As Robin himself notes, the licensing of florists, funeral directors, and interior designers is not a big deal–certainly nothing on the order of the problems caused by overfishing, say, or by various trade and migration restrictions, or even the (arguably) large problems caused by policies such as the mortgage tax deduction which reduce people’s ability to move.

Nonetheless, Robin writes of economists’ disinclination to fight the licensing battle that it “saddens me more than I can say.” I don’t doubt his sincerity. but what’s most interesting to me here is to think about why this bothers him so much.

P.S. I certainly don’t mean this to be a personal criticism of Robin in any way. I certainly have my own things that piss me off for no particular reason, ranging from socks lying around on the floor–they’re not a practical obstacle so why does the messiness bother me so much–to misinterpretations (as I see them) of Bayesian statistics–things that are probably lower on the scale of importance than the net welfare loss caused by economists not fighting the licensing of florists.

There are so many things to be pissed off about, that the choice of what we decide to let bother us can perhaps be revealing.

The first paradigm–the one we’re taught in statistics classes–is of progress via “interventions” or “treatments.” The story is that people come up with ideas (perhaps from fundamental science, as we non-biologists imagine is happening in medical research, or maybe from exploratory analysis of existing data, or maybe just from somebody’s brilliant insight), and then these get studied (possibly through randomized clinical trials, but that’s not really my point here; my real focus is on the concept of the discrete “intervention”), and then some ideas are revealed to be successful and some are not (with allowances taken for multiple testing or hierarchical structure in the studies), and the successful ideas get dispersed and used widely. There’s then a secondary phase in which interventions can get tested and modified in the wild.

The second paradigm, alluded to by my colleague above, is that of the checklist. Here the story is that everyone knows what works, but for logistical or other reasons, not all these things always get done. Improvement occurs when people are required (or encouraged or bribed or whatever) to do the 10 or 12 things that, together, are known to improve effectiveness. This “checklist” paradigm seems much different than the “intervention” approach that is standard in statistics and econometrics.

The two paradigms are not mutually exclusive. For example, the items on a checklist might have had their effectiveness individually demonstrated via earlier clinical trials–in fact, maybe that’s what got them on the checklist in the first place. Conversely, the procedure of “following a checklist” can itself be seen as an intervention and be evaluated as such.

And there are other paradigms out there, such as the self-experimentation paradigm (in which the generation and testing of new ideas go together) and the “marketplace of ideas” paradigm (in which more efficient systems are believed to evolve and survive through competitive pressures).

I just think it’s interesting that the intervention paradigm, which is so central to our thinking in statistics and econometrics (not to mention NIH funding), is not the only way to think about process improvement. A point that is obvious to nonstatisticians, perhaps.

Christian began by describing Eliezer's article about constructing Bayes’ theorem for simple binomial outcomes with two possible causes as "indeed funny and entertaining (at least at the beginning) but, as a mathematician, I [Christian] do not see how these many pages build more intuition than looking at the mere definition of a conditional probability and at the inversion that is the essence of Bayes’ theorem. The author agrees to some level about this . . . there is however a whole crowd on the blogs that seems to see more in Bayes’s theorem than a mere probability inversion . . . a focus that actually confuses—to some extent—the theorem [two-line proof, no problem, Bayes' theorem being indeed tautological] with the construction of prior probabilities or densities [a forever-debatable issue].

I replied that there are several different points of fascination about Bayes:

1. Surprising results from conditional probability. For example, if you test positive for a disease with a 1% prevalence rate, and the test is 95% effective, that you probably don’t have the disease.

2. Bayesian data analysis as a way to solve statistical problems. For example, the classic partial-pooling examples of Lindley, Novick, Efron, Morris, Rubin, etc.

