Steven Levitt says that he has a “good indicator” that Aaron Edlin, Noah Kaplan, Nate Silver, and I are “not so smart”

by Andrew Gelman on October 25, 2012 · 47 comments

in Campaigns and elections,Methodology

Here’s the transcript (link from here):

DUBNER: So Levitt, how can you in your life, when you wander around, tell the difference between a smart person and a not-so-smart person?

LEVITT: Well, one good indicator of a person who’s not so smart is if they vote in a presidential election because they think their vote might actually decide which candidate wins. . . . there has never been and there never will be a vote cast in a presidential election that could possibly be decisive.

In Illinois in 2012, sure, I don’t think there’s any chance that a single vote, or any thousand votes, could determine the presidential election. So I’m with Levitt regarding his particular vote in his state. In swing states (or for close non-presidential elections), though, it’s a different story Aaron, Nate, and I have estimated the probability of your vote being decisive in a swing state as being in the range 1 in a million to 1 in 10 million. Low, but not zero, and Aaron, Noah, and I argue that it can be make sense to vote because of the social benefits that a voter might feel arise from his or her preferred candidate winning.

I have no problem if Levitt wants to argue that it doesn’t matter who wins the election—I disagree with him, given the evidence that the positions of the Democratic and Republicans in the U.S. are farther apart on economic issues than are left and right groupings in many other countries, but Levitt can make that argument if he wants to. And I have no problem if Levitt wants to say that, for a one in a million or one in ten million chance, he doesn’t think it’s worth it to vote. As Aaron, Noah, and I write, we think of such a vote as equivalent to the purchase of a lottery ticket which, if it wins, corresponds to a huge donation to a charity—but I realize that not everyone will agree with this. But I don’t think Levitt is making sense when he writes that “there never will be a vote cast in a presidential election that could possibly be decisive.” A low probability is not a zero probability.

Levitt follows up:

And one thing we see for sure, and we saw it in the Gore versus Bush election is that if it’s even within thousands of votes it’s not the votes themselves that decide the election, because nobody can figure out how many votes were cast. It’s the courts that always decide, the judges that always decide. It’s virtually impossible that any vote you cast in a national election could ever actually be decisive.

This reflects a common misunderstanding and probability and uncertainty. At a purely technical level, it’s not true that litigation of elections means that a single vote can’t matter. Most elections are not litigated, and your vote can be the one that makes the election close enough to send it to the courts. Under any reasonable model, the probability that your vote determines the election is the same whether or not the courts are involved, and you can show this by adding up the probability of any vote margin being decisive. For a mathematical derivation, see page 674 of our article in the British Journal of Political Science.

This confuses a lot of people, so I can understand Levitt missing the point, but it’s important. Just cos you don’t know whether a particular vote was decisive, that doesn’t mean a single vote can’t be decisive. Or, to put it another way, when he says “virtually impossible,” I’d say “1 in a million to 1 in 10 million if you live in a swing state.” Levitt’s statement, “It’s the courts that always decide, the judges that always decide,” misses the point in that your vote can be the one that triggers the recount or that sends the case to the courts.

Levitt also says:

If anything I think you want to go in the other direction and find ways to let people who care a lot vote repeatedly. That’s really more in the spirit of trying to get to the right answer. That way you get the people who have the strongest convictions acting most aggressively to express those convictions.

I don’t know if this will make Levitt feel any better, but this is the system we currently have in the United States! We have lots and lots of elections, with relatively high turnout (60%) in presidential elections, lower for governors and congress, still lower for state legislators and local elections, etc. Indeed, people who care more about politics do get to vote “repeatedly,” while people who are more indifferent can vote never or only occasionally. I’d never thought of this as a feature of our electoral system but I suppose it is.

P.S. I would not conclude from the above discussion that Levitt is not so smart. Of course he’s very smart, he just happens to be misinformed on this issue. I applaud Levitt’s willingness to go out on a limb and say controversial things in a podcast, to get people thinking. I just wish he’d be a bit less sure of himself and not go around saying that he thinks that Aaron, Noah, Nate and I are not so smart.

