Conservation of Blame

I know I haven't posted much in a while, but it's the middle of NaNoWriMo so I've been busy writing other things.  I'm still 30,000 words from my goal (possibly more if it takes another 40-50 thousand to finish the book which is the real goal). Meanwhile, we're wanting to build out recruitment of an important clinical trial, so I'm going to keep today's post short.

There's a common intuition I think is usually wrong, and I want to spend a few minutes convincing you of this.  First, some context:  In many disciplines where we deal with finite systems and allocation of scarce resources we run into different types of 'conservation' laws.  This is especially true in physics, where all sorts of things are conserved like energy, charge, mass, etc.  Even probability is conserved at a quantum level!  I think there's a natural tendency to want to think in terms of conservation in other areas as well, and this intuition is not always wrong.  For example, if I'm paying for half of lunch and you're paying for the other half then we might surmise that payment was conserved.

We could imagine a situation where it's not conserved.  Perhaps the word "you" above was intended to be plural, such that each reader of this post paid for fully half of lunch.  I paid for half, Joe paid half, Susan paid half, Adele paid half, and so on.  Thus, many people paid for half of lunch, which adds up to multiple times the actual bill.  The implication is that someone got paid a lot more than they were actually owed because either the lunch bill is conserved, or something has gone wrong with how we divided the bill.

What about a system where the contribution of each of a number of parties is necessary but not sufficient to achieve an outcome?  We could use any manufacturing process as an example.  We might refer to the outcome as being contingent proportionally on the actions of each person, and assign responsibility by percentage to each person.  Joe tightened five bolts and was ultimately responsible for 1.8% of the output.  None of this, I think, violates our intuitions of how to assign ownership for the outcome.  We can measure this, and if Joe quits we know how much slack each of the others will have to pick up.

Those are the simple examples.  What about the case where everyone works toward a common outcome, but if any one person decides to quit they aren't replaceable.  Either everyone participates, or you get a different result.  In my opinion, this is often an apt description of blame.  There is a common heuristic that assigns levels of blame to each participant, "You were 90% responsible for not taking the trash to the curb, and I was 10% responsible for forgetting to remind you.  You bear most of the blame for why we didn't get the garbage out on trash day."  But this violates the calculations we were making above.  If you remind me to take out the trash, it doesn't get 10% of the way to the curb.  Meanwhile, if I take the trash out and you never reminded me you don't retain 10% blame for a bad outcome that was never realized.

It's strange, then, to assign blame the same way we might assign manufacturing output, since the ultimate output can be influenced by any one of the actors involved.  This approach effectively treats blame like it is conserved.  Maybe sometimes that's a useful way of viewing blame, but it's entirely inadequate for many situations.  It ignores most of the nuance, and goes against many of our intuitions.  Instead, I think it's fair to ignore conservation when talking about blame.  You can be 100% responsible for an action without absolving me of all blame for that action.  Let's start with a dispassionate example: who is responsible for World War I?  We'll limit our blame to asking who is responsible for the outbreak of war among the European powers, not ask who is responsible for every shell in every battle of the war.

Who Caused WWI?

The proximate cause was Gavrilo Princip, who assassinated the archduke Franz Ferdinand.  Maybe he didn't intend to start a horrific world war, but he should have known he was lighting a firecracker while surrounded by gunpowder.  We might blame Ferdinand or his driver, but then they weren't willing participants in the murder plot so maybe we could give them a bit of a pass.  Still, they each made their own bad decisions that lead to the breakout of war.  Let's start assigning blame to each of these people:

Princip - 25% (One murder against what the conflict evolved into?  I think this is probably too high.)
Ferdinand - 12%
Driver - 1%

All values are gross estimates and subject to error of at least one order of magnitude.

Now, the war wouldn't have happened if Austria had accepted the decline of its empire and reacted more reasonably toward Serbia than an ultimatum that effectively denied them national sovereignty.  The Serbians, for their part, weren't exactly vigilant in rooting out subversive groups like the Black Hand that carried out the assassination attempt.

Austria - 22%
Serbia - 10%

Now, Germany bears a lot of blame here, and this part of the analysis is likely going to be controversial for my historian readers.  Forgive me, as this isn't my field.  All I know is from the few books I've read about the subject, and many of those are a few years old.  That said, Germany seems to have seen a European conflict as inevitable, and therefore that it would be more desirable to have one sooner than later.  They had a whole plan to win that war, but I've never read anything about a plan to actively avoid it.  On the other hand, why did Germany feel this way?  They had just lost a naval arms race with Great Britain, who viewed the up and coming Germans as stepping out of their proper place in the world.  How dare they demand greater political representation on the global scene just because they were an emerging economic power?  The British and many of the other great powers who benefited from the status quo thought war could never happen because it would destroy everyone's economies.  They didn't stop to think that by holding Germany back they were creating a situation where one nation had no other option than war if it wanted to get ahead.  Had the British and their allies taken a different stance toward Germany, one which shepherded it onto the world stage instead of elbowing it off, perhaps a general European war could have been avoided.

Germany - 60%
Britain et al. - 25-50%

What about Russia?  Germany wasn't interested in being blamed for starting the war, even if they were ready to see it through.  The Russians certainly knew it was a possibility.  Now, the German plan hinged on how long it took the Russians to mobilize their army.  Once the Russians mobilized, that gave the Germans no window to enact their plan, since waiting meant fighting a losing war on two fronts.  Any simultaneous conflict with Russia and France would be an academic exercise in German defeat.  Therefore mobilization of the Russian army was as good as a declaration of war for the Germans.  The Tsar, for a variety of reasons, was perceived as weak, and the story goes that when he was challenged about whether the army should mobilize he thought the person asking the question was doing so in a way that challenged his resolve.  Rather than appear weak before his underlings, he made a rash decision to mobilize.  He could have made a lot of decisions both at that time and leading up to it that were more wise than what he actually did.  Indeed, since he was going to be overthrown anyway it hardly seems worth it to uphold the dynasty for a little longer in exchange for the horrors of WWI.