3. Bayesian inference as a way to include prior information in statistical analysis.

4. Bayes or Bayes-like rules for decision analysis and inference in computer science, for example identifying spam.

5. Bayesian inference as coherent reasoning, following the principles of Von Neumann, Keynes, Savage, etc.

My impression is that people have difficulty separating these ideas. In my opinion, all five of the above items are cool but they don’t always go together in any given problem. For example, the conditional probability laws in point 1 above are always valid, but not always particularly relevant, especially in continuous problems. (Consider the example in chapter 1 of Bayesian Data Analysis of empirical probabilities for football point spreads, or the example of kidney cancer rates in chapter 2.) Similarly, subjective probability is great, but in many many applications it doesn’t arise at all.

Anyway, all of the five items above are magical, but a lot of the magic comes from the specific models being used–-and, for many statisticians, the willingness to dive into the unknown by using an unconventional model at all–-not just from the simple formula.

To put it another way, the influence goes in both directions.  On one hand, the logical power of Bayes' theorem facilitates its use as a practical statistical tool (i.e., much of what I do for a living).  From the other direction, the success of Bayes in practice gives additional backing to the logical appeal of Bayesian decision analysis.

Goetz reports an estimate by Donald Redelmeier that there is an 18% increase in motor vehicle deaths on election day, corresponding to an average of 24 deaths per year and compares it to the 1 in 60 million probability of decisive vote estimated a few days before the election by Aaron Edlin, Nate Silver and myself.  (If anyone is interested in the details of our calculations, they are in this article.)

So the quick calculation goes like this:  24 out of 300 million is about five times 1 in 60 million.  So, according to these numbers, the chance of your vote making a difference is about five times, on average, as being killed in a car accident on the way to the polls.  On the other hand, people notoriously behave as to underestimate the risk of car crashes, so it’s not quite clear what to make of this.

Some other quick calculations might help make sense of this.  The probability that your vote will swing the election is essentially equal to 1/10,000 times the probability that a change of 10,000 votes will swing the outcome.  This has an average probability of about 1 in 6000, which is a little easier to grasp.

Or you can think about Congress.  There were about 20,000 elections for the House of Representatives in the twentieth century.  None were tied, but about 50 of them were within 100 votes.  (See Exercise 1.5 of Bayesian Data Analysis.)  So the probability your vote is decisive in a random congressional election is about 1 in 40,000.

Finally, Goetz comes back to the argument in my article with Edlin and Kaplan in the journal Rationality and Society on the rationality of voting: voting can be rational for people who care about others.  And, conversely, if you do vote, it is rational to choose the candidate whom you think is best for the country as a whole rather than who you think would happen to benefit you personally.

Goetz also writes, "Rationally, people should be much more interested in local elections, which they have a much greater chance of affecting."  I disagree, and this is actually something we discuss in our Rationality and Society article:  yes, the chance of your vote being decisive is much higher (on average) in a local election, but the stakes are lower.  And it is the product–the probability times the stakes–that is relevant.

None of this explains why people voted in New York (where the probability of a decisive vote was essentially zero) but it gives a reasonable justification for voting as a general habit.

Also–because this point always comes up–let me link to my note on why we can compute the probability of a decisive vote, even though the election might be decided by a recount.

Finally, in response to some of the discussion in the comments about rationality and behavior, I’d like to point you to a wonderful article, The Norm of Self-Interest, by psychologist Dale Miller, in which he argues the following:

A norm exists in Western cultures that specifies self-interest both is and ought to be a powerful determinant of behavior. This norm influences people’s actions and opinions as well as the accounts they give for their actions and opinions. In particular, it leads people to act and speak as though they care more about their material self-interest than they do.

The short answer is, quite a lot. First the bad news. With 100 million voters, your chance that your vote will be decisive–even if the national election is predicted to be reasonably close–is, at best, 1 in a million in a battleground state such as Ohio and less than 1 in 10 million or less in a less closely-fought state such as New York. (The calculation is based on the chance that your state’s vote will be exactly tied, along with the chance that your state’s electoral vote is necessary for one candidate or the other to win the Electoral College. Both these conditions are necessary for your vote to be decisive.) So voting doesn’t seem like such a good investment.

