Maximizing geography of losing candidates

[Adam Griffin]

So I thought this might be an interesting project.

Analyze a county-by-county election result for a 2014 gubernatorial or senatorial contest, and without changing the overall result, maximize the number of counties the losing candidate won without pushing them over the top. Start out with the counties that had the closest margins (percentage) and give the losing candidate a one-vote victory, rinse and repeat. While the goal is to maximize the number of counties, please do not skip large counties for the sake of flipping multiple smaller ones if the margin (percentage) is closer in a large county. If you get to a county and the shift in the margin would put the losing candidate over the top in the overall contest, then obviously do not flip that county, and stop there.

Here's FL:

Actual:

Rick Scott   2,865,343 48.14%
Charlie Crist 2,801,198 47.07%



Alternate:

Rick Scott   2,865,343 47.66%
Charlie Crist 2,861,249 47.60%

[Adam Griffin]

Georgia, Governor:

Actual:

J. Nathan Deal 1,345,237 52.75%
Jason J. Carter 1,144,794 44.89%



Alternate:

J. Nathan Deal 1,345,237 48.90%
Jason J. Carter 1,345,121 48.90%

[Miles]

Good idea!



Tillis- 1,399,913 (48.13%)
Hagan- 1,399,822 (48.12%)

[Adam Griffin]

South Carolina, Governor:

Actual:



Nikki R. Haley 696,645 55.90%
Vincent Sheheen 516,166 41.42%

Alternate:



Nikki R. Haley 696,645 49.01%
Vincent Sheheen 691,243 48.63%

[politicallefty]

I realize there are some outstanding ballots and the results aren't finalized yet, but it's extremely unlikely anything will change in terms of the maps. (I used the most recent numbers from the CA SoS.)

Actual:


Jerry Brown     4,314,612  59.92%
Neel Kashkari  2,886,025  40.08%

Alternate:


Jerry Brown     4,314,612  51.07%
Neel Kashkari  4,134,613  48.93%

The last county to flip was Marin, which actually voted for Brown by a 79.4%-20.6% margin. Only San Francisco and Alameda remain, both of which were D>80%.

[Bacon King]

Wow that California map is insane

[muon2]

Mathematically, there is an equivalent, simpler procedure. Take the margin of victory for the loser in those counties won by the loser, call it L. Count the number of counties won by the winner, call it C. L+C is the winning margin for the loser if all of the winner's counties just flipped to the loser by one vote. To solve the problem select the smallest number of counties that voted for the winner (n < C), such that the total margin of victory w in those counties is greater than L+C-n.

Since C and n are generally going to be small compared to the difference between w and L they can be usually be neglected. Then the problem simplifies to finding the smallest set of counties that gives a value for w that is larger than L.

For example, for IA Gov, Hatch only won Johnson county and the margin was 10,568 (Politico). Branstad won the other 98 counties. The only county Branstad won by more than that was Scott, with a margin of 15,073 (Woodbury was just short with 10,245). So flipping all other counties except Scott to Hatch would give Branstad a margin of 15,073 - (10,568 + 98 - 1) = 4,408.

[muon2]

Wow that California map is insane

It could be even more insane. Kashkari's winning margin in the states he won was 215,555 (again Politico numbers). Los Angeles county provided a margin for Brown of 405,230 so it alone could balance Kashkari's win plus all other flipped counties, not unlike the way Cook balances the rest of IL.

But it gets better, Alameda had a 226,726 vote margin for Brown which is larger than Kashkari's in his winning counties. So, you can take politicallefty's CA map and flip San Francisco, too and it's still a Brown win - with only Alameda!

[Adam Griffin]

Mathematically, there is an equivalent, simpler procedure. Take the margin of victory for the loser in those counties won by the loser, call it L. Count the number of counties won by the winner, call it C. L+C is the winning margin for the loser if all of the winner's counties just flipped to the loser by one vote. To solve the problem select the smallest number of counties that voted for the winner (n < C), such that the total margin of victory w in those counties is greater than L+C-n.

Since C and n are generally going to be small compared to the difference between w and L they can be usually be neglected. Then the problem simplifies to finding the smallest set of counties that gives a value for w that is larger than L.