P.P.S. I live in New York, so, like Levitt, I don’t think my vote has any chance of making a difference in the presidential election. But if I were voting in a swing state, that would be a different story.

P.P.P.S. Yes, this has come up before.

P.P.P.P.S. The linked podcast also includes some very reasonable comments by Bryan Caplan on the motivations of politicians trying to get the support of confused and ignorant voters.

{ 47 comments }

TM October 25, 2012 at 2:10 pm

Saying that a vote is wasted if it’s not decisive is a pretty clear sign to me that Levitt is not a smart person. Collective action requires many people to act in unison while simultaneously realizing that their own particular contributions would not be missed.

Besides, if you don’t vote, maybe some people you know see your behavior and decide not to vote either. Any then their behavior affect some other people, and so on.

Also, it’s perfectly rational to vote for your candidate in a non-swing state. The size of the popular vote victory is not legally binding, but it can influence the political environment. This year, while the electoral college might depend only on a couple swing states, Obama might need to run up to score in states like California and New York to maintain a popular vote victory.

zbicyclist October 26, 2012 at 7:30 pm

I might change “collective action” to “social capital”.

Nearly all the individual actions that contribute to social capital are done by people who seem to be suckered into serving on meaningless government boards, being the 9th person to show up to cook a meal at a shelter when it turns out they only need 8 people, volunteering to drive a neighbor to the hospital even when it turns out she dies in the hospital and can’t thank you, holding the door for a person who’s clearly healthy enough to hold it open themselves, buying cub scout popcorn when you have only grown daughters in other states and other stupid things.

Besides, I’ve actually voted in an election (mayoral) decided by one vote.

Bill Jefferys October 26, 2012 at 9:14 pm

So, did your candidate win or lose?

zbicyclist October 27, 2012 at 3:01 pm

Lost. This seems to mean that my wife’s vote was decisive ;)

Sebastian October 25, 2012 at 2:26 pm

The other thing is, that even if Levitt weren’t wrong, it would still not be a good indicator for “being smart”, especially for a situation that’s described as “when you wander around”.

How would you learn that about a person? It’s clearly not enough to check whether a person votes – there can be all kinds of reasons. Nor is an opinion along the lines of “every vote matters” going to tell you much – that may just as well be an expression of a normative position on the civic duty of voting.
So you’d have to, while you “wander around”, ask people a very specific question about their probability estimate that their vote in a Presidential election would be decisive. That’s a rather odd thing to do.
But even with that knowledge, you don’t learn anything about “smartness” – you learn whether a person has good statistical intuition or training. You’re also going to consider people with some training in political science and economics disproportionally smart.
So if Levitt thinks this is a good indicator, that doesn’t really say anything about how “smart” he is, but it does show that he hasn’t spend much time thinking about, let alone studying, what constitutes a good indicator.

Rob October 25, 2012 at 2:26 pm

Levitt is, in a sense, defeating his own argument when he brings up Bush v. Gore and the idea that judges decide the outcome of close elections. When we stop to think about it, the 2000 election was decided by a single vote…Anthony Kennedy (or any of the other 4 who ended the recount in FL). How did they get into a position to do that? Based on the winner of the 1980, ’84, or ’88 Presidential Election. So, in a convoluted sort of way, an individual’s vote in the present election may not decide the outcome in that particular year but it may help elect the president who nominates the judge that eventually casts the single deciding vote!

Bill Jefferys October 26, 2012 at 9:17 pm

It was actually Sandra Day O’Connor’s vote that was the deciding vote.
She has since regretted that vote.

Jason October 25, 2012 at 3:01 pm

Elections are determined by votes, and the votes have to come from somewhere!

Joel October 25, 2012 at 3:05 pm

Theoretically, you’re right that there’s a big difference between 0 and 1 in 10 million, but is there a practical difference? Even if the United States keeps having elections every four years for many millennia (which seems like a generous assumption), the expected number decided by a single vote is still zero.

Joel October 26, 2012 at 5:58 pm

Not it.

Africanist October 25, 2012 at 3:18 pm

“Under any reasonable model, the probability that your vote determines the election is the same whether or not the courts are involved, and you can show this by adding up the probability of any vote margin being decisive.”

