Articles by Jason Brennan

I just wanted to announce the publication of my book with David Schmidtz, A Brief History of Liberty.

It’s something of an unusual book for philosophers, because it’s as much a genuine history (and economics, psychology, law, and sociology) book as it is a philosophy book. I’d summarize our motivation for the project as follows: Dave and I note that historically, philosophers and regular people have used the word “liberty” to refer to a wide range of related things. When philosophers debate what the word “liberty” refers to, or which kind of liberty is most important, they often have a background assumption that liberty, whatever that is, is to be promoted by government in a particular way. But that’s not a good assumption. What role government, or any institution, ought to play in promoting a particular kind of liberty is determined not by conceptual analysis, but by investigating (empirically) what government and other institutions are likely to accomplish. What value any kind of liberty has is also for the most part contingent—we need to see what having certain kinds of liberties does to people, and what happens to people when those liberties are absent. Again, this goes beyond philosophy and requires empirical work. Also, what relationship different kinds of liberty with one another requires empirical work. For instance, while people might debate whether negative or positive liberty is more important, we instead note that empirically, it looks like protecting negative liberty has a long and non-accidental historical track record of promoting positive liberty.

Here’s the table of contents:

Introduction: Conceptions of Freedom.

1. A Prehistory of Liberty: Forty Thousand Years Ago.

2. The Rule of Law: AD 1075.

3. Religious Freedom: 1517.

4. Freedom of Commerce: 1776.

5. Civil Liberty: 1954.

6. Psychological Freedom, the Last Frontier: 1963.

Some of you may be familiar with Richard Tuck’s recent book Free Riding. It’s a fascinating and valuable work, but I think much of the central argument, especially about the rationality of voting, is deeply flawed. Anyways, here’s a link to my short critical note on Tuck at JESP: Tuck on the Rationality of Voting: A Critical Note.

Ok, if the mathematics discussed in my last post are right, here’s the upshot:

Condorcet’s Jury Theorem (in its original formulation) says that in an election between A and B (where A  is the right choice and B is the bad choice), for an electorate in which each voter has an independent probability p>.5 of voting for A (the right choice), then as the size of electorate increases, the probability that the electorate will elect A (the right choice) approaches 1. Even for a low value of p, such as p=.51, the probability that the electorate will choose A approaches 1 rather quickly. For instance, with 10,001 voters, the electorate already has about a 99% chance of picking A.

Some epistemic democrats defend democracy using Condorcet’s Jury Theorem. They claim that democracies are adequately modeled by the Jury Theorem, and that the average voter is more likely than not to make a good choice. There’s debate about whether democracies are well-modeled by the theorem (e.g., whether voters make statistically independent choices, and if they don’t, what impact that has). (E.g., see the chapter “The Irrelevance of the Jury Theorem” in Estlund’s [i]Democratic Authority[/i].) I’m with Jerry Gaus and Estlund–I don’t think actual democracies are adequately modeled by the theorem, so I don’t think that we can use the theorem to conclude that they tend to make good choices. (Nor can we use it to conclude that they tend to make bad choices. Note that if p>.5, then as the size of the electorate increases, the theorem says that voters are certain to choose the bad choice. And I think the evidence, if anything, points to p<.5. So, from my perspective, it’s a good thing Condorcet’s Jury Theorem doesn’t apply.)

;However, suppose you do believe that democracies are well-modeled by the theorem. If so, then it’s worth asking how many voters you really need. After all, the probability that the electorate will make the right choice shoots up near 1 pretty quickly, even when p is only slightly higher than .5. Every additional voter adds some small probability that the electorate will make the right choice. However, we get diminishing returns. The question is how rapidly the returns diminish. After all, in a high stakes election, the net value of A over B might be, let’s say, on the order of $10 trillion.

