模倣子 SUSPECNA Idaho Contemplates Ranked Choice Voting

 Memetics Index - Idaho Bill on Ballot (Prop 1) - SUSPECNA Article & Notes 

Introduction

Idaho is talking about switching to ranked choice voting, which is an interesting idea, but I wanted to look at it from a practical standpoint, as it how could it be done by a manual system, as opposed to a computer-only one?

I mistrust any such system (especially to do with voting) that cannot be laid out in a paper-based system (even if such system should be prohibitively inefficient). Also, I want to lay things out so that voters and legislators and party folks can look and see if I got it basically right.

Proposed Scenario

The Idaho law proposes a primary system (already in place?) where four candidates are selected from a relatively unlimited field by traditional first past the post voting.

Let's imagine that four parties get their candidates on the general election via the primary election, for example, the Republicans (R), the Democrats (D), the imaginary "Farmers' Party" (F), and the "Green Party" (G).

Which party gets the "most votes" is not just a simple counting up at this point, as I'll dive into. But to start with we can toss out something for the "first choice vote" which might be suitable for Idaho, along the lines of:

Republicans: 40%
Democrats: 30%
Farmers: 20%
Green: 10%

At this point the Republicans have a plurality, but not a 51% majority. How can they get it?

How Many Different Ballots? 

What I propose, and I welcome comments, is that the total number of "ballot types" is 24, in other words, the election counters at the county and the State Elections Board level can count these and determine the winner of the election.

One question is what is the simplest way to count these up, but first what do these "ballot types" look like?

Every ballot has a first choice, a second, a third, and finally a fourth. This means that each ballot looks something like first Republican, then Farmer, Democrat, and last, Green, or RFDG. A ballot favoring the Greens and then the Democrats might look like GDFR.

So the number of different first-choice ballots are four, R, D, F, or G, and each of those can have one of the three remaining parties as a second, leaving two for the third, and then the remaining party as fourth. Arithmetically this looks like 4 x 3 x 2 x 1 = 24, or twenty-four different types of ballots.

In other words, four different ways to choose the first party, then three to choose the second, and two to choose the third, and then the last is decided. The Idaho law keeps the number of "piles" of ballots down to a "manageable" number. The human brain can deal with what is basically a five-by-five grid of piles, while if it's starting to grow up to fifty, or a hundred (a bunch of piles of ballots ten on a side). A computer can handle any number of choices on the ballot, but it does grow exponentially.

Now for the Ranking Stuff...

Each party can "gain votes" from the second, third, and fourth choices of voters. Can the Republicans get a majority from the above scenario? The Farmers and Greens are probably out of luck, but can the Democrats come ahead and still win?

The ballots look like:

Republicans as first choice: RDFG, RDGF, RFDG, RFGD, RGDF, RGFD = 40%
Democrats first: DGFR, DGRF, DFGR, DFRG, DRFG, DRGF = 30%
Farmers first: FRDG, FRGD, FDRG, FDGR, FGDR, FGRD = 20%
Greens first: GDFR, GDRF, GFDR, GFRD, GRFD, GRDF = 10%

...so that's 24 different choices a voter can make. 

Let's make up some numbers for all of these types of ballots:

RDFG:   1%
RDGF:   1%
RFDG: 18%
RFGD: 12%
RGDF:   3%
RGFD:   5%
Total Republicans first choice: 40%
DRFG:    5%
DRGF:    5%
DFRG:    2%
DFGR:    3%
DGRF:   10%
DGFR:    5%
Democrats first choice total: 30%
FDRG:      1%
FDGR:      1%
FRDG:      5%
FRGD:      8%
FGDR:      2%
FGRD:      3%
Total Farmers: 20%
GDFR:       3%
GDRF:        3%
GFDR:       2%
GFRD:        1%
GRFD:        0%
GRDF:        1%
Total Green: 10%

My understanding is that if a party is eliminated, gets the lowest of a given round of counting the votes, all of its votes go to the party who is second in that pile of ballots.

Each of them gets a percentage of the votes. If the Green Party gets the lowest of the first-choice votes, then the remaining parties pick up the Green votes. 

Republicans: RDFG, RDGF, RFDG, RFGD, RGDF, RGFD + GRFD, GRDF
Democrats: DGFR, DGRF, DFGR, DFRG, DRFG, DRGF + GDFR, GDRF
Farmers: FRDG, FRGD, FDRG, FDGR, FGDR, FGRD + GFDR, GFRD

So the Republicans now have 41%, the Democrats 36%, the Farmers 21%.

So the Farmers now have the lowest votes, so their votes, and the votes they got from the Greens go to the Republicans and the Democrats. The Republicans get FRGD and FRDG, FGRD, and GFRD, or 17% and the Democrats get FDRG, FDGR, FGDR, and GFDR, or 6%. So the Republicans now have 58% and the Democrats 42%. End of election.

Questions for Later...

Is there a way so that nobody wins? Is there a simple way to express which party is going to win just from some kind of a sum of all of the types of ballots?