In the U.S. of Voronoi, which state do you live in?

[Vosem]

I stay in Ohio on the US states map, and I barely stay in the US over Canada on the world map as well.

[Sir Tiki]

Still North Carolina.

[justfollowingtheelections]

Beautiful maps

[justfollowingtheelections]

Can someone make a map of 50 states with the 50 largest cities from this list as capitals?
http://en.wikipedia.org/wiki/List_of_United_States_cities_by_population

[justfollowingtheelections]

Here's my attempt at doing that map:


Alaska is in Seattle and Hawaii in San Francisco

[Goldwater]

Here's my attempt at doing that map:


Alaska is in Seattle and Hawaii in San Francisco

I live in Seattle.

[Goldwater]

Although I wonder if that map would work better using either MSAs or CSAs.

[justfollowingtheelections]

MSAs:

[jimrtex]

MSAs:

One could use this process to draw legislative or congressional districts, through an iterative process.

Michigan has around 6600 election precincts, and each could be considered a potential candidate for one of Michigan's 14 congressional districts.  Each iteration roughly 20% of the candidates would be eliminated.  We can determined the number of iterations by solving for x in the following equation.

6600 0.8^x = 14

x = (ln 14/6600) / ln .8

x = 27.59, which is rounded to the nearest integer, n, which is 28.

We can then solve for the actual decay rate, d.

6600 dⁿ = 14

ln d = (ln 14/6600) / n

d = e ^{(ln 14/6600) / n}

d = .80264

We can easily calculate the target number, t, for iteration i

t_i= nint (6600 dⁱ)

t₁ = 5297
t₂ = 4252
...
t₁₀ = 732
...
t₈₁ = 81
...
t₂₈ = 14

We can reduce each of our 6600 proto-districts to a single point, their center of population, and then calculate a Voronoi diagram, and determine the center of population and total population of each.

We keep the t₁ (5297) most populous proto-districts, and eliminate the 6600 - 5297 (1303) least populous proto-districts, and repeat the process.

We can visualize the elimination of these smallest districts as somewhat analogous to the popping of soap bubbles, and the surviving neighboring bubbles expand to fill the space left by the eliminated soap bubble (proto-districts).

Let's say that the Salt Lake district in the above map is the least populous and were eliminated.  The Denver, Las Vegas, Sacramento, Portland and Seattle districts would expand to fill the void.  Note that we would have used the center of population for the districts, so the centers of the districts would have been somewhat different.  The centers for Seattle, Portland, and Sacramento districts would have been pulled inward to begin with, and even further after Salt Lake were eliminated.

After 28 iterations we would have 14 districts of roughly equal population.

We can then adjust these districts by weighting the distance measure, so that less populous districts would expand towards more populous districts until the populations were equalized.

The survivng proto-districts in less densely populated areas will expand quickly, while in urban areas it will be slower.

[Adam Griffin]

Light colors mean that I'm unsure/it's close but it seems to lean in one direction
Purple (IA) looked so close that I couldn't make a call one way or another

Areas like NC I did personally assess via DRA to see what the actual numbers were

[Ebsy]

Are you sure about the Springfield, Illinois one? It includes St. Louis and some democratic portions of Iowa, and the Republican parts of St. Louis look to be outside of it, so that would add a couple hundred thousand Democratic votes.

[justfollowingtheelections]

Although I wonder if that map would work better using either MSAs or CSAs.

CSAs:

[Del Tachi]

Still in Mississippi

[Adam Griffin]

Are you sure about the Springfield, Illinois one? It includes St. Louis and some democratic portions of Iowa, and the Republican parts of St. Louis look to be outside of it, so that would add a couple hundred thousand Democratic votes.

Looks like you're right. FWIW, I was using DRA where applicable to project 2012 results in some cases (didn't use it on this state), but on this, seeing how much the area in general swung to Romney, I was thinking there was no way Obama could have won.



The IL area swung from 50-47 to at least 53-45, and the MO part appears to have swung from 70-28 to 66-32. I went back and calculated it - the state appears to be around 50-48 in 2012.

[Antonio the Sixth]

Although I wonder if that map would work better using either MSAs or CSAs.

CSAs:

You should use the 50 biggest CSAs and unincorporated MSAs instead. It's a bit ridiculous that Phoenix and San Diego aren't included.

[TNF]

Born in Tennessee, live in Wisconsin

[Skill and Chance]

Light colors mean that I'm unsure/it's close but it seems to lean in one direction
Purple (IA) looked so close that I couldn't make a call one way or another

Areas like NC I did personally assess via DRA to see what the actual numbers were

What do you have for Voronoi GA?  The new areas are less populous than what it loses but more R, so I can't tell if it shifts left or right.

[Anti-Bothsidesism]

I'd still be in Texas.

[Simfan34]

NJ! Which now includes NYC and Philadelphia...

[Figueira]

Right around the New York-New Hampshire-Connecticut tripoint.