 Imagine that, just like the other voters, my p is .51. Still, suppose that my vote increases the likelihood that we’d make the right choice by 1% or even .001% Because the value of making the right choice is so high, then my additional vote counts for a lot–it has a lot of expected utility. [The expected utility of my vote in this case is the difference in value between A and B times the marginal increase in the probability that the electorate will make the right choice.] So, for example, the 1001st voter is adding only about .02% accuracy to the electorate, but that means her vote is worth $2 billion! [Note: I have the exact number at work, but I’m typing this at home. So it might a little off.] Think of the electorate as being like a machine making a choice that’s worth $10 trillion or $0. If you increase the likelihood that this machine will make the right choice by .02%, you’re increasing the expected utility of the machine’s choice by $2 billion.

So, at what N is the Nth voter only contributing a few dollars worth of accuracy? Let’s suppose that every voter has an opportunity cost of $100. That is, during the time she votes, she could have done something else worth $100 either to her personally or to promote the common good. At what N does adding additional voters become wasteful?

Now that it seems like I’ve gotten Mathematica to cooperate, it looks like for this example, where each voter has a p of .51, the net value of making the right choice is $10 trillion, and where we’re calling votes wasteful when they have an expected utility under $100, votes become wasteful at about N=100,001. (This isn’t exactly right–it’s just about the order of magnitude where the value of a vote is in the 10s. In fact, I’m calculating the value of 100,001st voter at about $26.) Note that if p is higher than .51, the net value of the right choice is lower, or if opportunity costs are higher, then N will be lower. So, N=100,000 might be a high estimate.

So, if you defend democracy using the standard formulation of Condorcet’s Jury Theorem, it seems that you should think having 120 million Americans vote is kind of a waste of time. It would be far better just to have a small number of people vote and have everyone else go about their day. 119,899,999 of these people are just adding unnecessary accuracy to an already impressively accurate machine. They should go do something else instead. We just don’t need mass democracy. It doesn’t do us that much additional good. The first 100 thousand voters contribute more than the next 100 billion. Etc.

Of course, you might say, “Well, if only 100,000 people voted, they might not vote for the common good but for their self-interest at the expense of the common good.” Maybe so. But if you’re saying stuff like that, I take it you don’t think democracies are well-modeled by Condorcet’s Jury Theorem.

All this hangs on my having done the mathematics correctly. So, I’ll double-check the results when I get back to work on Monday.

If the conditions of the Condorcet Jury Theorem hold, then every additional jurist/voter adds some marginal amount of accuracy to the jury as a whole.  However, this jury experiences diminishing marginal returns.  If every juror has a 51% chance of being accurate, then the jury of 101 members has about a 57% chance of being accurate, a jury of 501 members has a 67% chance of being accurate, a jury of 1001 members has a 73% chance of being accurate, a jury of 5001 members has 92% chance of being accurate, and a jury of 10,000 members has a 99.99% chance of being accurate.I’d like to know what the marginal value (in terms of her contribution to accuracy of the jury) of the Nth voter is when N is rather large.

The accuracy of a jury of N members when each juror has  a 51% chance of being accurate is given by the formula below:

Pa (probability the jury is accurate) = SUM [upper bound = N, lower bound = (N=1)/2] (N!/(N-i!)i!) * (.51^i) * (.49^(N-i))

Since that’s likely to be unclear, here’s a link to a nice print out of the formula:http://books.google.com/books?id=CdIOKZWc3oMC&lpg=PP1&dq=public%20choice%20iii&pg=PA129

It’s easy to calculate Pa using Mathematica for values where N < 6500.  After that, Mathematica and other programs can’t handle it. So, what I’d ideally like to do is find some program that can calculate Pa for higher values of N, such as N=50,000, N=500,000, N= 1,000,000, etc.

Alternatively, if there is some way to find the first derivative of this function, that might be helpful as well. Does anyone know how to do this?

