What's your vote really worth? Updated with post-election data.

In mid-October, I described a formula I developed to compare the value of a U.S. Presidential vote among states. The model takes into account the built-in advantage that smaller states enjoy under the Electoral College system, as well as the competitiveness of each state. The goal was to compare a voter's relative influence on the electoral vote tally. We're not looking for a voter's chance of being the single vote that decides the Presidency; we simply want to know how much they can tip the needle, compared to other states. If you haven't read my previous post, I suggest taking a look to see how I'm coming up with these values.

In the original post, which was three weeks before the election, I calculated the index using projections of the vote to come. Now that the election is over, let's see how those numbers hold up. Please note that the final numbers in many states have not been officially released, and some states are still counting. The numbers I am using are from David Wasserman's 2012 National Popular Vote Tracker as of November 25. The numbers will be updated over time, so this index is still preliminary.

As before, the values in the index use the least valuable vote in the nation as a baseline. Post-election, New York has edged out Oklahoma for the dubious honor of having the least valuable Presidential votes. All other states' scores are expressed as multiples of the New York value.

Rank: State: Value Index: 51 NY 1.00 50 OK 1.11 49 UT 1.26 48 MA 1.28 47 MD 1.28 46 CA 1.38 45 TN 1.50 44 KY 1.50 43 AL 1.65 42 IL 1.68 41 NJ 1.88 40 AR 1.90 39 LA 1.91 38 TX 1.98 37 HI 2.17 36 KS 2.22 35 WA 2.29

Rank: State: Value Index: 34 CT 2.33 33 ID 2.35 32 WV 2.50 31 DC 2.68 30 MI 2.82 29 OR 2.87 28 IN 3.03 27 MO 3.05 26 SC 3.60 25 NE 3.65 24 MS 3.73 23 AZ 3.95 22 GA 4.11 21 WI 4.66 20 PA 4.77 19 MN 4.88 18 ME 5.41

Rank: State: Value Index: 17 RI 5.53 16 VT 5.77 15 MT 6.18 14 CO 6.19 13 DE 6.21 12 NM 6.73 11 IA 6.78 10 WY 6.92 9 VA 7.25 8 SD 7.47 7 ND 9.05 6 NV 9.58 5 OH 12.65 4 NC 12.72 3 AK 13.87 2 NH 15.66 1 FL 30.18

As it turns out, there are some pretty major differences between the projected values and the actual. There are three main reasons for this. The first, and most important, is that when a state's competitiveness is included in the formula, it's going to bring a lot of volatility. Whether a state is considered a safe or swing state, the margins are going to fluctuate from one election to the next, changing the index. And because we used projections in the pre-election index, it was even more volatile. The projection data came from Nate Silver's FiveThirtyEight blog as of October 15. Silver's predictions were overall quite accurate on election day, but as the data was based on ongoing polling, the projections moved around throughout the campaign. Virginia had a particularly high Value Index in mid-October because the polling was razor-thin there at the time; Silver projected the margin at 0.1%. The actual margin in Virginia on election day was 3.9%; still close, but an order of magnitude from the projection three weeks prior. This is not a criticism of Silver's predictions; his numbers were based on polling, which was constantly affected by events in the campaigns and movements in popular opinion. If the vote in Virginia had remained that close on November 6, it would have easily deserved its lofty score; the closer the state's margin is, the more likely that a voter can push the needle and affect the electoral vote.

The second change in the data was the populations used. The formula does not use the state's total population, but rather the voting-eligible population (VEP), which includes residents who are U.S. citizens, at least 18 years of age, and not otherwise barred from voting (due to a felony, for example). For the previous post, I could not find VEP data that was current, so I used the 2010 VEP numbers from the United States Elections Project. Since the election, they have updated their VEP data for 2012, and therefore so have I.

The final change in the data is due to an error I made in the original data set. Remember how I tried to explain away the high score Delaware rated on the index? As it turns out, I had transposed the VEP amounts for Delaware and the District of Columbia. This caused Delaware's score to be inflated, and DC's to be deflated. I apologize for this error.