For example, for IA Gov, Hatch only won Johnson county and the margin was 10,568 (Politico). Branstad won the other 98 counties. The only county Branstad won by more than that was Scott, with a margin of 15,073 (Woodbury was just short with 10,245). So flipping all other counties except Scott to Hatch would give Branstad a margin of 15,073 - (10,568 + 98 - 1) = 4,408.

Very interesting! Now I'll just have to read it over about seven more times before I get it, since I'm so bad with equations.


Minnesota, Governor:

Actual:



Mark Dayton 989,100 50.07%
Jeff Johnson 879,249 44.51%

Alternate:



Mark Dayton 989,100 49.43%
Jeff Johnson 904,543 45.21%

EDIT: Messed up original alternate map.

[Adam Griffin]

Pennsylvania, Governor:

Actual:

Thomas W. Wolf 1,912,003 54.87%
Thomas W. Corbett 1,572,382 45.13%



Alternate:

Thomas W. Wolf 1,912,003 51.11%
Thomas W. Corbett 1,828,882 48.89%

[IceSpear]

Wow that California map is insane

But Jeb Bush could win California in 2016 ~ Mark Halperin

[IceSpear]

Pennsylvania, Governor:

Actual:

Thomas W. Wolf 1,912,003 54.87%
Thomas W. Corbett 1,572,382 45.13%



Alternate:

Thomas W. Wolf 1,912,003 51.11%
Thomas W. Corbett 1,828,882 48.89%

Checkmate Toomey.

[Adam Griffin]

Oregon, Governor:

Actual:

John Kitzhaber 730,715 49.89%
Dennis Richardson 646,411 44.13%



Alternate:

John Kitzhaber 730,715 47.97%
Dennis Richardson 704,924 46.28%

[muon2]

Mathematically, there is an equivalent, simpler procedure. Take the margin of victory for the loser in those counties won by the loser, call it L. Count the number of counties won by the winner, call it C. L+C is the winning margin for the loser if all of the winner's counties just flipped to the loser by one vote. To solve the problem select the smallest number of counties that voted for the winner (n < C), such that the total margin of victory w in those counties is greater than L+C-n.

Since C and n are generally going to be small compared to the difference between w and L they can be usually be neglected. Then the problem simplifies to finding the smallest set of counties that gives a value for w that is larger than L.

For example, for IA Gov, Hatch only won Johnson county and the margin was 10,568 (Politico). Branstad won the other 98 counties. The only county Branstad won by more than that was Scott, with a margin of 15,073 (Woodbury was just short with 10,245). So flipping all other counties except Scott to Hatch would give Branstad a margin of 15,073 - (10,568 + 98 - 1) = 4,408.

Very interesting! Now I'll just have to read it over about seven more times before I get it, since I'm so bad with equations.

It's really not very complicated if you don't think about the totals but only the margin between the candidates. The loser has a fixed total margin in the counties won by the loser. Each county flipped adds one to the margin for the loser. To keep the winner in front requires one or more counties not flip where the winner's total margin exceeds the total held by the loser.

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Is there another combination of Ramsey + something smaller that also holds for Dayton? Hennepin supplied about 60K more votes than needed.

[Adam Griffin]

Is there another combination of Ramsey + something smaller that also holds for Dayton? Hennepin supplied about 60K more votes than needed.

Maybe I'm not following, but the general idea was to flip each county based on the margin of victory for the winning candidate, starting with the counties with the smallest margins of victory and ascending from there. The secondary goal is to see how many counties that would result in the losing candidate winning, while still ultimately losing, but keeping the counties that flip in line with that first goal was the idea.

However, I just realized that I messed up Minnesota by flipping Cook County and St Louis County, both of which had larger margins of victory for Dayton than Hennepin. Unfortunately, after subtracting these from Johnson's total and then adding Hennepin in, Johnson would be ahead by 20,000 or so, so this is the actual map based on the criteria I outlined instead:

Mark Dayton 989,100 49.43%
Jeff Johnson 904,543 45.21%

[muon2]

Is there another combination of Ramsey + something smaller that also holds for Dayton? Hennepin supplied about 60K more votes than needed.

Maybe I'm not following, but the general idea was to flip each county based on the margin of victory for the winning candidate, starting with the counties with the smallest margins of victory and ascending from there. The secondary goal is to see how many counties that would result in the losing candidate winning, while still ultimately losing, but keeping the counties that flip in line with that first goal was the idea.

