Positive Liberty

I have just engaged in a long and bitter debate on Ed Brayton’s Dispatches from the Culture Wars blog about the power of one vote. Many Democrats are concerned about a repeat of 2000, when Ralph Nader stole enough votes from Al Gore to cost Gore Florida’s electoral votes (conveniently ignoring the other causes of Gore’s loss, such as his failure to win his own home state), and some of Ed’s readers were outraged that he plans to vote Libertarian–voting Libertarian, they fear, will take votes from Obama and allow McCain to win. Setting aside the dubious proposition that there are enough libertarians who might actually vote Democrat to make the difference in the election, the argument was stimulated by my claim that one vote can’t change the outcome of the election, and so no individual should change their vote for fear they’ll help their least-preferred candidate to win. This simple, and logically irrefutable proposition, caused a firestorm of disagreement and claims that voting Libertarian was “dishonest,” “illegitimate,” and ‘inexcusable.” Setting aside also these readers’ disturbing reluctance to grant their fellow citizens freedom of conscience at the ballot box, these arguments were all based on the continued belief that one vote can make a difference. It is fairly easy to see where this belief comes from, but it’s based on a continued confusion of two distinct levels of analysis, group-level vs. individual level, a distinction which is easily sorted out, for those willing to set aside their preconceptions and think analytically.

Strategic Voting

What the Obama supporters are arguing is that one should vote Democratic this year, even if that is not one’s real preference, in order to ensure McCain does not win the election. Voting against your true preference, in order to achieve another goal, is called <i>strategic voting</i>, and it’s both entirely legitimate, and in some cases quite sensible. For example, let’s say there are three friends deciding what to do this evening, and each proposes a different option. Angie asks to go to an art gallery, Barbara begs for a baseball game, while Connie cries for a concert. Let’s say that Angie’s <i>preference order</i> is art, baseball, concert (that is, she prefers art to baseball, baseball to a concert, and, of course, art to a concert). Barbara’s preference order is baseball, concert, art. And Connie’s preference order is concert, art, baseball. That’s hard to remember, so let’s make it more visual.

Angie art baseball concert

Barbara baseball concert art

Connie concert art baseball

Being fair-minded (but naive) friends, they agree to vote. When each votes their real preference, however, they reach a three way tie. Connie, being somewhat cleverer than her friends, realizes the value of strategic voting–that is, she realizes that if Angie votes strategically, choosing baseball over art, then baseball will win and she, Connie, will have to go along with her least preferred option. As she despises baseball, and doesn’t really mind going to an art gallery, Connie suggests they vote again, and switches her vote to “art.” There are now two votes for art, and 1 vote for baseball, so baseball loses, and Connie breathes a big sigh of relief as strategic voting has saved her from the worst outcome. (If Connie is really clever, she now proposes a vote between the two finalists, art and a concert–a close look at the preference orders will show that she would win that vote and get her preferred outcome.)

This is exactly the type of strategic voting that the Obama supporters were urging–shift from first preference (Libertarian) to second preference (Democrat) in order to prevent a win by third preference (Republican).

Of course that depends upon that being my preference order. I doubt it necessarily is for most libertarians, but it depends on what their strongest issues are. For those libertarians whose strongest issues are civil liberties, gay rights, the rule of law, and avoiding more wars, Libertarian > Democratic > Republican might actually be their preference order. For those whose strongest issues are low taxes, low business regulation, free trade, and gun rights, the preference order is more likely to be Libertarian > Republican > Democratic, in which case the Obama supporters should <i>not</i> want them to vote strategically: for all their fear that a Libertarian vote is actually a vote for McCain, an actual Republican vote is even more of a vote for McCain. So they really don’t want all all Libertarians to vote strategicallly. The implicit assumption was that Obama was my second choice. But I gave them my actual preference order, which, at present, is: Libertarian = Obama = McCain. In fact because I rate the options equally, it is actually impossible for me to engage in strategic voting–I have no first preference to set aside, no second preference to select instead, and no third preference to want to avoid. It may seem illogical–downright bizarre and irrational–to many that I don’t have a strong preference, but it’s true. I’m unable at this time to decide which values matter most to me, so although I recognize the differences between McCain and Obama I can’t decide which set of differences to use to determine my preference order. And while I usually vote Libertarian, the selection of Bob Barr as the candidate, has dropped them from first preference to a tie (I am not convinced Bob Barr is not still a traditional southern conservative, a group I despise).

