Should Mayor Daley Decree that All Chicago Bears Fans be Happy Tomorrow?

On the first day of class, I tell my undergraduates that if they only learn one thing in my course, I hope that it will be to recognize and appreciate the difference between correlation and causality. Most of the students laugh smugly, thinking they already know the difference. It never ceases to amaze me, however, when a cleverly designed exam question reveals how easily they can be tricked into forgetting the distinction.

Even among people who know the difference between correlation and causality, there is a lack of appreciation of the fact that when it comes to making public policy, only causal relationships are relevant. I’ve even attended lectures given by tenured professors at Harvard who fail to understand this simple point.

The example I often use to demonstrate why we don’t want to make public policy based on correlations is particularly relevant today in light of the Chicago Bears playing in the Super Bowl. In my example, Chicago’s beloved Mayor Daley is trying to think of ways to increase the likelihood that the Bears win the game. He’s noticed that whenever the Bears win, people in Chicago are happy. Which sparks a great idea: decree that all Bears fans have to be happy on Super Bowl Sunday. It has always been true in the past that winning games and being happy go together, so by demanding the Bears’ fans are happy, it will cause the Bears to win the Super Bowl.

Of course, Mayor Daley is smarter than that. Hopefully you are too and you understand why such a decree would be ludicrous. If not, I encourage you to start over at the beginning of this blog entry and try again. 🙂

It is an open question right now, however, whether Mayor Bloomberg of New York understands this simple point. In an article in the New York Times a few days ago, Jack Curry writes about how Yankee Stadium will host one last All-Star game. In the story, Curry writes:

It will be the fourth time the All-Star Game will be played at the Stadium. The Yankees made it to the World Series in the three previous seasons in which the game was played in the Bronx – 1977, 1960 and 1939 – winning two titles.

Which prompted Bloomberg to say:

“So while the 2008 All-Star Game will be one of the wonderful events staged in the Stadium’s final season, my hunch is it won’t be the only one,” Bloomberg said.

Which sounds suspiciously similar to thinking that decreeing that Bears’ fans be happy will lead to a victory in the Super Bowl.

Knowing that Bloomberg is a very intelligent man, I’m guessing he said this in jest. But how many New Yorkers who aren’t so clever do you think made a visit to their local bookie to plunk down some money on the Yankees to win the World Series after the announcement?

(Hat tip to Tim, a Yankees fan stranded in Boston.)


mgroves

"Correlation is not causation" is such a simple thing to understand, but it is mistaken so frustratingly often by the media.

pkimelma

I think the real problem is that we naturally want to see causation, when there is only correlation. Religions and mysticism alone should demonstrate that. But, it is an easy trap to fall into, since we rarely can see the invisible hand of causation when it is there, we impute it even when it is not.

Andy Perrin

While it's true that correlation does not imply causation, sometimes it can make a tentative causal statement more plausible. There's a nice book on Bayesian probability and probability as extended logic by E.T. Jaynes, and you can read the first few chapters here.

He makes the argument that while seeing dark clouds in the morning does not imply that it will rain in the afternoon, it does make it more plausible because of our past knowledge of cloudy days.

pkimelma

Andy, you make a good point. The broken windows theory follows this. Although broken windows in a city (or other defacement) does not cause crime, its correlation has hidden common linkages. We can use "correlated symptoms" to predict things with less certainty than causality, but more than just random correlation. This works especially well when the causal elements are not (easily) directly detectable.

simper5

Checking the recent betting lines to answer that last question should be easy enough, shouldn't it? This post about conclusions unsupported by evidence advances no evidence to support its speculation about reaction to the Yankee Stadium example--the only example in the post.

What's an example of a cleverly worded exam question that can trap unwary students?

chimp

I basically agree with #3 and #4 above. You don't need definite causality for prediction. Above chance predictions can be made based on statistically significant correlations, even if the correlations are not well understood.

sean stephenson

I did not fully appreciate the difference between correlation and causality until I was studying for the lsat (in Ukraine) and had the point nailed home to me while reading a schlew of those prep books. the difference between the two terms is one of the central point tested in the exam....so, hopefully there is an army of lawyers out there who are solid with what's going on with correlation and causality.

chimp

By the way, the case in Chicago and the case in New York are different even in terms of correlation and probablity. We only know P(people happy|bears win), but not P(bears win|people happy), so the decree probably won't work. However, we do know P(all star|world series) as well as P(world series|all star), and the latter P happens to be 100% according to the blog.

pkimelma

"We only know P(people happy|bears win)" - the idea was to get people to "be happy" before the game, so the Bears win. That is, they are assuming that Chicagoens' happiness is causal to winning, and so by forcing happiness, the causal effect would take place.

chimp

pkimelma are you disagreeing with me? I think we were talking about the same thing. My points are:

1. We can use correlations to make predictions, such as in the Yankee example (caveat being a tiny sample size of three past years).