This, of course, assumes that there is some vote margin that will be decisive, and I don’t find that to be very accurate. A better assumption is that there is always some actor with the capacity to overturn an election result (a Supreme Court, the military, an incumbent who refuses to cede power, etc.) Such an actor is likely to overturn the result if they think that they can get away with it. Vote totals may factor into this analysis, but not necessarily in an especially important way. Whoever is thinking about overturning an electoral result is going to be mostly interested in the reaction of either other key actors (whose opinions won’t be reflected in a vote total) or of the masses in general, in which case they’ll care about the opinions of the whole population, not just the voters, and will need to evaluate the opinions of those who did not vote. Either way, your influence is the same whether you stay home or go to the polls.

Now, that’s an extreme view and probably more descriptive of the developing countries I study than of the United States (where realistically the vote margin is influential – the Supreme Court probably couldn’t’ve gotten away with giving Bush the election if Gore had won Florida convincingly), but Levitt’s claim is not without justification.

Andrew Gelman October 25, 2012 at 3:50 pm

Africanist,

No no no no no. You write, “Such an actor is likely to overturn the result if they think that they can get away with it.” But your vote could be the one to make the election not-close enough that they won’t “think that they can get away with it.” The argument on p. 674 of that article applies.

Africanist October 26, 2012 at 12:35 am

Not my point; sorry if I was unclear. The idea is that, in many systems, thinking you can “get away with it” is unconnected to what the vote total was. It’s a function of the militaries preferences or some such.

Sebastian October 26, 2012 at 11:05 am

but think about the situation in those systems:
If the military can overthrow the election results no matter what, then it’s not just your vote doesn’t matter, it’s that elections don’t matter, which means the country isn’t just a low quality democracy, but no democracy at all. That’s not the universe of cases discussed here and I think regardless of how bad you think the US situation is, it doesn’t apply here.

But consider a case where the voter is uncertain about the ability of the military to overthrow post election (lets call p_o the probability of an overthrow given an undesirable outcome). Then you have a two-stage game:
1. Election
2. Military decides to overthrow

Now, if the military’s favored candidate wins the election, she is going to be the next president with probability 1. But if the opposition candidate wins, he is going to become president with probability 1 – p_o –> Hence, the electoral outcome does matter, just that the probability of you deciding get reduced by p_o.
This is not my specialty, but I think these types of models are standard for the electoral authoritarianism literature.

Africanist October 27, 2012 at 5:44 pm

That’s simpler than the model I was proposing. The model I have in mind is this. Suppose for simplicity that we’re just dealing with a military who prefers to overturn an election if they can get away it. Their concern is popular protest/uprising if they overturn, so they prefer to stay out of politics if at least X citizens support the election result. Importantly, they don’t just care about the preferences of voters, they care about the entire population. The election result provides perfect information about the preferences of those who vote, but the military also noisily observes support in the rest of the population. In this sense, the election does matter but it’s not deterministic. My claim is that given this form of relationship, the probability that your voter “matters” is dependent on X (contra Andrew’s claim for what might be called deterministic election systems).

How is this so? Fix the number of supporters at 80 (perhaps out of a total population of 80), so that the only action is in changing X. Next, for simplicity suppose that the observation of support is distributed uniform on its actual level +/- 10% (and thus unbiased in expectation).

First, if the military sets some level X <= 72, then no one's vote ever matters. No matter what, the military observes sufficient support that it stays out of politics.

Next, suppose the military sets X = 75. If turnout among supporters is at least 30, then your vote doesn't matter because the military observes a minimum of 30+(80-30)*0.9 = 75 supporters. Your vote is never decisive in the sense of shifting the outcome with certainty, but for any level of turnout below 30, your vote matters in the sense of shifting the probability of military intervention (e.g., if 10 people vote, the probability of military intervention is (75-73)/(87-73) = 0.143 but if you switch to voting, then this probability is (75-73.1)/(86.9-73.1) = 0.138 and so on). So the probability of your vote mattering is just PR(Turnout < 30). Just what this is will depend on the distribution from which we draw turnout, but given a reasonable one, this is strictly greater than 0 and thus than the probability of mattering given X=72.