However, I just realized that I messed up Minnesota by flipping Cook County and St Louis County, both of which had larger margins of victory for Dayton than Hennepin. Unfortunately, after subtracting these from Johnson's total and then adding Hennepin in, Johnson would be ahead by 20,000 or so, so this is the actual map based on the criteria I outlined instead:

Mark Dayton 989,100 49.43%
Jeff Johnson 904,543 45.21%

Perhaps the confusion was mine. Is your OP about percentage margin or vote margin? When margin is used without an adjective it usually means vote margin. Your revised MN map suggests that you mean percentage margin.

[RI]

Idaho Governor, 2014:


I ended up with a lot of the extra vote left over after changing the winner in as many as I could, so I started ratcheting up Balukoff's percentage based on the Atlas scale.

The final result was

Otter: 202,554 (46.05%)
Balukoff: 202,407 (46.02%)

[Adam Griffin]

Perhaps the confusion was mine. Is your OP about percentage margin or vote margin? When margin is used without an adjective it usually means vote margin. Your revised MN map suggests that you mean percentage margin.

Yes, sorry: I meant percentage margin. I figured that would be more realistic for such a scenario (relatively speaking).

[Nichlemn]

This results may look interesting, but they don't really tell us very much. As muon was saying, you basically just flip every county except for a few high vote margin counties for the winner, such that this is equivalent to the margin of victory the loser had in the counties that they won. The maps are not at all realistic because they have utterly bizarre non-uniform swings.

[Bacon King]

So if you do this exercise in a race where the loser didn't win any counties the results are wacky

Nevada Governor: Actual



Sandoval 70.6%
Goodman 23.9%


Nevada Governor: Alternate



Sandoval 47.3%
Goodman 47.2%

[ElectionsGuy]

This results may look interesting, but they don't really tell us very much. As muon was saying, you basically just flip every county except for a few high vote margin counties for the winner, such that this is equivalent to the margin of victory the loser had in the counties that they won. The maps are not at all realistic because they have utterly bizarre non-uniform swings.

Can we do uniform swings for every county? For example, the only counties that would flip are the counties that have a lesser margin than the state margin. I think that would be more interesting.

[muon2]

Perhaps the confusion was mine. Is your OP about percentage margin or vote margin? When margin is used without an adjective it usually means vote margin. Your revised MN map suggests that you mean percentage margin.

Yes, sorry: I meant percentage margin. I figured that would be more realistic for such a scenario (relatively speaking).

I also went with your statement in the OP of the overall problem.

Analyze a county-by-county election result for a 2014 gubernatorial or senatorial contest, and without changing the overall result, maximize the number of counties the losing candidate won without pushing them over the top.

I took your statement that followed the quote to be your method, rather than the problem itself. As clarified, the problem becomes a brute force math exercise of moving through the sequence of counties from narrowest to widest percentage. My math solves the problem in the quote above, but not by a percentage margin basis, nor by your sequence. It creates the opportunity to explore individual county results with especially large vote margins.

[Adam Griffin]

This results may look interesting, but they don't really tell us very much. As muon was saying, you basically just flip every county except for a few high vote margin counties for the winner, such that this is equivalent to the margin of victory the loser had in the counties that they won. The maps are not at all realistic because they have utterly bizarre non-uniform swings.

Can we do uniform swings for every county? For example, the only counties that would flip are the counties that have a lesser margin than the state margin. I think that would be more interesting.

I've done that before as well (though I never made a thread); would be interesting.

To be fair, any scenario like this is going to be unrealistic in reality and quite predictable since we're dealing with basic math here. Flipping counties by their percentage margins isn't realistic in the confines of a campaign, nor is flipping counties by their nominal margins (whether you start from smallest margin or largest margin). And of course doing a uniform swing isn't going to be realistic, either, but we all love to make maps anyway.

[Adam Griffin]

I took your statement that followed the quote to be your method, rather than the problem itself. As clarified, the problem becomes a brute force math exercise of moving through the sequence of counties from narrowest to widest percentage. My math solves the problem in the quote above, but not by a percentage margin basis, nor by your sequence. It creates the opportunity to explore individual county results with especially large vote margins.

Ah, then maybe I'll be eating my words on the previous post. I'm going to give this a try later.

[Miles]

Edwin Edwards- 864,150
David Duke- 863, 890