模倣子 More Ranked Choice Voting

 Previous Prop 1 Post 

Introduction

Last time I posited an election between the Republican, Democrat, Farmer, and Green parties in Idaho.

I want to come up with a straightforward way to add up the totals, and see how parties "dropping out" of the ranked choice vote impacts the overall results.

An Initial Sample Vote

From the last post I made, I laid out the votes as follows.

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

Adding up the Totals

With four parties, the percentage of votes for the winning party should be:

P1 = total percentage of votes to the winning party
P11 = votes where the winner was the first choice
P13 = where the winner was the third choice
P14 = where the winner was the fourth choice

Each Loser, Pn+1, e.g., P2, P3, P4, with P4 being the first party eliminated and P# the second, and P2 being the party that comes in second place.

P1 = P11 + P13 + P14 > P2

In other words, even if party #3 gets votes from the eliminated party #4, party #3's votes go to the remaining two parties according to the third and fourth choices of the party #4 votes.

Is this correct? Or are eliminated party votes distributed differently?

Losers Votes go Where?

If the Greens lose, then their votes go to:

Republicans GRDF + GRFD = 1%
Democrats  GDRF + GDFR = 6%
Farmers GFRD + GFDR = 3%

How Can the Republicans Lose?

The only way for the Republicans to lose is if the net total of the votes for the Farmer and Green parties to be greater than 21%, going to the Democratic party. That is if all the Greens go to the Democrats and more than half of the Farmers going to them. Unless of course the Democrats get eliminated first, which is not possible. It might look like this:

Republicans first	RDFG 1%	RDGF 1%	RFDG 18%	RFGD 12%	RGDF 3%	RGFD 5%	Total 40%
Democrats first	DRFG 5%	DRGF 5%	DFRG 2%	DFGR 3%	DGRF 10%	DGFR 5%	Total 30%
Farmers first	FRDG 4%	FRGD 3%	FDRG 5%	FDGR 2%	FGRD 2%	FGDR 4%	Total 20%
Green first	GRDF 0%	GRFD 0%	GDRF 3%	GDFR 4%	GFRD 0%	GFDR 3%	Total 10%

Here we see the Democrats getting 11% of the badly split Farmer vote while the Republicans get 9%, and the Democrats get all of the Greens, or 10%, giving the Democrats 51%.

So the Democrats win despite being well behind in the first choice vote. It depends on an entire third party voting for them as second choice, and in this case, the strongest other party being badly split. It does give voters the chance to vote for their favorite third party, but still having their votes count.

模倣子 Settling the Votes in a Ranked Choice Vote

Previous Post on Prop 1 - Macromemetic Index - Math of Elections 

Introduction

I wanted to take a closer look at how the votes of the defeated parties get rolled up into the winning parties' totals.

How Ballots Look

Let's say we have the Republican, Democrat, Farmer's, and Green parties running after having made it through the primaries as the top three parties. A ballot has a first pick, a second, a third, and a fourth choice, so a shorthand for a ballot could look like RDFG, where Republican is first choice, then Democrats, then Farmers, then Green. Every ballot looks like this.

There are six kinds of ballots where the Republicans are the first pick: RDFG, RDGF, RFDG, RFGD, RGDF, and RGFD.

How a Vote Might Look

There are 24 different kinds of ways to cast a ballot. Here's a sample vote below. I've marked in Blue and Red the ballots that go to the winning party (Republicans) and the runner-up party (Democrats) when the other two parties are taken out.

Rep	RDFG 1%	RDGF 1%	RFDG 18%	RFGD 12%	RGDF 3%	RGFD 5%	Total 40%
Dem	DRFG 5%	DRGF 5%	DFRG 2%	DFGR 3%	DGRF 10%	DGFR 5%	Total 30%
Farm	FRDG 5%	FRGD 8%	FDRG 1%	FDGR 1%	FGRD 3%	FGDR 2%	Total 20%
Green	GRDF 1%	GRFD 0%	GDRF 3%	GDFR 3%	GFRD 1%	GFDR 2%	Total 10%

So the Republicans get their 40% plus 16% from the Farmers and 2% from the Greens, for 58% and a win. The Democrats pick up 4% from the Farmers and 8% from the Greens, for 42%. 

Is it possible for the Democrats to win with the initial 40%-30% first choice vote, if the other parties votes go differently?

Coming Back from a Bad First Choice Vote

If the Greens all go to the Democrats, and the Farmers split both ways, the Democrats can actually win.

Rep	RDFG 1%	RDGF 1%	RFDG 18%	RFGD 12%	RGDF 3%	RGFD 5%	Total 40%
Dem	DRFG 5%	DRGF 5%	DFRG 2%	DFGR 3%	DGRF 10%	DGFR 5%	Total 30%
Farm	FRDG 4%	FRGD 3%	FDRG 5%	FDGR 2%	FGRD 2%	FGDR 4%	Total 20%
Green	GRDF 0%	GRFD 0%	GDRF 3%	GDFR 4%	GFRD 0%	GFDR 3%	Total 10%

Here the Republicans pick up 9% of the Farmers vote, for a total of 49%. The Democrats pick up the whole 10% of the Greens, and then 11% of the Farmers split vote for 51%.

So even if one is not most peoples' first choice, or even if one is, one can be the second or third choice after more minor parties, and pick up those ballots when those smaller parties drop out. This can only really happen if said smaller parties have the amount of votes making the difference between winning and losing. If they are smaller than that, and the gap is wide, then they can't make much of a difference.

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?