Suppose we increase the threshold further to, say, X=78. Here, we see your vote matters for any turnout below 60 (78 = 60+(80-60)*0.9). Again, your vote "matters" for any lower level so the probability it matters is just PR(Turnout < 60) which of course is greater than PR(Turnout < 30).

This is what I've been claiming, hopefully the example clarifies it. There are many electoral systems in which powerful actors have the ability to overturn an election if they can "get away with it". Within these systems, those actors observe the vote total as a component of their overall calculation. Thus, election results genuinely do have effects; however, the probability that your vote will "matter" is conditional on the threshold set by that actor. I'm not necessarily claiming this for the U.S., but it certainly applies to many unconsolidated democracies.

Ted October 28, 2012 at 4:27 pm

That’s pretty neat and interestingly counterintuitive. I would tend to expect the opposite.

Sebastian October 28, 2012 at 6:16 pm

I’m not an Africanist, but my sense is that most elections in unconsolidated democracies are relatively competitive and that the actor able to overthrow the elections (typically the military or the incumbent) is backing one of the candidates. Unless I’m misunderstanding your model, you’re treating the election as a vote for a single candidate which seems odd and leaves out the possibility that the military backed candidate could win. I know the Latin American cases better, at least there, rigging of elections typically happened in at least moderately close contests (e.g. Mexico 1988, Peru 2000).

Africanist October 28, 2012 at 6:41 pm

I was just abstracting away from the issue of the military backed candidate winning in order to make the example simpler. I’m not trying to present a fully-specified model. It doesn’t really matter that the military-backed candidate could win for the generic results.

Taylor Harris October 25, 2012 at 5:02 pm

It seems obvious from the comments and the post that Levitt’s comments were not listened/read carefully. He does not say someone is stupid if they vote and has said many times that there are many rewards one could receive from voting. You also didn’t mention in your probability numbers whether you factored for your vote being counted in the first place. (One reason Levitt gives for why an individual vote will not make a difference.) I liked your observation that passionate citizens DO receive the opportunity to vote more than once. Thank you for the post.

Sebastian October 25, 2012 at 5:45 pm

Gelman specifically addresses the “believing your vote is decisive” question, not the “is it rational to vote” question. Same for my comment above.

I’d guess that the probability of your vote not being counted in the US is quite small and even if it were larger that also increases the chance that another tie-breaking vote isn’t counted.

Peter T October 25, 2012 at 11:13 pm

Levitt has millions of brain cells. The activity of any one of them cannot possibly matter. So he doesn’t bother thinking.

Alan (@SlackerInc) October 26, 2012 at 2:12 am

I feel like Levitt and even Gelman (sorry) are missing something important, having to do with collective action. They are both so focussed on an election decided by one vote, one wonders if they are befuddled by Zeno’s Paradox.

TM and especially Peter T in the comments are thinking about this more properly.

I brought this up to my son, and he immediately grokked it, objecting without hesitation that “it would be like saying that no single soldier can tip the balance of the war, so it doesn’t matter if they shoot or not”. Hadn’t thought of that analogy–smart kid! (And proud dad.)

Look at it this way: if it is a logical and sensible proposition not to bother voting because your vote won’t make a difference, this is not going to occur to just one person. There are a variety of psychological profiles among us, but given the vast numbers of us there is still plenty of repetition, plenty of people who think like one another. So any such idea, if it really did make logical sense, would be thought of by a significant number of people. And when collectively acted on by that significant number, it *would* have the power to swing elections (especially if, as I suspect would be the case, the types of people who would have this idea would not mirror the general population in their voting preferences). Thus it is a sort of paradox, as I alluded to in my reference to Zeno.

If you’re at a stadium, and you don’t participate in “the wave”, the wave goes on, right? Unless a lot of people think the same way. When you’re at the theatre seeing a superb production, and the cast goes out for their bows, they will still get the same feeling of recognition if you don’t add your clapping to the general applause–unless a lot of other people decide to do the same thing. If you’re a pallbearer at a funeral and decide to slack off, the casket won’t tumble to the ground, unless…well, you get the idea.

