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The political penumbra of the political science of voting

- January 3, 2009

A couple of months ago, my article on the probability of a single vote being decisive in the presidential election (at most 1 in 10 million, according our calculations) was picked up by the Associated Press, and shortly after I received the following email from Deron Reynolds, a pilot in the U.S. Air Force:

After spending the better part of an hour yesterday composing and sending an email for my 12, 10, and 7 year old daughters extolling not just the right, but the responsibility of citizens of our country to vote, I opened the Stars and Stripes this morning to find an article titled, “Does Your Vote Really Matter?”

I’d like to start by saying that merely from the perspective of responsible citizens (which you all should be first and foremost, before journalist, professor, statistician, or soldier), the timing of this article being published on the eve of a national Presidential election is at best irresponsible, and at worst detrimental to the well being of the future of our country. Your statistical pursuit of – and your attempt to convince the public of – the notion that individual votes don’t matter undermines one of the basic tenets of our democracy. This alone should have derailed your misguided efforts to pursue this study or publish its “findings.” I’m sure you’re all justifying your actions now by thinking, “freedom of speech”, and “freedom of the press.” The problem with these rights of expression is that – just like the absence of laws to the contrary – just because you may do something doesn’t mean you should do something. With every “right” comes and equally important “responsibility” that increasingly is lost on citizens, and journalists and educators specifically. I hold the authors of the study and the publishers of the story in equal contempt, because such misguided words could not make it into the newspaper without the cooperation of both.

Responsible citizen argument aside, I’d like to challenge the logical fallacy in your argument of how individual votes “matter.” The article stated that the study, “examine[s] the likelihood that a single vote will carry a state and that particular state in turn will tip the balance in the Electoral College.” I can understand the intellectual curiosity in attempting to quantify this statistically, and I don’t see anything irresponsible with it at all. But where you miss the boat is when you make the leap to the statement, “What is the probability your vote will make a difference?” This is where you depart from an intellectual exercise and enter the realm of logical fallacy, demoralization, and misinformation.

Let’s take a fictional state as an example – call it Dantucky Suppose Dantucky has 101 eligible voters and the vote tally (after counting all votes, including absentee ballots of course) comes down to 50 for Candidate X, and 51 for Candidate Y. The individual who cast the “winning” vote for Y (call her “Jane”) could not have done so unless all previous 100 voters voted exactly as they did. Thus the effect of Jane’s vote could not have been possible if only one other citizen changed their vote. Therefore, every vote in the contest made the difference. But the contest doesn’t have to be that close for the same effect to be true. If the contest had come out with 46 voting for X, and 55 voting for Y, Jane and her four friends who cast the “winning” votes could not have done so if the other 96 voters had voted differently. Thus regardless of how close the election is, every single vote in the election “made the difference.”

Along the same lines, an even more misguided principle in the study/article is the question of whether “your vote will make a difference.” In the first Dantucky example, I placed the “winning” vote of Jane in quotations for a reason: who is to say it was Jane’s vote that was the swing vote? Who voted last? How would any citizen ever know that their individual vote put their candidate over the top? The obvious answer is all of the individual votes made the difference – every vote for Candidate Y put him/her over the top, and every vote for Candidate X gave the election its overall outcome. Every vote mattered.

While we’re talking statistics: according to your analysis, what were the chances (prior to the election) that 200 votes in Florida could have made the difference in the outcome of the Presidential election? A million to one? Worse? Nonetheless it happened. I can guarantee you that far more voters around the country realized that their vote really did count after that race. So should citizens of this country listen to your demoralizing “statistics” of how they are “far more likely to be hit twice by lightning,” than to make a difference in the election, or should they foolishly vote anyway?

Another danger of attempting to undermine the importance of a single vote is the fact that in the last 30 years, anywhere from 35-50% of the eligible voting population has chosen not to vote at all – probably because they didn’t think their vote mattered. However if those voters had participated in any of the previous seven Presidential elections, they could have not only changed any of the outcomes, but in most cases they could have elected someone different outright that was neither of the two major party candidates.

Finally, the immediate outcome of elections is not the only purpose of casting a vote. I personally have voted Independent and Libertarian before, and never felt that I was “throwing my vote away.” There are armies of people who study demographics and voting trends, and if every citizen in this country voted, and voted their conscience rather than trying to play politics with their vote (“If you vote for Barr you’re handing the election to Obama!”), you would see some fairly significant changes in the Candidate’s positions, issue choices, proposed legislation, campaign coverage, etc. But so long as the true power of the population remains dormant, and their actual thoughts and feelings on issues and character are not expressed in the voting booth, candidates and parties will continue to pander to what they currently see – a generally self-disenfranchised, somewhat disillusioned and uninterested voting population. While voting participation has improved recently, a great many Americans are still not wielding the power granted them by the Constitution of the United States. Studies and articles like yours are not helping at all.

Please take the time to ask yourself the following question next time you chose to create another study or publish an article: “Does this piece help the United States of America, or does it diminish it?” This filter would have prevented your terrible lack of judgement with this article.

I replied:

I appreciate your putting in the time to write me this note. In all of my statements on this topic, including research articles, blog posts, and interviews, I have emphasized that I vote myself, and that I consider it a privilege and a duty to do so. I consider our research to be in strong _support_ of political participation, and I wrote these articles to counteract the argument I sometimes hear, along the lines of “your vote has such a low probability of mattering, so don’t bother voting.” Our point is that, yes, your vote has a low probability of mattering, but that low probability is not zero, and it still makes sense (in many states) to vote, because of the huge impact your vote
would have, in the unlikely but not impossible event that it is decisive. Beyond that, as I said, I vote for president even though I live in New York because I see it as a privilege and a duty. I regret if I did not make this clear in my writings.

Deron then wrote:

I also appreciate both of you taking the time to respond. The article in the Associated Press/Stars and Stripes was not terribly detailed, and in typical fashion it did not include any background information. It certainly appears that you value not only the right, but the responsibility to vote. Now that I’ve seen your web site Iunderstand your intent is to help change public opinion away from its apathetic state toward voting participation.

I guess the phrase that I still take issue with is “low probability of mattering.” I don’t know if this term started with your research, the above mentioned article, or from the general public. But in my mind, there is no “probability of mattering”: _every_ vote matters _every_ time. The only _probability_ involved is whether or not an individual (or group of individuals) happens to be involved in an election that is particularly close, so that they might mistakenly
believe that “their” vote was the “deciding” vote.

In reality, _everyone_ who voted in the 2000 election participated in just such an event. My vote in Michigan was one of many that determined Michigan’s electoral votes went to Al Gore. The outcome in Michigan – and every other state in the union – set up the scenario that allowed the recount in Florida to be chronologically the last (but not the only) determining factor in the electoral vote count. But Florida wouldn’t have mattered if any one of a dozen states had voted differently, and many of them would have had different outcomes if small percentages had voted differently. The very idea that individuals in West Palm Beach believe they could have “single-handedly” changed the outcome of the election is just as flawed a belief as those that think that their votes don’t “matter.” In fact, every one of the roughly 100 million that voted in the election made the difference (mattered), and together they created the drama that ensued.