Analyzing The Power of One Vote

But the example above shows when strategic voting does work, when the voting group is small. There’s no absolute group-size threshold for strategic voting, but as the group gets larger, the possibility of successfully engaging in it diminishes rapidly, as illustrated in the following figure.

Why is this so? It’s a simple matter of how likely the electorate is to make a decision by one vote. When the decision is made by one vote, then one vote can make the difference. In an electorate of 3, as in the example above, the probability of a decision by one vote—or a tie, which can be broken by one vote—is very high. In small electorates in general, the probability is substantial enough to take seriously. In my college’s faculty meetings, I’m always on the lookout for the probability of strategic voting (although, in practice, we rarely vote until there’s something near consensus). Anyone who reads the newspaper obsessively after elections will nearly always find a story about some election that was tied, or decided by a single vote, but those are always in small electorates, generally where less than 100 people have voted. An example from this year’s August elections came from Tennessee, where a candidate won the position of county constable by one vote—where hers was the only vote cast. In an electorate of one, that one vote will always determine the outcome.

But what about in a presidential election? In the last presidential election, around 100 million votes were cast, and it’s likely there will be around that many again. The odds of 1 in 100,000,000 being decisive are beyond remote, but that’s not the accurate calculation, due to the electoral college. As one state can be decisive in a presidential election (in each of the last two, a switch by any one state would have changed the outcome), let’s consider my vote in my state, Michigan, which is considered by many to be a swing state. Michigan is an apt example, too. Having gone Democratic in the last four presidential elections, we can—all else being equal—expect it to go Democratic again, but if it did go Republican, it would be nearly impossible for Obama to win. So if my vote could affect the outcome in Michigan, it could affect the ultimate outcome in the presidential election.

Pretty heady stuff! I suspect nearly everyone would like to be in that position. But how likely is it? In 2004, 4.7 million votes were cast for John Kerry and George W. Bush (and about 48,000 for other candidates). Kerry received 2,479,183 votes, and Bush received 2, 313,746. The percentage difference was 3%, and the absolute difference was 165,436 votes. If the differential was over 165,000 votes, it takes a bit of credulity to believe that one vote could make the difference.

But let’s give the other side the benefit of the doubt, and assume the election is much closer. Let’s say turnout drops to only 4 million (the lower number helps my opponents’ argument by shrinking the electorate slightly, and is easier to work with mathematically), and the race is so close that there’s only .01% difference between Obama and McCain. A .01% difference would have everyone talking about the amazing closeness of the Michigan vote—although it would not equal the astounding closeness of the Florida vote in 2000—and would mean a differential of 40,000 votes. That is, even if the race in Michigan is closer than Michigan has ever been (at least in my memory), the differential between the candidates will still outweigh my vote by a ratio of 40,000:1. So no one need fear that I might vote Libertarian: If I do, the outcome won’t change.

Groups vs. Individuals

The most common response to this is to ask, but what if everyone else thought the same way? Indeed one commenter on Dispatches asked about the hypothetical of going back in time to tell the Ralph Nader voters in Florida the consequences of a Bush presidency. If they all changed their minds, Bush would never have been president. Indeed, it would only have taken about 1,726 of the 96,837 Nader voters, a mere 1.7% of them, to change the election. But again, we’re now talking about a group rather than an individual. It is absolutely critical to not confuse the two.