One more example, to illustrate the power of collective action in a slightly different way and bring it back to voting: Truman was able to famously hold up the false headline because he won Ohio and California by fewer than one vote per precinct. So given the massive scale of American elections, if we think of them as an agglomeration of many local elections conducted precinct by precinct, history was changed by one voter in each of those precinct elections in those states.

Sebastian October 26, 2012 at 11:15 am

I think you’re underestimating political scientists and economists, collective action problems are a constant presence in both fields. Both Levitt and Gelman are aware of this. It’s just not the question they’re discussing here.
Re-read Levitt’s quote. He says: if they vote in a presidential election because they think their vote might actually decide which candidate wins.
That second part is crucial to his statement and to Gelman’s answer. As Taylor Harris points out, Levitt agrees with you (and presumably Gelman) that there are many other reasons to vote – including a sense of civic duty or pride or colletive responsibility, or collecting “I voted” stickers, or getting a kick out of pouring over ballot booklets etc. etc.
The point that Levitt argues and Gelman disputes is a small subset of the reasons to vote, namely, that your individual vote has no chance of deciding the election.

Alan (@SlackerInc) October 27, 2012 at 5:23 am

“Levitt agrees with you (and presumably Gelman) that there are many other reasons to vote”

Were you intending to reply to a different comment? Because this doesn’t seem to relate to what I wrote at all. I’m not arguing about other reasons to vote, but arguing that yes, my vote can make a difference in a presidential election, at least if I’m in one of the states that my candidate of choice wins and said candidate does win the election. But it doesn’t have to be true that the candidate wins by one vote–that’s a fallacy, a variation of Zeno’s Paradox or perhaps the tragedy of the commons. My candidate wins by collecting a giant pile of votes that is greater than the number of votes the other guy gets. My vote is part of that collective pile, therefore it did make a difference.

Look, you might as well argue that an individual raindrop did not topple the levees in New Orleans. But without the combination of that raindrop and billions of others, the levees would have been just fine. Just because there is a little overkill does not mean each individual raindrop was not a factor.

How about this: if the candidate I prefer wins 55 to 45, then essentially s/he needed at least 90 percent of his/her supporters to show up and cast their votes that day. So I can look at it as my vote having counted as nine-tenths of a vote, in a way.

Sebastian October 27, 2012 at 12:20 pm

But then you’re just understanding of “decisive” differently than Gelman, Levitt, and most social scientists: For us, “Decisive” means that if everyone else voted the same way but you did/did not go vote the outcome would change.
That’s not the case in a 55/45 election, hence there is no “decisive” vote.
I’d also say that this isn’t a particularly unusual understanding of the word “decisive” – e.g. since people talk about SCOTUS decisions above: I’ve never seen a vote in a 6-3 or 7-2 decision described as “decisive”: A decisive vote is the one vote that tips the outcome.

I understand your moral position here – you “have to carry your weight” etc. – but “moral” and “individually rational” aren’t necessarily the same: That’s why we need morality. It’s also the reason why there is a huge literature on collective action dilemmas – something that wouldn’t exist if everyone was always “decisive”.

SlackerInc October 28, 2012 at 3:30 am

But it’s not just a moral position. When a candidate wins an election, it’s because s/he gets more votes than his/her opponent. Those votes are a collective pile that is made up of the individual votes of individual people. All of them are responsible for the win, collectively. It’s not as though there is even any attention paid to what time people vote, like “by the time I voted, my candidate had enough to win”.

Did you read my comment about stoning someone to death? By the logic you are promoting, the people who each cast a pebble can have a clear conscience about the victim’s death because (a) a single pebble by itself would not kill someone and (b) throwing one fewer pebble would not have saved the victim’s life. But surely you would agree that in fact all those who threw stones were culpable–not just collectively but individually. By the exact same principle, all those who vote for a winning candidate are responsible for his/her win.

Sebastian October 28, 2012 at 2:23 pm

responsibility and conscience are moral categories, not analytical ones.
Take your stoning example: Morally, I agree that all those throwing stones are culpable, analytically, though, I know that one more ore less person throwing stones doesn’t make a difference (i.e. “isn’t decisive”).
Again, this is where morality (and law) counterbalance the collective action issue: By holding everyone involved individually responsible, they take away the excuse that “my vote/stone wasn’t going to make a difference”.