2. We can't predict bears' likelihood of winning from pre-game happiness, because we only have the correlation between winning and post-game happiness. This does not refute the idea that we can use correlations to make predictions (if the pair of variables is constant).

pkimelma

Chimp, sorry, I am agreeing with you. I was simply saying that they assumed the order of the correlated (and "presumed causal") events. You were reasonably assuming that people are happy when their team wins (so causal win->happiness). They were (facetiously I hope) presuming that they are happy and so the team wins (ie. happiness->win).
The interesting thing this always raises even when you have causal links, is whether they are natural or hard-linked. If measures of happiness support a causal link of unhappiness->suicide, could you tell people to act happy and so reduce suicide? In effect, that is what the Mayor is doing (based on absurd causal links of course). Likewise, when football outcomes seemed to predict Presidential outcomes, could a team throw the game to change the other outcome? I raise this because it links back to things like the broken windows theory - even if not causal, fixing the broken windows has a well correlated "effect" on crime, even if you are not fixing the other causes of crime (poverty, lack of education, lack of hope, opportunity, etc). Equally, the placebo effect can be quite powerful.
So correlation for prediction may also have the interesting effect that if many believes the linkage, they act differently, and so also support the prediction even more indirectly.

Read more...

synapticmisfires

Well, I certainly hope that Mayor Bloomberg is smarter than that. However, there is one variable that could increase the incidence of both of those things. In baseball, especially since there isn't a salary cap, the Owner's willingness to invest in his team more than usual would cause both a better team to be on the field and the stadium to be in better shape and so more likely to win a hosting bid. Obviously, this is not causation, and I'm not saying that it will have a huge effect on anything. However, I can sort of believe that the variables aren't 100% independent. Maybe 96%.

synapticmisfires

You know, just to play the role of devil's advocate, because I rather enjoy that.

pparkmanlg

Assuming that correlation and causality are disconnected is frequently wrong. We've all heard of the self-fulfilling prophecy. While in physics causality may be independent of correlation, in human affairs, they are intermingled.
In the current case - if the Bears were playing at home rather than Miami, Mayor Daley's proclamation, assuming it could be enforced might lead to an extremely supportive crowd, and this 12th man could give the Bears the edge that they need to defeat the Colts, despite the odds.
It all comes down to feedback of foreknowledge .. . if the subject of the experiment knows of a correlation in advance of the experiment, it can affect the outcome. ie become causality.

DWSUWF

As important as the distinction between causality and correlation, is the distinction between prediction and prescience. Example: I know the final score for the Super Bowl tomorrow is:

Bears 41
Colts 13

This is not a prediction. Earlier in the week I was visited by the Ghosts of the Chicago Bears Past, Present, and Future in a dream. I peeked at the final scoreboard while the Spirit of the Chicago Bears Future was dragging me around Miami. That was a mistake - there is no real suspense in watching the game for me now.

Anyway, the whole Dickensian tale is linked below, but will probably only be understood and appreciated by Bears fans:

"Da Bears Song in Prose - Being a Ghost Story of the Superbowl"

casinoblang

Perhaps this post is an example of mistaking correlation with causality. Perhaps the poor answers on the exam are not due to student overconfidence regarding the distinction between the two but rather, deficient/overconfident teaching in the subject area and the students never learned the distinction in the first place. In such a case obviously the "smug" laughter, while seemingly related would not be responsible for the poor exam grades

lermit

I lost my ticket and can't find a way to make it up to my gir. Is that economically competitive or efficient?

.lermit

lermit

girl

Kent

This post has nothing to do with economics. It's a thinly veiled attack on Mayor Daly. "Decree that all fans be happy." The insinuation that Daly is a fascist is utterly gratuitous.

puneetvohra

Should Mayor Daley really ask the fans to be happy?

Here is something you may find interesting: In a lot of cricket games played in the sub-continent, we have a member among the spectators for whom we dont have a name, but lets call him the cheerleader for the lack of better name. The name is close to appropriate because his role is something very close a cheerleader.

Every once in a while, when the home team is not doing well, his job is to ensure that the crowd support does not die down. He initiates waves, cheers (and sledges against the opponents). He gets the crowd going, cheering and supporting their team, whenever their team is down.

Now, just like basketball, this cheerleader is generally sponsored by the home team. the idea here is that the team plays better if the crowd is vocal in its support. And a cheerleader gets vocal support for the team.

Would you say that the Sri Lankan cricket board just decreed that all the Lions fans be happy for the match?

Just because there isn't an obvious causation for a correlated set of data, doesn't mean its random noise. Just my belief, but a lot of things in this universe are connected much more subtly than we would imagine...

Read more...