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.