But here’s the good news. If your vote is decisive, it will make a difference for 300 million people. If you think your preferred candidate could bring the equivalent of a $50 improvement in the quality of life to the average American–not an implausible hope, given the size of the Federal budget and the impact of decisions in foreign policy, health, the courts, and other areas–you’re now buying a $1.5 billion lottery ticket. With this payoff, a 1 in 10 million chance of being decisive isn’t bad odds.

And many people do see it that way. Surveys show that voters choose based on who they think will do better for the country as a whole, rather than their personal betterment. Indeed, when it comes to voting, it is irrational to be selfish, but if you care how others are affected, it’s a smart calculation to cast your ballot, because the returns to voting are so high for everyone if you are decisive. Voting and vote choice (including related actions such as the decision to gather information in order to make an informed vote) are rational in large elections only to the extent that voters are not selfish.

That’s also the reason for contributing money to a candidate: Large contributions, or contributions to local elections, could conceivably be justified as providing access or the opportunity to directly influence policy. But small-dollar contributions to national elections, like voting, can be better motivated by the possibility of large social benefit than by any direct benefit to you. Such civically motivated behavior is consistent with both small and large anonymous contributions to charity.

The social benefit from voting also explains the declining response rates in opinion polls. In the 1950s, when mass opinion polling was rare, we would argue that it was more rational to respond to a survey than to vote in an election: for example, as one of 1000 respondents to a Gallup poll, there was a real chance that your response could noticeably affect the poll numbers (for example, changing a poll result from 49% to 50%). Nowadays, polls are so common that a telephone poll was done recently to estimate how often individuals are surveyed (the answer was about once per year). It is thus unlikely that a response to a single survey will have much impact.

So, yes, Virginia–and Ohio, and Florida, and Pennsylvania, and New Jersey–it is rational to vote. Utah, Wyoming, and Massachusetts: maybe it’s not worth your time. On the other hand, there’s a chance you could swing the national popular vote (which can affect the perception of a mandate) and in any case you’re likely to have close local races that can ultimately affect policies from schools to taxes to crime and punishment, so if you have any preferences there, it might very well be worth your time to cast your ballot and have a small chance of making a big difference.

Here’s our research article in the journal Rationality and Society spelling out the reasoning and evidence in more detail.

P.S.  I realize I’m doing something that’s generally not done here by reposting an entry from elsewhere.  However, I think it’s relevant given the discussion on the recent blog entries here on voting.  I think this is one case where a "reprint" adds to the blog discussion.

P.P.S.  Take a look at the comments here for some arguments back-and-forth on this.  Just to answer one objection right now:  by saying that people vote to make the economy better, to make America stronger, etc etc., I’m not making some sort of "paternalistic" claim that I know better than others.  I’m just saying that people have legitimate differences of opinion about what policies are good for the country, and voting gives us a small chance to make a big difference.

Anyway, this reminded me of some other biases that are inherent in our political system:

Even if our political system is working perfectly as designed, not all individuals and groups will be treated equally.  Kids don’t get to vote and can’t hold political office, even though they are nominally represented in the government.  Voters in small states are vastly overrepresented in the U.S. Senate.  Votes for minor parties are generally wasted (at least in their direct effects), and proportional representation creates other problems (that’s a story for a different day).  And as long as campaigns need money, rich people and better-funded groups can expect disproportionate representation of their political views.

Looking at representation in terms of decisive votes creates other paradoxes. If you want politicians to fight for your vote, then elections have to be close (or at least potentially close), but when an important election actually is close (as in the 2000 Presidential election), half the people are going to feel unrepresented.

Two other systematic biases that have been studied by political scientists relate to the tyranny of the majority and the median voter.  Majority rule has always been considered dangerous since, for example, 51% of the people could get together and vote to tax the other 49% out of existence (as conservatives were worried about during the New Deal in the 1930s).  The founders of the U.S. Constitution created various checks and balances to slow this down, but it is still somewhat of a mystery why the majority in a democratic system is not more tyrannical.  Perhaps one reason is that most people do not trust politicians enough to lend them this power.

