Probability and Causal Density

“Scott Alexander” writes,

If ten different factors caused the decline in crime, that would require that ten different things suddenly changed direction, all at the same time in 1994. That’s a pretty big coincidence. . .we should give some credibility penalty to a story with ten factors.

I do not buy this argument. I do not think that one should automatically penalize a study more for claiming that there are ten factors rather than one prominent factor.

My view would be that when there is a lot of causal density, one should be skeptical of any study that claims to have the answer, whether the answer consists of one factor or many. Take as an example the financial crisis of 2008. There are many plausible causal factors. Should we prefer a study that attributes the crisis entirely to one factor rather than a study that attributes it to a combination of factors? I think not. Instead, given the non-experimental nature of the problem, I think we need to accept the fact that we will have to live with some uncertainty about what exactly caused the crisis.

For a phenomenon that is amenable to replicable experiments, it may be possible to obtain evidence against causal density and in favor of an explanation based on one or two factors. But not for something like the drop in crime over the past two decades.

13 thoughts on “Probability and Causal Density

  1. The ten factors don’t all have to change direction in 1994. Even less do they have to “suddenly” change direction. By 1994, there simply has to be enough change in direction for enough of the factors that the total effect is a decline in crime.

  2. Having read the Scott Alexander post and the Vox article it riffs on I don’t think there’s anything interesting going on in either place. He and Vox are aguing about Narrative Causalities, not actual causality.

  3. Maybe the single causitive factor in the reduction of crime is just … the high level of crime.

    When a social problem gets completely out of control is a society as decentralized as ours, then it should be no mystery or cause for skepticism when many actors under the same general pressures and incentives act within the narrow scope of their own expertise and authority to try and make a small improvement in their own domain. And when you add up all the small percentages over time, you get a massive change.

    The unprecedented explosion in crime rates in only fifteen years from 1958 to 1973 – largely as a result of the coming of age of baby boomers and a spirit of profound leniency towards criminals throughout much of the political class and legal community – led to major responses on every front, trying to find away to route around the jurisprudential new normal. Long sentences and massive improvements in investigative technology provided that work around, and eventually started yielding major results.

    There was also a gradual sea change in attitudes amongst prominent mayors and judges, when the ideological commitments of the 60’s began to wane and it became possible – even popular – to admit that the former policies were all a grave and naive error.

  4. From the world of engineering and accident analysis high causal density with one final factor is in fact the norm.

    Well summarized by the remark “we find that for a plane crash, we have at least 8 or 10 things go wrong in a chain, and having any one of those things not go wrong means we don’t get the crash”

    What’s more, for most everything we deal with in our lives, there are lots of necessary but insufficient prerequisites. This happens so often we take it for granted, yet people somehow don’t want to apply it to social policy issues?

  5. Security in general tends to have local equillibria that persist. One equillibrium is almost no crime: once criminals feel like an attack is unlikely to work, they all stop.

    Similarly, if one criminal sees another succeed, then they ramp up their own efforts.

  6. Suppose there are a million factors that affect crime. 999,900 are random and independent. The last 100 aren’t independent — they have some common cause, like the culture condoning crime, or more criminals in jail, or an improving economy.

    When you look at the stats, the 999,900 factors will generally cancel out, and the remaining 100 will be the cause. But some of the 999,900 will be of high magnitude, in the “right” direction, just from pure luck.

    Some of those may *appear* to have caused the drop in crime, if they’re high enough.

  7. Also, and as someone mentioned on Scott’s blog, “cause” is usually an interaction of many factors. I’m speeding, without snow tires, after a couple of drinks, and there’s a sudden snow squall, and I rear-end someone. What was the cause: the tires, the speed, the drinking, or the snow? It’s the interaction of all four.

    I’m skeptical of explanations that cite many causes separately, but find it plausible that unusual events result from the interaction of many improbable factors together.

  8. “Crime” is also threshold variable with a range. The justice system can only produce so much “crime” per unit time. Then perhaps at some saturation margin the system actually works to reduce crime.

    I like the lead idea but my other guess is video games helped a lot. That is about the time of sega genesis, super nintendo, and playstation.

  9. As an example of moderate complex historical causality, here’s the opening of the 1971 Encyclopedia Britannica’s article on the Italian attack of Ethiopia in the 1930s:

    “The motives of Fascist Italy in attacking and annexing the ancient, independent Christian state of Ethiopia (Abyssinia) were complex but easily intelligible. They included the desire for national greatness and empire; the personal megalomania of Benito Mussolini and glorification of his regime; the need for new resources for crowded and impoverished Italy; vengeance for the humiliating defeat of Adowa (1896); and the ambition to substitute Italian civilization for the black barbarism alleged to be dominant in Ethiopia.”

    • So, that’s an “easily intelligible” historical event, one that’s never been subject to much controversy. Events whose root causes are subject to continuing controversy are likely to be even more complicated.

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