Let’s extend this example a bit. Let’s say we could go back to Florida, and give the Nader voters full information, giving them information showing how bad the Bush presidency has been (and I do think it’s been disastrous), telling them there will be 96,837 Nader voters, and that if just 1,726 will change their vote to Gore, Bush will never win. Let’s also assume that in fact they do have a strong preference for Gore over Bush, so that they would in fact strongly prefer Gore to win. Now, does any one of those Nader voters have an incentive to switch their vote? The answer is no. Again, let’s focus at the individual level, and don’t get confused by sliding up to group level. Let’s say Floridian Andy Andrews is a Nader voter who mildly prefers Nader to Gore, and strongly prefers Gore to Bush. He seems like a natural switch, but he’s not. Let’s say he, and only he, switches his vote—Bush still wins, and Andy cast his vote for someone he didn’t prefer; it’s a lose-lose for him. Now let’s say every single Nader voter, including Andy, switches his vote—Gore wins, but Andy didn’t need to vote that way to make it happen. In either case, his vote is washed out by the mass. Yes, he is a part of that mass, but he could have kept his vote for his most preferred candidate and the outcome wouldn’t have changed.

What if everybody thought like that? Well, then nobody would change their vote, in which case we’d have the first example, where only Andy changed, and as we saw, it was pointless for Andy to do so. That’s why it is critical to distinguish between group level and individual level analysis, and not get them confused. What the group does affects the outcome, but what the individual does has no effect—and so the individual, who has only his/her own vote, need not worry about the whole group.

Of course if we did the time machine trick, some people would change their vote. We’re not all perfectly rational. But the fact that they would change their vote has no bearing on what effect their vote actually has.

So Is Your Vote Meaningless?

Another response to this argument is that I am stripping the vote of all meaning, and the idea that someone would claim that their vote is meaningless is very offensive to people. But meaninglessness is not a logical corollary to the ineffectiveness of the vote. There are two different types of meaningfulness, or value, to the vote. One is it’s instrumental value, that is, using it as an instrument to effect a particular outcome. As I’ve argued, a single vote in a large electorate is meaningless in that sense, as it has zero instrumental value. But the other type of value is consumption value—the direct value to the person who casts a vote, so as long as the person is able to cast that vote, their vote will be meaningful. They will feel good about having exercised their constitutional rights; about having been a part, however small, in the grand spectacle of democracy; about having demonstrated their support for their candidate. So yes, the vote has meaning, but little is gained by misinterpreting the argument as an attack on the concept of voting.

I think part of the underlying concern is that by denigrating the value of the vote in any way, I appear to be refuting the general thrust of U.S. history, which has been the struggle to extend the vote to more and more groups. In the 1830s it was the extension of the vote to non-propertied white males, in 1920 it was the extension of the vote to women (in practice, white women only), and in the 1950/60s it was the extension of the vote to African-Americans (finally realizing a constitutional right created a century earlier), and by extension to all minorities, and in 1971 it was the extension to young males who might be drafted to fight in Vietnam. Most important in this history is the battle of women and of African-Americans to get the vote, and it might seem that my argument diminishes the importance of their struggles. Again, that is an inaccurate extension of the argument, because although it is the individual that votes, it was the class, the whole group that was denied the right to vote, thus leaving the group without representation in government. If one African-American person chooses not to exercise his/her right to vote, that is not a tragedy, but if the whole group of African-Americans were disallowed that right, it becomes a tragedy. Again, this is the distinction between a group and an individual.

Here’s a simple thought experiment to compare the value of an individual vote vs. a group vote. If, through some form of magic, you could save the lives of 5 children by sacrificing your right to vote for the rest of your life (but not any of your other political rights, such as to speak, contribute to candidates, etc.), would you do so? Personally, I would—the lives of 5 children are far more valuable than my individual vote. But what if you could only save those 5 children by sacrificing the voting rights of all members of your class (whether you’re male, female, black, white, etc.), for the rest of your life? I, at least, don’t like that tradeoff and would decline. If you don’t like that particular example, find some other that suits you better and ask yourself whether your own vote is really as valuable as the collective votes of your whole ethnic or gender group.

And the moral of this story is that the collective vote of the whole group is more important because it really can have an effect. Thus, whether or not any particular African-American votes, the effort of those who fought for, and in many case sacrificed their lives, for the right to vote was worth it.

So Why Do People Believe Their Votes Can Affect the Outcome?

This is the question that puzzles me. In fact I also used to believe in the importance of each vote, also. The turning point for me came on a job interview when a professor said he never voted; he gave money because he had more influence that way. I can’t say for sure where the idea comes from, but I think it stems from our civics education in elementary through high school, where we are taught that voting is a sacred act, and that every vote matters. We also get it through our media: I vividly remember after the 2000 fiasco in Florida, one talking head on television saying, “This proves that every vote counts.” Even though it was astonishingly close (less than a hundredth of a percent), it was still decided by 1,725 votes—meaning 1725 Bush voters could have stayed home without changing the outcome.

