Recently, I was surprised to see a long-term Libertarian’s car sporting a Kerry/Edwards bumper sticker. “What’s with the Kerry bumper sticker?” I asked my friend. “Isn’t it self-explanatory?” he replied sarcastically. “Okay, okay, I see that you're going to vote for Kerry. I just want to know why. I thought you would be voting Libertarian.”
He then proceeded to tell me that while he doesn’t like Kerry, he simply despises George W. Bush. “You don’t want to waste your vote on somebody that you fundamentally disagree with, do you?” I asked him. “I’ve been wasting my vote for years by voting Libertarian,” he replied bitterly.
“Ah, but you will be wasting your vote this year because Kerry is almost assured to take California. One extra vote won’t make a difference.” I hadn’t run the numbers, but I was sure that my friend’s vote wasn’t going to affect the California electoral vote and, therefore, had no chance of affecting the national result.
Since our conversation I have run the numbers, and they are mind-boggling. Based on these results, reasonable people may conclude that they should never vote. But if you do decide to cast your vote, as I have, you should vote for the best candidate and abandon any attempts to displace the disliked Kerrys, Bushes, Clintons, Reagans, Carters, and Gores of the world.
To run the numbers, I created a Monte Carlo computer simulation model and ran well over 300,000 simulations. My model has two pretty evenly matched main political parties and three smaller ones that fight over roughly ten percent of the vote total. I defined voting groups, each with probability distributions. With these groups defined, I ran multiple runs of the model at 5,000 iterations (5,000 elections) each while varying the number of total voters.
It turns out that your one vote, and mine too, has a probability of swinging any evenly-matched election based on the following formula: Probability equals 3.64 divided by N, where N is the total number of votes cast. So for a small election, say for a homeowners’ association with 100 members, your probability of casting the vote that determines the outcome is about 3.64 percent (or 0.0364). Stated differently, you’d have to vote in 27.5 elections to determine a single one. As we move up to the state and national level, the odds fall dramatically. With 11 million voters in California, where my friend and I live, the probability drops to 3.3 x 10-7 (0.00000033), which means that you’d have to vote in over three million presidential elections to determine the winner in California just once.
Of course, California isn’t the whole country. California currently has 55 electoral votes out of a total of 538, with 270 needed to elect a president. Since 1852, when Californians first voted for U.S. president, California has been a key swing state in only two presidential elections. In 1876, California cast 6 electoral votes for Rutherford B. Hayes, who beat Samuel J. Tilden by the razor-thin margin of 185 to 184. In 1916, California cast 13 electoral votes for Woodrow Wilson, who beat Charles E. Hughes by 277 to 254. In either election, if California voters had gone the other direction, the national totals would have followed. In every other presidential election, however, the winner was determined regardless of how Californians voted. By acknowledging that California has been a swing state in only two of its 38 elections (5.3%), we can get to our final answer: A voter in California would have to vote in 57.5 million elections to determine one President of the United States.
This ignores voting error and fraud, but even with them, there is still a point at which the official vote total swings from candidate A to candidate B. The question is whether you will cast that key vote. And the answer is that it's extremely unlikely.
What does this mean? Well, first of all it means that you’d have to vote for a very long time – 230 million years – to swing one election and all you’d have to show for it is a Bush in the White House instead of a Kerry (or visa versa). If you are like me and many other voters, you can’t get very excited about either Bush or Kerry, so your final payoff would be lackluster, at best. For those who still think these odds look acceptable, consider the following comparisons. You are 12 times as likely to die from a dog attack, 34,000 times as likely to die in a motor vehicle accident, and 274 times as likely to die in a bathtub drowning as you are to swing a presidential election.
My friend thinks that his Libertarian votes have been wasted and that his vote for a Democrat will matter. This analysis shows that his vote for Kerry has a vanishingly small expected value. Even if he would be willing to pay $10,000 to determine the winner in November, the expected value (probability times value) of his vote for Kerry is only $0.00017. Americans won’t even stoop to pick up a penny on the ground yet every four years they happily cast votes worth one fiftieth as much. Voting may still make sense, but the overall satisfaction of participating in a great democracy must be compared to the time and costs of voting. The expected vote-swinging outcome is rounding error. In fact, if you drive to your polling place, you are approximately ten times more likely to die in an accident on the way than you are to swing that presidential election.
Now, what if my friend votes for Michael Badnarik, the 2004 Libertarian candidate? Is that vote wasted? Well, it is clear that no third-party candidate will win the 2004 election, but my friend’s support would certainly help his favorite political party stay in business and therefore get noticed. While it is in business, his party will help define election issues and could even get lucky and elect a president. Abraham Lincoln and Jesse Ventura are good examples of third-party candidates who were elected. Ross Perot in 1996 and 1992, American Independent George Wallace in 1968, and Progressive Robert LaFollette in 1924 were presidential candidates who got a large percentage of the popular vote. More likely, as any third party becomes successful, the Democrats and Republicans will simply adopt that party’s platforms. The same thing happened with the Socialist party early in the 20th century. As Milton Friedman points out, the Socialists failed miserably with a popular vote total that peaked at only six percent in 1912. But they succeeded in the way that matters most. Dig below the surface and you’ll find that virtually every economic plank of the Socialist’s 1928 platform has since been written into law. The votes cast for these Socialists certainly weren’t wasted from the point of view of those who cast them.
Your one vote has the same power to affect the results whether you vote for a major or minor candidate, but a vote for the candidate you respect and agree with gives you the expectation of a better outcome. If you are like me and do take the time and effort to vote, you should put your X beside the candidate you think will be the best president, not the one most likely to beat the guy you dislike. The myth of the wasted third-party vote is just that – a myth. If there is a wasted vote, it is the one cast futilely against the candidate you dislike in an attempt to swing the national election.
September 21, 2004