Russia - 30%

There are certainly others we could name.  For example, Bismark should bear some blame for setting up a system of alliances that only he understood and could work with.  Without his work a few decades before, there wouldn't have been a general feeling by some nations that war was inevitable.  Or if there was, it might not have devolved into a 50/50 split among belligerents.

Bismark - 25%

If we add these all up, we come to a total of between 210% and 235% blame.  That's okay, though, because there's no such thing as a law of conservation of blame.  Germany can bear the brunt of responsibility at the same time we look back and ask whether Britain did something seriously wrong here.  For example, we might take the lesson of history and say that for an established major power like the USA to avoid a similar fate; they could be careful to give countries with emerging economic power a path toward legitimate global political influence.  Something other than a choice between outright war or abject submission.  This doesn't absolve Germany of responsibility, or deny it was fully an agent in shaping its own choices.

A New Heuristic

The heuristic, "blame is not conserved" helps drive us toward a better understanding of the world.  Years ago, my apartment was robbed and all my valuables were stolen.  My wife's biggest complaint was that they stole a pillow case to use as a bag, which ruined the set.  Of course, there was also the fact that they stole a bunch of stuff we couldn't afford to replace.  But years later she still remembers that pillow case.  I still remember how horrible, how violating it felt to get robbed.  Who's to blame for the crime?  Let's say, based on the specific things they stole, the part of the country we lived in, and a few other factors, that the criminal was an addict trying to drum up funds for their next hit.

Thief - 100%
Opioids - 40%
Me (for living in that neighborhood, which I knew was unsavory) - 25%

Assigning blame by percentages like this feels very imprecise.  The reason I'm doing it this way is to try and build a new heuristic: blame should be assessed independently for each actor.  Seeing numbers that don't add up to 100% is part of this.  It's a heuristic that fits in with our expectations, too.  Under the law in the US, an accomplice is as liable for the crimes committed as the person they aided.  That means that if you drive the getaway car you'll get the same sentence as the person who committed the crime.  You're 100% to blame.  And so is the person you helped to commit the crime.

Me?  I took out the trash last night, so I'm blameless for the next week.


  1. Interesting, but I had a hard time focusing after this sentence:

    "All values are gross estimates and subject to error of at least one order of magnitude."

    Which would seem to indicate that in theory Princip could have been 250% responsible, or the Germans 600% responsible. And while your point is that blame is not conserved it does seem odd to suggest that any individual actor more than 100% responsible.

    Also I would think that as long as you're using percentages it's going to be hard for people to get around thinking of it as something that should add up to 100. That you probably really need an entirely different framework for blame to substitute in.

    While I don't know exactly how this addresses your concerns, I prefer one-step responsibility. When I was in high school my dad let me take one of his books (I think it was Hunt for Red October) to school. I then lent it to a friend, who then lent it to someone else, and that someone else lost it or otherwise failed to return it to my friend.

    By and by my Dad wanted to know where his book was, and I told him the story of how I'd lent it to a friend, and how he lent it, etc. My dad told me that I couldn't transfer my responsibility to my friend. Regardless of what happened to the book, I was still responsible for returning it (or another copy which is what ended up happening) to him, and then my friend had one-step responsibility to me, etc.

    The application to blame is obvious, my dad isn't going to blame my friend, or my friend's friend, even if that's the person who truly lost the book. He's going to blame me. As I said this probably doesn't directly address your concerns, since it's not clear (at least to me) how to scale this up to the level of a World War...

    1. That sentence wasn't meant to allow greater than 100% blame for individuals, but rather to note that the process of assigning fractional blame to individuals is obviously a subjective exercise. For example, if you look at European history leading up to WWI there were multiple conflicts that might have spiraled into a general European war, but didn't. So the powder keg was going to explode whether it was Princip who lit the fuse or it was something else. So maybe instead of blaming Princip at 25%, it might be more fair to blame him in the range of 2.5%.

      Whatever, I'm less interested in adjudicating the specific magnitudes of each actor as I am in the principle that blame should be assigned for each actor independent of what the other actors are doing. I think this is what you're talking about, and it probably does need a different conceptual model than percentages. I think you're right that the percentages are misleading, and I considered abandoning them at one point but left them in on purpose. The aim of the post was to work against the popular heuristic of assigning blame relative to what others are doing. The percentages model what's going on in people's heads when they say things like, "My responsibility for losing the book is reduced because someone else contributed to the outcome as well."

      The WWI example is useful, because if you're trying to assign a cause for the conflict based on breaking everything down into percentages it doesn't work. There's always another factor that could be considered, so you can never truly get to 100%, or at least you have to keep reassigning blame as you add more and more factors ad infinitum. And removing any one factor might render everyone else's blame moot, which doesn't match our expectations if we're assigning based on percentages.

      That said, I'm not sure how else to include magnitudes in the model in an intuitive sense. Too often we're trained in school to think of things as having single causes. But 'messy' fields like biology, psychology, and history have multiple causes for nearly every effect. A model that doesn't take magnitude into account is not likely to be preferred against one that does. This may be how assignment based on fractional blame became popular in the first place, because it's the most commonly used system that laypeople understand and that also includes built-in magnitudes. The problem with defaulting to that system is that it assumes magnitudes must all add up to one, which isn't the case since blame isn't a conserved value.


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