So, now that we have the post-election scores, what can we learn from this? For one thing, the "swing states" don't have quite the stranglehold on vote value that we saw previously. In October, the top seven states in the index (not counting Delaware) were the most-watched swing states in the election. In the final numbers, however, those seven states (VA, CO, NV, IA, NH, FL, OH) are spread out through the top 14 positions of the index. Most of the other states in between (such as Alaska, #3 on the index) were pretty solid in color. What gives? The swing states fell in the index in large part because they were not nearly as close as predicted in mid-October, with the exception of Florida. The collective margin of the six non-Florida swing states was 3.9% on election day, as opposed to 1.2% in the projection. This lowered their scores enough to be overtaken by a second effect: the small-state advantage. The Electoral College is designed to give states with small populations have more electoral votes per capita than larger states. This makes a vote much more valuable in a small state, even one that tends to vote solidly for one party. Alaska voted for Romney with a 14% margin, but since its population is so low, it would take a smaller number of voters to change that margin (and potentially, the electoral vote) than it would in a larger state with the same margin.

So we see that voters in both swing states and small states have an inherent advantage when it comes to the electoral math. We already know how this affects Presidential campaigning, as the swing states are cluster-bombed with negative attack ads, while the other states' issues and concerns are largely ignored by both sides. But there is a more fundamental problem with this system: it practically disenfranchises some voters, while others are "über-enfranchised," wielding outsized power compared to many of their fellow citizens. As the index shows, a vote in Florida in 2012 was worth more than 30 votes in New York.

Under a popular vote system, however, every citizen would have an equal vote, and their concerns could not be ignored due to accidents of geography. How does the current system compare to such a nation? Again, I compared the Vote Value Index to a one person-one vote system to see how the value stacks up. Below, the states are listed with the amount of value their citizens' votes hold, compared to their value under a popular vote.

Rank: State: Value vs. Pop Vote: 51 NY 19.8% 50 OK 22.0% 49 UT 25.0% 48 MA 25.5% 47 MD 25.5% 46 CA 27.4% 45 TN 29.7% 44 KY 29.7% 43 AL 32.7% 42 IL 33.3% 41 NJ 37.2% 40 AR 37.7% 39 LA 37.9% 38 TX 39.2% 37 HI 43.1% 36 KS 44.1% 35 WA 45.4%

Rank: State: Value vs. Pop Vote: 34 CT 46.3% 33 ID 46.6% 32 WV 49.5% 31 DC 53.1% 30 MI 55.9% 29 OR 57.0% 28 IN 60.1% 27 MO 60.5% 26 SC 71.4% 25 NE 72.4% 24 MS 73.9% 23 AZ 78.4% 22 GA 81.6% 21 WI 92.4% 20 PA 94.6% 19 MN 96.8% 18 ME 107.4%

Rank: State: Value vs. Pop Vote: 17 RI 109.7% 16 VT 114.4% 15 MT 122.6% 14 CO 122.8% 13 DE 123.2% 12 NM 133.5% 11 IA 134.5% 10 WY 137.2% 9 VA 143.9% 8 SD 148.2% 7 ND 179.6% 6 NV 190.0% 5 OH 250.9% 4 NC 252.2% 3 AK 275.1% 2 NH 310.6% 1 FL 598.8%

A vote in Florida under the current system is worth six times its value under a popular vote, whereas a New York vote only holds one-fifth of the value of a popular vote. Eighteen states, comprising 23% of eligible voters, hold an advantage, with their votes more valuable under the Electoral College. In the other thirty-two states and one district, 77% of us have less power to elect the President than they would under a popular vote.

This may all seem like a moot point, since the Electoral College is a part of our Constitution and cannot be abolished without amending it, which is a long shot at best. However, there is a practical way to institute a popular vote within the framework of the Electoral College, and without Congressional action. The National Popular Vote Plan, advocated by organizations such as FairVote, is a pact between states that can be passed by state legislatures. These states agree to allocate their electoral votes to the winner of the national popular vote. However, this agreement only takes effect when enough states have entered the pact to total at least 270 electoral votes, the number required to win the Presidency. This pact has already been passed into law by nine states, with 132 electoral votes among them (just under half of the requirement), and is under consideration by several other states. When you look at how many states are disadvantaged under the Electoral College, it is easy to imagine enough states joining the pact to change the system. This will only happen, however, with enough pressure from citizens on their state governments.

For anyone wanting to look at the data behind the Vote Value Index, I have a Google spreadsheet with the data.

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.