The median voter rule was formulated by Harold Hotelling as an application of a theorem in economics  and was developed further in a book by Anthony Downs in 1957.  The basic idea is that any voter will choose the candidate who is ideologically closest to him or her.  Then all the voters to the left of the D position will go for the Democrat, all the voters to the right of R will side with the Republican, and the voters in the middle will go for whichever is closest.

In this scenario, the Democrat will gain votes by moving to the right–he or she will still get all the voters on the left and will also gain some votes in the center.  Similarly, the Republican should move to the left.  Ultimately, the only stable position for the candidates is for them both to be at the position of the median voter (labeled M in Figure 2).  If either candidate deviates from this position, the other can move to the median and get more votes.  It’s not that there are no voters at the extreme, it’s just that these extreme voters have nowhere else to go.  (All the minor-party candidates together typically get less than 5\% of the vote.)

Getting back to representation, this theory suggests that the median voter is strongly represented by the political system, whereas voters away from the center have no representation.  This translates into less representation for groups such as African Americans and other ethnic minorities whose political views are far from the center.

In real life, however, Democrats and Republicans do not occupy the same point at the center of the political spectrum, and so the median voter rule does not tell the whole story.  The differences between parties can be studied in various ways; for example, when the 435 Congressmembers were ranked from left-wing (negative scores) to right-wing (positive scores) based on their roll-call votes (Poole and Rosenthal, 1997), you find that Democratic and Republican politicians differ a lot in their ideologies (as measured by their actions in Congress), even after controlling for the political slants of their districts.  There are many reasons for this, including competition in primary elections, the need of politicians to secure funds and backing from interest groups closer to the political extremes, and party discipline within Congress.  The point here is that the median voter rule gives some insights into political representation, but it is not completely borne out by the data.

P.S.  Unlike Eliezer, I’m not so worried about voters identifying with the Democrats and Republicans as sports teams.  I take the standard political science line on this, which is that somebody has to do the organizational work of representative politics, and that’s what political parties are for.

This is interesting in its own right–if elections can be predicted, how do we make sense of fluctuations in the polls–but what I thought would particularly interest the Overcoming Bias community is Hibbs’s discussion, in his recent article, of an article by William Nordhaus that claimed that economic forecasts did not actually work well in 2004.  Nordhaus writes, "the Republican incumbent candidate in 2004 did significantly worse than would be predicted based on economic and political variables such as incumbency and economic performance."  Hibbs, however, makes a convincing case that Nordhaus just looked at some bad models.  Here’s Hibbs’s paper; the discussion of different forecasting models begins on page 5.

As a bonus, here’s an article by Bob Erikson and Chris Wlezien on why the political markets have been inferior to the polls as election predictors.  Erikson and Wlezien write,

Election markets have been praised for their ability to forecast election outcomes, and to forecast better than trial-heat polls. This paper challenges that optimistic assessment of election markets, based on an analysis of Iowa Electronic Market (IEM) data from presidential elections between 1988 and 2004. We argue that it is inappropriate to naively compare market forecasts of an election outcome with exact poll results on the day prices are recorded, that is, market prices reflect forecasts of what will happen on Election Day whereas trial-heat polls register preferences on the day of the poll. We then show that when poll leads are properly discounted, poll-based forecasts outperform vote-share market prices. Moreover, we show that win-projections based on the polls dominate prices from winner-take-all markets. Traders in these markets generally see more uncertainty ahead in the campaign than the polling numbers warrant—in effect, they overestimate the role of election campaigns. Reasons for the performance of the IEM election markets are considered in concluding sections.

- How much money would you accept in exchange for a 1-in-a-billion chance of immediate death? Students commonly say they wouldn’t take this wager for any amount of money. Then I have to explain that they will do things such as cross the street to save $1 on some purchase, there’s some chance they’ll get run over when crossing the street, etc. (See Section 6 of this paper; it’s also in our Teaching Statistics book.)

- Goals of bringing the levels of various pollutants down to zero. With plutonium, I’m with ya, but other things occur naturally, and at some point there’s a cost to getting them lower. And if you want to get radiation exposure down to zero, you can start by not flying and not living in Denver.