I feel like you’re unfamiliar with the thinking on collective action problem and free riding more generally. This is a nice introduction:
http://plato.stanford.edu/entries/free-rider/

Alan (@SlackerInc) October 29, 2012 at 5:04 am

I reject your distinction, because the election of a president has moral consequences. People may get fed, or medical care, or not; people will be killed, or not, depending on who wins.

So while the mechanism is more indirect than throwing a stone, the culpability (or credit as the case may be) is similar

And I’ll just laugh off your attempt to patronise me (“nice introduction”, pffft), thanks all the same, as it’s abundantly clear to me that I possess an intellect far keener than yours.

Sebastian October 29, 2012 at 11:06 am

chill – I’m not patronizing – but it’s pretty clear that you don’t have an academic background in social science. Which is obviously fine and probably does show that you make better life choices than I do. But it does mean you’re missing a key distinction and key concepts that everyone else here is aware of.
I suggested a quick intro to get you up to speed on this – it’s fine if you’re not interested in that, but that means you’ll just keep talking past everyone else.
I’ll note that your last comment boils down to: “but Presidential elections are super important” – as if that’s something you’d have to convince people that study politics for a living of…

Alan (@SlackerInc) October 29, 2012 at 1:49 pm

Whether you really don’t understand my argument, or are purposely distorting it into an infantile platitude for the purpose of making it a straw man, it is evidently futile to attempt to engage you on the merits.

I will respond however to your supposition that “it’s pretty clear that [I] don’t have an academic background in social science”. My area of study as an undergraduate was history, undertaken at two different institutions. In one, history was classified as a social science; in the other, it was grouped among the “humanities”. An admittedly awkward fit either way.

However, I am married to a sociologist (master’s at KU), and we lived together during her graduate studies, when she and her cohort (and thus, by extension, I–particularly since I was not employed at the time) were steeped in “sociological imagination” . I read extensively from her seminar readings at that time. Additionally, my mother has a Ph.D. in sociology from UNC-Chapel Hill, and my father a Ph.D. in anthropology from Stanford. So in fact I do think I know a little about the social sciences, credentialled or not.

Economists, of course, are (Paul Krugman notwithstanding) generally outliers among social scientists given their right wing, libertarian views. Other social scientists, and especially sociologists, are at the opposite pole from that kind of individualistic ethos. So while it’s not entirely surprising that an economist would take a wrongheaded, reductionist position on voting that refuses to acknowledge people’s “influence” on an election unless it can be wielded by an individual *alone*, in a vacuum, I’m not sure why you would maintain that this would be a notion broadly accepted among the social sciences given their antipathy to most of the tenets of the “dismal science”.

BTW, the Russell Hardin article you linked is not in fact a “nice introduction” to anything, except as an illustration that no matter how impressive someone’s CV, they can still be spectacularly wrong. Brings to mind the mathematics Ph.D.s who bombarded Marilyn vos Savant with missives insisting she was wrong in her solution to the so-called “Monty Hall problem”, when of course it was they who were incorrect and she had been absolutely right all along.

Alan (@SlackerInc) October 26, 2012 at 2:26 am

Sorry, one more point that I just thought of. Anyone who would shrug and say “I won’t bother voting because my single vote doesn’t matter” is–if they think that the *outcome* of the election *does* really matter–essentially shirking their share of the “work” toward achieving a preferable outcome, dumping it off on a bunch of other people.

This occurs to me more readily because I not only vote, I also “GOTV” (get out the vote), volunteering every two years to call people and go door to door, reminding those that share my beliefs of the importance of voting in the election. So along with my actual vote, I might drum up at most a few dozen votes from other people (just a guess as I can never know for sure). Still not enough *by itself* to swing a presidential election, not even Florida 2000. And unlike voting itself, which as Levitt notes is pretty easy and sort of fun, GOTV is (for me at least) a royal pain in the ass. It’s drudgery, and I don’t like doing it. But I do it because I feel that it’s important (just like I donate a few bucks to the candidates I support, even though that too is just a “drop in the bucket”). And if I don’t do it, I’m essentially asking other fellow partisans to do my drudgework for me, because if all the GOTV volunteers decided to blow it off, in a close swing state like mine that would be enough to doom our side to defeat.