So it’s taught to us early, at least by implication, and reinforced by the media. And it’s appealing because it seems to add more meaning to our vote. But ultimately it’s self-contradictory—if everyone’s vote could decide the outcome, and there can, in the end, be but a single outcome, how could we decide which of everyone’s votes were the deciding factor?

Understanding Democracy

I also think that the myth of the effective vote is appealing because it fits our general conception of democracy, which is that the purpose of elections is to elect good officials who will give us good outcomes. We do after all, vote for Obama over McCain, or vice-versa, because we like his policies better, so it is hard to think of democracy in any way but as being about choosing good government. (And, before I proceed, let me hasten to say that I think it’s wholly appropriate that people vote on these grounds—it would be rather perverse to vote for bad government.)

A real life example helps illustrate this, and it’s another one of those moments that helped crystallize my thoughts on the matter. In 2005 I was asked to be on an interview panel for the local newspaper, to discuss the Iraq war on the second anniversary of the U.S. invasion. Also on the panel was a local Dominican sister from the Catholic university in my town. Dominicans are known for being liberal and pacifist, and she and I were substantially in agreement about the war. But then, while expressing her astonishment that George Bush had won re-election, she asked, “How can this be a democracy, if a person like him can be re-elected?”

The most direct answer is that in a democracy the majority rules, and sometimes the majority doesn’t agree with our views. Then the real question is “how can the majority be so wrong (from her perspective). But there’s a more subtle answer. It’s not necessarily that the majority is wrong (or stupid), but just that they have a set of values that differs from hers on some important issues. Those values are subjective, so we can’t actually say they are wrong. Only empirical claims can be wrong, and these values are not empirically testable.

But if we can’t say either side is objectively right or wrong, then how can we know if we got “the right” government in office? Simply put, we can’t. As deeply as I personally believe George W. Bush is the wrong answer to the presidency, his supporters believe he is the right answer, and there’s no way to empirically test it. Sure, we can measure him against a yardstick of our values, but that’s a biased test. It’s not replicable by his supporters who will measure him differently on those same values, or insist on a different set of values measurement. For example, if I value George W. Bush on national security, I give him a failing grade, but it’s easy to find intelligent people who give him a passing grade. There’s just no way to objectively say whether democracy gave us good government or not.

But perhaps that’s not the point of democracy. Perhaps the point is simply to ensure the worst don’t get into office—that is, to prevent tyranny. Tyrants nearly always take power by non-democratic means, and once they get in power they are sure to prevent real democratic referenda on their rule. The process of having to appear before the public and reveal so much of yourself allows us—at least as a general rule—to weed out the worst. The example I use in class is David Duke, a former Grand Wizard of the Ku Klux Klan. From my perspective, a Klan member is an example of the worst type of person, because they would deny rights to a class of people based solely on their innate characteristics. Although he could win some small scale elections, he never managed to win a race for the House or Senate. And while critics might consider Bush an example of the worst, it is clear that he is not a true tyrant in any meaningful sense of the word: following 9/11 he explicitly refused to blame Muslims or Arabs as a class; despite trying to pervert the justice system in pursuit of the war on terror, he has repeatedly bowed to the Supreme Court when it ruled against him; and he will not take any steps to remain in office if Obama wins the campaign.

This is not to say democracy will always fulfill that function. Nixon may have been a very close call, in that he actually did try to subvert democracy by rigging the 1972 election ( yet even he willingly relinquished power, rather than mobilize the army to suspend Congress and the Courts). But certainly democracy is the only system that has a meaningful chance to weed out the worst.

The implication is that, by the time we get to the general election, the worst have generally already been weeded out. And in my view, that is true for all the presidential elections of my lifetime, even for those presidents/candidates I personally dislike. That means I shouldn’t take my vote too seriously in November. First, it’s not going to change the outcome, and second, I can live with the outcome, however imperfect it I think it is.

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