- Pascal’s wager: that’s the argument that you might as well believe in God because if he (she?) exists, it’s an infinite benefit, and if there is no god, it’s no loss. (This ignores possibilities such as: God exists but despises believers, and will send everyone but atheists to hell. I’m not saying that this highly likely, just that, once you accept the premise, there are costs to both sides of the bet.) See also this from Alex Tabarrok and this from Lars Osterdal.

- Torture and the ticking time bomb: the argument that it’s morally defensible (maybe even imperative) to torture a prisoner if this will yield even a small probability of finding where the ticking (H)-bomb is that will obliterate a large city. Again, this ignores the other side of the decision tree: the probability that, by torturing someone, you will motivate someone else to blow up your city.

- Anything having to do with opportunity cost.

- The argument for buying a lottery ticket: $1 won’t affect my lifestyle at all, but even a small chance of $1 million–that will make a difference! Two fallacies here. First, most lottery buyers will get more than 1 ticket, so realistically you might be talking hundreds of dollars a year, which indeed could affect your standard of living. Second, there actually is a small chance that the $1 can change your life–for example, that might be the extra dollar you need to buy a nice suit that gets you a good job, or whatever.

There are probably other examples of this sort of argument. The key aspect of the fallacy is not that people are (necessarily) making bad choices, but that they only see half of the problem and thus don’t realize there are tradeoffs at all.

I’d like to see some graphs of the raw data, along with replicated datasets from the model. The paper admirably connects the underlying problem to the statistical model; however, the Bayesian approach requires a lot of modeling assumptions, and I’d be a lot more convinced if I could (a) see some of the data and (b) see that the fitted model would produce simulations that look somewhat like the actual data. Otherwise we’re taking it all on faith.

But, why, if this is such a good idea, do people not do it? 

I don’t buy the cynical answer that people don’t want to falsify their own models. My preferred explanation might be called sociological and goes as follows: We’re often told to check model fit. But suppose we fit a model, write a paper, and check the model fit with a graph. If the fit is ok, then why bother with the graph: the model is OK, right? If the fit shows problems (which, realistically, it should, if you think hard enough about how to make your model-checking graph), then you better not include the graph in the paper, or the reviewers will reject, saying that you should fix your model. And once you’ve fit the better model, no need for the graph.

The result is: (a) a bloodless view of statistics in which only the good models appear, leaving readers in the dark about all the steps needed to get there; or, worse, (b) statisticians (and, in general, researchers) not checking the fit of their model in the first place, so that neither the original researchers nor the readers of the journal learn about the problems with the model.

One more thing . . .

You might say that there’s no reason to bother with model checking since all models are false anyway. I do believe that all models are false, but for me the purpose of model checking is not to accept or reject a model, but to reveal aspects of the data that are not captured by the fitted model. (See chapter 6 of Bayesian Data Analysis for some examples.)

Hindsight bias is when people who know the answer vastly overestimate its predictability or obviousness, compared to the estimates of subjects who must guess without advance knowledge. . . . Shortly after September 11th 2001, I [Eliezer] thought to myself, and now someone will turn up minor intelligence warnings of something-or-other, and then the hindsight will begin. Yes, I’m sure they had some minor warnings of an al Qaeda plot, but they probably also had minor warnings of mafia activity, nuclear material for sale, and an invasion from Mars.

This doesn’t seem quite right to me:  I’d think the FBI and CIA would have the resources to investigate warnings of an al Quaeda plot, mafia activity, and nuclear material for sale (and I think they know enough to ignore warnings of invasions from Mars).  As Alex puts it here,

What about this specific threat, Osama Bin Laden? Well, he did have a past prior for trying to blow up the World Trade Center, didn’t he? I don’t think his past failure would have made it less likely for him to try again, do you?

The comments at that link are also relevant to this discussion.  Anyway, my key point here is that people do make mistakes–people even make mistakes that could’ve been realized ahead of time if proper procedure had been followed.  In these cases, the concept of "hindsight bias" can be used inappropriately as a blanket to cover up all failures.