What I’d really like to know is what the optimal number of jurors/voters is when the conditions of the Condorcet Jury Theorem obtain.  Even tiny increases in accuracy can have significant value if the value of being accurate is high enough.  So, for example, the marginal value of the 5007th voters is about 0.002%.  But if picking the better candidate is worth, let’s say, $1 trillion dollars, then the expected value of that vote is quite high.  But what’s the marginal impact of the 50,000th vote?  The 100,000th?  The millionth?I’m wondering if you think that democracies are adequately modeled by the Condorcet Jury Theorem (you shouldn’t, by the way), what’s the optimum number of voters?  Let’s say that the net value of being accurate is $1 trillion, and that adding additional voters is suboptimal once the marginal value of a vote goes below $1.  In that case, the optimal number of jurors (N) is given by the formula:1,000,000,000,000 * [Pa(N+1) - Pa(N)] = 1

Alas, despite trying many things over the past week or so, I have no idea how to solve this without a supercomputer.

Another alternative would be to find some upper bound and prove the the actual number is below this (already low) upper bound.  But I’ve been unsuccessful at that.

Yet another alternative is to calculate the real marginal value of votes at a bunch of Ns that Mathematica can handle, then run some regressions to find a function that models the marginal value well, and use that as substitute.  I’ve done that with a few different functions, but the problem is that these functions are of questionable accuracy for high values of N.Any ideas?

Here are some questions I’m thinking about, and I wonder what you think.

Suppose, for the sake or argument, I’ve established that voters have a duty to vote for candidates or policies which they justifiedly believe will promote the common good.  Otherwise, they have a duty to abstain from voting.

Suppose that vote buying and selling are not illegal.  Now, suppose when Alf votes, he only votes for candidates whom he justifiedly believes will serve the common good.   So long as Alf does that, is there anything wrong with him selling his vote?  Is there anything wrong with paying him to vote that way?

In the current draft of The Ethics of Voting, I argue that it’s not wrong.  So long as Alf is justified in voting a particular way for free, then it’s permissible for him to take money to vote that way and it’s permissible to pay him to vote that way.

I’m curious why anyone would think otherwise.  I’ve looked at the literature on vote buying, and I haven’t found any good objections to Alf’s vote selling.  Much of the empirical literature and the a priori public choice models describe vote selling as harmful, but that’s only because they discuss what happens or would happen when people don’t vote to promote the common good.  So while I think these arguments are good arguments for legally prohibiting vote buying, they don’t say much about Alf’s case.  For instance, many (but not all) public choice economists think legal vote selling would lead to rent-seeking, but these arguments assume that voters will vote in self-interested ways rather than abide by a duty to vote for the common good.

Rather than go on about why I think Alf’s case of vote selling is permissible, and rather than discuss some of the objections I consider, I’m just curious why some of you might think Alf would do something wrong in selling his vote.  It may be that I’m overlooking some killer objection.  Thanks!  -J

Hi everyone,I’m currently writing a book called The Ethics of Voting, and thought I’d ask you for advice and comments about what you’d like to see and what you think is important.  The book will cover the personals ethics of voting (questions concerning how individuals should behave) but not, for the most part, the political philosophy of voting (e.g., questions concerning who has the right to vote or how best to structure government institutions).

So, the basic questions of voting ethics that I plan to respond to are 1) Do I have an obligation to vote?  2)  If I do vote, do I have obligations to vote in particular ways?  3)  Is it acceptable to buy, trade, or sell my vote (not my right to vote, but my how I will vote)?  Related questions concern the source of any obligations, epistemic or other justificatory requirements, issues concerning whether citizens should be directed toward the common good or some other end, and so on.

