A:2, B:5, C:2, D:0 20 = A:2, B:2, C:5, D:0 40 = A:0, B:0, C:0, D:5
I begin my analysis of the situation by asking how fear may play into the voters' considerations. The Dlovers are in a plurality, so the fears of the A, B, and Clovers, I predict, center on D. So I'm going to have them vote their first line toward doing their best to eliminate D.
Alovers:
1. K(D) P(A B C).
2. K(A) P(A).Blovers:
1. K(D) P(A B C).
2. K(B) P(B).Clovers:
1. K(D) P(A B C).
2. K(C) P(C).Dlovers:
1. K(D) P(D).Round the first:
A 60, B 60, C 60, D 40.
Eliminate D.Second round:
A 20, B 20, C 20.It's a tie. Usually ties are decided randomly with all voting systems, and if that is done in this case, A, B, or C should win. Let's say it is A.
Voter satisfaction or disappointment by linear and sumofsquarederrors methods:
My questioner used a scale of 05, but I'm going to normalize it to 01.
Linear method:
For the linear method, I will treat satisfaction rather than disappointment.
Alovers: 20 people completely satisfied, so sum is 20.
Blovers: Their true score for A is 2/5, which is .4, and they number 20 people, so their total satisfaction is 8.
Clovers: similarly, 8.
Dlovers: 0.
Total over all voters: 36.
Sumofsquarederrors method:
I probably have less understanding of statistics than most people ought to have. My education is weak in that area. So, I could be off the deep end by thinking of this method of evaluating overall electoral outcomes. But because I have heard of leastsquares curvefitting, and know that squared errors figure into variance, I have a general idea that errors are usually squared. And I have a notion that compassion and fairness maybe should consider that mild pain distributed among many is better than sharp pain visited on a few. And it occurs to me that from a voter's viewpoint, a disappointing outcome is kind of an error caused by poor reasoning or lack of morals on the part of the other voters with whose positions and values the voter disagrees. So that gives me a rationale to treat voter disappointment like a measure of error. So for these naive reasons, I think to use this method. Here I treat disappointment rather than satisfaction.
Alovers: no disappointment, so error is zero and squared error is zero.
B and Clovers: Satisfaction of each individual was .4 so I calculate disappointment by subtracting from 1 and arrive at .6. Squared is .36. Multiply by 40 people, get 14.4.
Dlovers: total disappointment, 1 for each person. Square is 1. Total for 40 people is 40.
Sum of squared errors for election 40 + 14.4 = 54.4.
Now I will repeat the election but using finegrained Score Voting. Coarsegrained is inappropriate for this small a count of voters.
Score does not provide a strategic incentive to invert rankings. But because of fear, the A, B and Clovers will exaggerate their support for their compromise candidates. Each of them knows that overall support for their top candidate is only 20/100 = .2. My tentative model of exaggeration of support for compromise candidates says they should score their compromises at 1  .2 = .8.
Alovers: A 1, B .8, C .8, D 0.
Blovers: A .8, B 1, C .8, D 0.
Clovers: A .8, B .8, C 1, D 0.
Dlovers: A 0, B 0, C 0, D 1.Multiply by numerosity of each faction:
A B C D 20 16 16 00 16 20 16 00 16 16 20 00 00 00 00 40
totals:
52 52 52 40
It is the same outcome as with my system, a tie among A, B, and C for the win.