Feli on US Elections (SUSPECNA - REPOST)

This is a repost to remind me about all this stuff. I need to collect the results down to the district level for all of the elections, probably since Eisenhower, and work out how they would have gone based on SUSPECNA (ranked choice voting) and no winner-takes-all. I'm imagining a spreadsheet with each sheet being an election, and each row is a district in a State, and then various columns for the number of electoral college votes and the total real popular votes that went one way or another.

Plus I need to start actually drafting the law, and I guess contacting all of the State election boards and legislatures.

Great video! The Electoral College is a problem, but fixing it poses a couple of problems: it would require amending the Constitution, it's unclear which system could replace it (mainly agreeing on it), how the "popular vote" is counted, i.e., each State's election board totals the results from each county, but they don't necessarily publish these results (I think) and it's unclear which authority (Congress, the Supreme Court?) could collect and adjudicate these results, or how they would be officially certified and delivered by the several States in some hypothetical "national vote counting," and so on. America is a republic, and the only real electoral decision that requires all of the States to get together and decide on one thing is the Presidential election. One problem is the "at large electors" i.e., those that match up with the "Senators" from the given State. In small States, which have only one seat in the House of Representatives, they still get two "at large" votes, for three times as many total votes.

One thing is that the State elections are based on laws which differ from State to State. Hence the "winner take all" thing. Also, most States have a "first past the post" vote counting system, as opposed to a "ranked choice voting" system (which we are voting on starting in Idaho, by the way, and I think they already have in Maine and other places). One possibility of interest to me, in the spirit of changing as little as possible, one bit at a time, to get the most impact at each step, is to put out a "uniform law" (a law that is passed by each State, which gets around the need for a Federal-level law) that would standardize voting laws, getting rid of things like "winner take all" and adding things like ranked choice voting, perhaps allow small states to "donate" their at large votes to other states (voted by their legislature? For whatever reason...?), and report an actual certified (by the governor, State supreme court, et al -- just like the Electoral College Certificates) Statewide vote count to the joint session of Congress (and to the Supreme Court and to the National Archives and wherever, like the EC certificates). You could then talk about, if the joint session received a set of EC certificates from the several States, ALONG WITH official certified popular vote counts, and in the case (rare but disturbing, especially when one party successfully "games" the electoral college in swing States and such) where the EC did not reflect the popular vote, the joint session has, I believe, the power to decide the President based on that (or anything else), i.e., override the EC result. I THINK the joint session on January 6 has the power to do that (as long as no violent and heavily-armed mobs don't break into the Capitol Buidling and stop them...but when has that ever happened?) I came up with the acronym of SUSPECNA (I'll have to look up what it meant) for this new uniform law. How does that sound for a start? If anybody wants to help me draft it and promote it, I welcome you! Simplified Uniform State Popular Electoral College Normalization Act

SUSPECNA on A Medium 

SUSPECNA Notes

Ranked Choice Voting and MORE Ranked Choice Voting 

Idaho Prop 1 stuff...

Prop 1 Volunteering

 Volunteers can do a number of different things! We have opportunities for phone banks, canvassing, and tabling! If you sign up, you can choose which options sound fun for you: yesforopenprimaries.com/volunteer

Ranked choice voting piece 

Feli on US Elections (SUSPECNA)

Great video! The Electoral College is a problem, but fixing it poses a couple of problems: it would require amending the Constitution, it's unclear which system could replace it (mainly agreeing on it), how the "popular vote" is counted, i.e., each State's election board totals the results from each county, but they don't necessarily publish these results (I think) and it's unclear which authority (Congress, the Supreme Court?) could collect and adjudicate these results, or how they would be officially certified and delivered by the several States in some hypothetical "national vote counting," and so on. America is a republic, and the only real electoral decision that requires all of the States to get together and decide on one thing is the Presidential election. One problem is the "at large electors" i.e., those that match up with the "Senators" from the given State. In small States, which have only one seat in the House of Representatives, they still get two "at large" votes, for three times as many total votes.

One thing is that the State elections are based on laws which differ from State to State. Hence the "winner take all" thing. Also, most States have a "first past the post" vote counting system, as opposed to a "ranked choice voting" system (which we are voting on starting in Idaho, by the way, and I think they already have in Maine and other places). One possibility of interest to me, in the spirit of changing as little as possible, one bit at a time, to get the most impact at each step, is to put out a "uniform law" (a law that is passed by each State, which gets around the need for a Federal-level law) that would standardize voting laws, getting rid of things like "winner take all" and adding things like ranked choice voting, perhaps allow small states to "donate" their at large votes to other states (voted by their legislature? For whatever reason...?), and report an actual certified (by the governor, State supreme court, et al -- just like the Electoral College Certificates) Statewide vote count to the joint session of Congress (and to the Supreme Court and to the National Archives and wherever, like the EC certificates). You could then talk about, if the joint session received a set of EC certificates from the several States, ALONG WITH official certified popular vote counts, and in the case (rare but disturbing, especially when one party successfully "games" the electoral college in swing States and such) where the EC did not reflect the popular vote, the joint session has, I believe, the power to decide the President based on that (or anything else), i.e., override the EC result. I THINK the joint session on January 6 has the power to do that (as long as no violent and heavily-armed mobs don't break into the Capitol Buidling and stop them...but when has that ever happened?) I came up with the acronym of SUSPECNA (I'll have to look up what it meant) for this new uniform law. How does that sound for a start? If anybody wants to help me draft it and promote it, I welcome you! Simplified Uniform State Popular Electoral College Normalization Act

SUSPECNA on A Medium 

SUSPECNA Notes

Ranked Choice Voting and MORE Ranked Choice Voting 

Idaho Prop 1 stuff...