What's the value of your vote? Virginians hit the jackpot.

With the U.S. Presidential election close at hand, I've been thinking a lot about the electoral college. We can all see the effect that the electoral college has on Presidential politics, with a handful of swing states lavished with attention, while most of the states are largely taken for granted by both sides.

It's clear that a voter in the swing states has much more power to influence an election's outcome, but can this difference be measured? I had wondered this idly, but it began to crystallize for me when I read this article by Alan Green, a friend of my wife's, for The State (SC). Alan created a vote value index based on a state's likelihood to have a very close vote, less than 1%. Since that likelihood is very small in most states, the value differentials were very large. I think that his index makes a good measure of the relative odds that one voter in a given state might cast the "magic vote" that tips the national election. However, I wanted to measure a vote's value on a more fundamental and tangible level: one voter's power to move the needle.

I created a formula of my own, which consists of two parts. The first part is an electoral college modifier. This modifier gives a state's electoral votes either a boost or a handicap, depending on how the state's share of the national voting-eligible population compares to its share of the electoral vote. The Electoral College was designed to give smaller states an advantage, and that advantage is reflected in the formula.

The second part of the formula is a margin index. This index measures one individual vote's proportion of the state's probable vote margin, based on current projections. This is designed to account for two facts: a vote is more valuable in a close election, and when two states are equally close, a vote in the state with a smaller population accounts for a larger portion of the margin and is, therefore, more valuable.

I'll get into the math in a moment, but in the meantime, let's find out what your vote is worth. In the final index, I used Oklahoma as a baseline, because I determined that Oklahoma voters have the least valuable votes in the country. Each other state's index is expressed as a multiple of the value of an Oklahoma vote.

Rank: State: Value Index: 51 OK 1.00 50 NY 1.03 49 AL 1.17 48 DC 1.22 47 LA 1.31 46 UT 1.34 45 IL 1.37 44 TN 1.49 43 MD 1.50 42 MA 1.57 41 KY 1.59 40 CA 1.64 39 MS 1.75 38 TX 1.77 37 KS 1.83 36 AR 1.87 35 ID 1.95

Rank: State: Value Index: 34 SC 2.40 33 WA 2.42 32 HI 2.57 31 GA 2.71 30 OR 2.77 29 IN 2.82 28 NJ 2.83 27 NE 3.10 26 CT 3.35 25 MO 3.45 24 WV 3.51 23 MI 3.84 22 AZ 3.96 21 PA 4.33 20 MN 4.76 19 ME 5.71 18 RI 5.72

Rank: State: Value Index: 17 VT 5.74 16 NC 6.36 15 WY 6.90 14 MT 7.10 13 NM 7.67 12 SD 7.92 11 WI 8.13 10 AK 8.31 9 ND 10.45 8 OH 10.94 7 DE 11.72 6 FL 19.19 5 NH 26.45 4 IA 32.51 3 NV 38.59 2 CO 107.42 1 VA 261.50

As you can see, the most valuable votes belong to Virginia's voters. Their votes are a whopping 261.5 times more valuable than an Oklahoman's vote.

Unsurprisingly, the top six states on the index - Virginia, Colorado, Nevada, Iowa, New Hampshire, and Florida - are all considered to be "swing states" this year. Another important swing state, Ohio, is close to its swingin' colleagues, but landed in the #8 spot behind Delaware. How did Delaware, a solidly blue state that FiveThirtyEight gives 99.7% odds of voting Obama, get so high on the list? There are two answers to this question: population and population. First, a Delaware voter punches more than twice his or her weight in the Electoral College, due to its small-state advantage. Second, the small population means that it takes less people to move the percentage margin within the state. Put simply, one person is a larger percentage of his or her state's population if they live in a small state than if they lived in a large state, making their vote more valuable in moving the needle.

Now comes the mathy bit. My teachers always told me to show my work, so I'm going to explain how my formula works, using my home state of North Carolina as an example. I've also posted a Google spreadsheet for those who want to really delve into the data.