JM October 26, 2012 at 11:09 am

Ok, let’s read the transcript as it is: “if they vote in a presidential election because they think their vote might actually decide which candidate wins”. He states that believing that a single vote (yours, in fact) might decide on its own the result of the election is foolish. He does not say (or implies) that voting is foolish, or that you should not vote because of this or any other thing.
Also, when he says “there has never been and there never will be a vote cast in a presidential election that could possibly be decisive”, he’s absolutely right. Each single vote is as valuable as the the whole set of votes for that candidate. Your vote is useless without the rest of votes for the same option. Therefore, a single vote cannot be solely responsible for the outcome of an election.

Andrew Gelman October 26, 2012 at 11:50 am

JM:

Neither Levitt nor I ever said “solely.” That is your word. What I wrote is that your particular act of voting can be determine the outcome of the election (if you live in a swing state), in the sense that there is a probability that the outcome of the election would be different if you voted than if you didn’t vote. Edlin, Kaplan, and I discuss the implications of this fact in our article linked-to above, and there are further details on p. 674 of the other linked article discussing how the probability is defined in a setting where there might be a recount.

FredR October 26, 2012 at 1:10 pm

Even if your vote doesn’t or couldn’t possibly determine the election, there might be a way where it would still have an impact. Is there any good data on how a president’s mandate or lack thereof influences their actions going forward? I’m thinking that the bigger the popular vote win, maybe the more likely the president will implement more radical goals.

Sam R October 26, 2012 at 2:42 pm

OTOH, Levitt’s wretched analysis and inane promotion of the abortion-crime “relationship” tells us all we need to know about smart vs. not-so-smart economists.

Alan (@SlackerInc) October 27, 2012 at 5:48 am

I just thought of another analogy that should, I believe, frame the matter in a decisively stark way:

Let’s say a large crowd stones someone to death. There were no large rocks available, so each person throwing stones was able to only throw a single pebble. There were so many people throwing them, though, that this was more than sufficient to kill the victim. Can any single one of these people, when interviewed, declare their conscience clear, with no moral culpability–since the victim still would have died had they alone decided not to throw their own pebble?

bob October 28, 2012 at 11:21 am

If the charitable lottery ticket was a key motivation, wouldn’t we expect substantially higher turnout in swing states versus the others? But even despite the vastly (and this is a great understatement) greater resources the parties put into turnout operations in these states, we see only a mild correlation between battleground status and turnout. Wisconsin and Minnesota are at the top, but borderline in terms of their battleground status. Florida and Nevada–states where the decisive vote scenario is the least implausible–are #20 and #44. Ohio is #15. And the variance in turnout is probably an order of magnitude smaller than the variance in the likelihood of casting a decisive vote. I submit that if you controlled for the resources put into turnout operations, the decisive vote likelihood would no longer correlate with actual turnout rates at all.

And as Andy Perrin notes on scatterplot, even under the most rosy scenario for the influential voter (1 in a million), she is far more likely to die in a car wreck on the way to the polls.

Andrew Gelman October 28, 2012 at 2:01 pm

Bob:

As we discuss in Section 5 of our article, we do not think rationality is they key motivation; rather, we think this rationality is part of the reason that the psychological motivations work. Certainly there are lots of people such as myself voting in New York even in the absence of any chance of making a decisive vote.

With regard to your last paragraph: yes, you can get run over on the way to the polls. You can also get run over going to the movies. Does that say that nobody should go to the movies? The risk of getting run over is something people accept, for better or worse, and it’s not part of usual day-to-day decision making.

bob October 29, 2012 at 10:07 am

I apologize for not having read the article, and given my workload at this point, I likely will not have time to do so. If all you are saying is that people are sometimes a little bit rational, then sure, I could hardly disagree with that. But are you now implying that we should discount the irrationality of driving to the polls because people are routinely irrational about their driving habits?

bob October 29, 2012 at 10:09 am

Also, this is way outside my substantive field, but has anyone actually tested whether turnout in battleground states is higher, net of voter turnout operations?