As I’m envisioning it now, the chapters will roughly go something like this.  The introduction explains why voting is morally important.  Chapter 1 articulates various arguments in favor of a duty to vote and shows why they fail.  However, it also produces three arguments that seem pretty plausible and don’t look like they fail.  Chapter 2 articulates a theory of civic virtue and of citizens duties which refutes these remaining three arguments.  So the conclusion is that citizens don’t have an obligation to vote.  Chapter 3 discusses cases where citizens should refrain from voting rather than vote.  My view is that citizens have duties regulating how they vote if they do vote, but not a duty to vote.  In particular, a necessary but not sufficient condition for good voting is that citizens must be justified in the beliefs they base their votes upon.  Chapter 4 considers a wide range of objections and issues having to do with deference, autonomy, and abstention.  For instance, it considers issues about whether abstention involves a loss of autonomy, or whether one should always defer to known epistemic and moral superiors.  Chapter 5 argues that citizens have an obligation to vote for the common good rather than narrow self-interest, at least under normal circumstances.  It also gives a liberal account of the common good.  Chapter 6 argues that there is no special ethics of vote buying, trading, or selling.  Instead, what determines whether these things are right and wrong is specified by the obligations we have not to vote badly and to vote for the common good when we do vote.  So long as we don’t violate these rules, we don’t do anything wrong by buying, trading, or selling votes, though doing so may not be admirable.  (For what it’s worth, I haven’t written chapter 6 yet, so I might change my mind about these conclusions once I sit down to defend them at length.)   Chapter 7 will discuss relevant social scientific research to ask, in light of this research and my theory, how good are actual voters.  Finally, I might have a chapter 8, which will go over some issues of policy, such as compulsory voting.  I’ve written drafts of the introduction and chapters 1-4 at this point.So, that’s roughly what I expect to do.

 My question for you, if you’re interested in helping me shape the project, is what do you think I should cover?  What are some important issues or questions?  Obviously I didn’t specify everything that will go in the book (e.g., I will cover tactical/strategic voting), so if I didn’t list it, it doesn’t mean I haven’t thought of it.  However, there’s no doubt that there’s at least one obvious thing that I’ve overlooked. If you were writing the book, what would you talk about? How would you organize it?  So, I’m open to any and all suggestions.

Thanks!  -J

PS. For what it’s worth, I’m already spending a few pages in the current draft responding to an objection from Aaron Maltais that he posted here in response to my “Polluting the Polls” post. So, I really do find your suggestions helpful.

Lately, I’ve been wondering what it means to be a good citizen.  I’ve been working to develop a liberal theory of civic virtue that is, I think, properly purged of certain republican ideas.  That is, I think civic virtue for liberals is exercised primarily in non-political arenas, via activities we wouldn’t normally think of as expressing civic virtue.  More on that some other time.  As a piece of this broader project, I have a paper coming out in The Australasian Journal of Philosophy on the ethics of voting by this title.

Here’s the abstract:  Just because one has the right to vote does not mean just any vote is right.  Citizens should not vote badly.  This duty to avoid voting badly is grounded in a general duty not to engage in collectively harmful activities when the personal cost of restraint is low.  Good governance is a public good.  Bad governance is a public bad.  We should not be contributing to public bads when the benefit to ourselves is low.  Many democratic theorists agree that we shouldn’t vote badly, but that’s because they think we should vote well.  This demands too much of citizens.

So, in summary, on my view, citizens don’t in general have an obligation to vote, but if they do vote, they should vote well.  What I do in the paper is outline broadly what it means to vote badly, explain why I think you ought not to do it, and then answer various objections.

An outline of the argument is: 1.One has an obligation not to engage in collectively harmful activities when refraining from such activities does not impose significant personal costs.  2. Voting badly is to engage in a collectively harmful activity, while abstaining imposes low personal costs. 3. Therefore, one should not vote badly.

Some of the worries about this argument that I respond to are (among others): A.  If good governance is a public good as I say, shouldn’t everyone who benefits from this good contribute to it? B.  Don’t individual bad votes have incredibly low expected disutility, and if so, why bother prohibit bad voting? C. Does this position imply epistocracy (Estlund’s term, meaning the rule of those who know better) or something like it?  D. Is this view self-effacing? E.  What if citizens are good at judging character, even if they are bad at judging policies?

So, if people are interested, I’ll be writing more about this in the next few days.  Feel free to email me at Jason_brennan [at] brown.edu if you’d like a copy.  (I’ve got to make a final few revisions over the next few weeks anyways, so any comments would of course be welcome.)

[Update: I’ve added a bloggingheads video of Jason and blogger Will Wilkinson (Cato Institute) on this paper below the fold — SCM]

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