As I stated, the formula has two parts. The total Vote Value Index at its simplest is as follows:

Where ECM is the Electoral College modifier, MI is the margin index, and n is a constant (to set the baseline state to 1 and all others relative to that).

The ECM is designed to show how a state punches above or below its weight in the electoral college:

Where VEP is the voting eligible population. This includes a state's residents who are U.S. citizens, at least 18 and not otherwise ineligible. I used the 2010 VEP numbers provided by the United States Elections Project.

The ECM compares the state's share of the national population to its share of the electoral vote. The national average is about 395,245 eligible voters per electoral vote (the national VEP divided by the total electoral votes, 538). States with more voters per electoral vote, generally large states, will have an ECM that is smaller than their electoral vote count. The opposite is true of smaller states, with more voters per electoral vote.

Using North Carolina as an example, we find an ECM of 13.1, a bit less than our 15 electoral votes.

Next, we determine the Margin Index, by multiplying the state VEP times the projected margin, and inverting it:

For the projected margin of each state, I used data from FiveThirtyEight as of October 15, 2012. If you've made it this far into this post, then I strongly suggest that you make FiveThirtyEight a part of your balanced blog breakfast.

Again, applying this index to North Carolina:

Right now, you might be saying, "Wow, that's a small number." To which I reply, well, yeah. We just divided one voter by the number of voters it would take to flip the state. This number represents one person's influence on that process. What's important here is how the states compare to each other; a larger state with a higher projected margin will have a much smaller margin index. Don't worry about the scientific notation; when we apply our constant, the numbers will be moved into a range we can wrap our brains around.

Which, incidentally, is where we are. It's time to combine the two parts of the formula to determine the Vote Value Index in North Carolina:

We determine that my vote is worth 6.36 times that of an Oklahoman's vote. But don't feel too good for me, because my neighbors to the north have a vote value over 41 times that of mine.

The absurdity of this situation leads us to a final question: if we were to scrap the electoral college and go to a straight popular vote, who would be the winners and losers? How does my vote compare in value between one system and another? Under a popular vote, everyone would have equal influence, and candidates would have to seek every vote they can get, in every state. No one could say that their vote was worth less than another's, no matter what state they live in. But how do we measure the difference?

I divided each state's VVI by the average of all states' VVIs to determine how valuable your vote is now, compared to a popular vote system.

Rank: State: Value vs. Pop Vote: 51 OK 7.7% 50 NY 7.9% 49 AL 9.0% 48 DC 9.4% 47 LA 10.1% 46 UT 10.3% 45 IL 10.6% 44 TN 11.5% 43 MD 11.6% 42 MA 12.1% 41 KY 12.2% 40 CA 12.6% 39 MS 13.5% 38 TX 13.7% 37 KS 14.1% 36 AR 14.4% 35 ID 15.0%

Rank: State: Value vs. Pop Vote: 34 SC 18.4% 33 WA 18.6% 32 HI 19.7% 31 GA 20.9% 30 OR 21.3% 29 IN 21.7% 28 NJ 21.8% 27 NE 23.8% 26 CT 25.8% 25 MO 26.6% 24 WV 27.0% 23 MI 29.6% 22 AZ 30.5$ 21 PA 33.4% 20 MN 36.6% 19 ME 44.0% 18 RI 44.0%

Rank: State: Value vs. Pop Vote: 17 VT 44.2% 16 NC 49.0% 15 WY 53.1% 14 MT 54.7% 13 NM 59.1% 12 SD 60.9% 11 WI 62.6% 10 AK 64.0% 9 ND 80.4% 8 OH 84.2% 7 DE 90.2% 6 FL 147.7% 5 NH 203.6% 4 IA 250.3% 3 NV 297.0% 2 CO 826.9% 1 VA 2,013.0%

So, my vote in NC is worth roughly half what it would be under a true "one person, one vote" system. An Oklahoman vote is worth only 7.7% of a popular vote, whereas a Virginia vote is worth more than 20 times as much as a popular vote.

As it turns out, the voters of only six states have an advantage this year under the electoral college. These six states represent about 16.8% of the national voting-eligible population. The other 83.2% are shortchanged.

Again, my full data set is available for perusal.