Antonio October 29, 2012 at 11:02 am

So, if I live in a country where there is a stricly proportional electoral system, my vote has a practically zero value.

Sebastian October 29, 2012 at 11:45 am

In a Presidential system like France – yes (if you equate value = chance of being decisive).
In a parliamentary system, the chance of a vote making the difference between your party getting one seat more or less in parliament is probably higher. The chance of that being the decisive vote to elect PM is probably lower.
In many countries, Germany e.g., parties get campaign financing based on individual vote counts btw – in Germany that’s 70cents/vote, so you’re also making a direct campaign contribution by voting.hh

arin October 30, 2012 at 7:54 pm

Here in Italy we speak about “voto di scambio”, which is when a candidate pays some money to a group of electors for voting him (obviously it is illegal). Recently it has been discovered that a politician arrested for corruption had paid 50€ to every of his fellow citizens during a public dinner.
I’m afraid to think that this behaviour is much more rationale that voting because the vote contributes to support the party with a small amount like 0.70€, or because the vote is like a lottery ticket that in case of victory will give a benefit like 50€ to each other citizen in the country.
But it is my limit to not be able to conceive such form of altruism in the voting vocation.

Alan (@SlackerInc) October 29, 2012 at 2:07 pm

The fact that so many ostensibly intelligent people (not just Levitt) see this in what I consider a spectacularly wrongheaded way is fascinating to me, and it is intellectual food for thought to dissect the nature of the fallacious reasoning therein.

It occurs to me that a major problem here is that people on the “individual votes don’t matter in large scale elections” are arbitrarily assigning the individual voter in question to the group of votes that are the excess beyond the number the winning candidate needs (I’m addressing only voters whose votes go to the winner, as I do think it’s reasonable to argue that votes for the loser are futile). But there is no particular reason to assign a vote to that pile rather than to the pile of votes the candidate does need to win (the number the second-place candidate received, plus an additional number sufficient to have a statistically significant lead and avoid a recount).

In a probabilistic sense, the vote of an individual who votes for the winning candidate “matters” in direct proportion to that minimum winning number of votes divided by the actual number of votes the candidate received. So if the candidate needed nine million votes but got ten million, each of the voters in the winning candidate’s coalition can be reasonably said to have cast votes that “counted” for nine-tenths of their maximum value.

Sebastian October 29, 2012 at 4:33 pm

I’ll try this one more time, then I’ll leave you alone.
The issue is not logic, the issue is semantics, specifically two different understandings of the word “decisive”
To Levitt, Gelman, me, and probably most others here, “decisive” means the following:
A vote is considered decisive, if and only if the casting of that vote – with all other people voting the same way – will change the outcome of an election.

To you “decisive” means:
A vote is considered decisive, if the casting of the vote contributes in any way to the outcome of the election.

Neither of these definitions is logically wrong in any way, but if you don’t agree on what “decisive” means, all the rest of the conversation will be meaningless.

Since your son brought up the war example – that’s actually particularly instructive:
Any individual soldier has basically no impact on the outcome of the war. So, although, presumably, each soldier strongly prefers his/her country to win, it is probably rational for her/him to try to get away from the frontline or get lightly injured on purpose. But, of course, if _everyone_ did that, the army would have no soldiers and lose. That’s the definition of a collective action dileamma. These are very real dilemmas armies face, particularly during wars like WWI and II with high numbers of theater deaths. As you, as a historian, know, this isn’t hypothetical. To counteract that problem armies go much further than appeals to duty and team-spirit: Punishments for desertion during wartime are severe and often public to deter others. And when you appeal to people’s duty to “carry their burden” – be it by voting or by doing GOTV – that’s – albeit in a much lower pressure way ;-) – exactly the same thing you’re doing.

Alan (@SlackerInc) October 30, 2012 at 9:51 am

I can buy this being in large part a semantic dispute. But I would maintain that using a definition of “decisive” that leads someone to dismiss the significance of their vote is one of the best examples I can think of of missing the forest for the trees.

Eli Rabett October 29, 2012 at 7:19 pm

The median vote in 2000 was Sandra Day O’Connor. So much for Levitt.

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