How to tackle the Biden accusation with decision theory

You need not conclude guilt or innocence when deciding your vote

Decision theory is the whole damn game. "Data science" is just making data-driven decisions. "Machine learning" is just training algorithms on data in order to automate decision-making.

It turns out, that it is a useful mental model for one of the thorniest issues in the #metoo era — how to view allegations of sexual misconduct by men in power, and how to treat the women who come forward.

Tara Reid worked for Joe Biden as a staffer in his Senate office in the early '90s. She has formally accused Biden of a sexual assault in 1993. Joe Biden has categorically denied the allegation.

We, the voting public, have to decide how to respond.

Start with the action set

It seems trivial, but the most important thing to do as we start is to enumerate our set of actions. Actions are what we must decide between after we've considered the problem.

Let's keep it to three actions:

  1. Vote for Biden

  2. Vote for Trump

  3. Don't Vote

I am being way over-reductive here, particularly about the merits of 3rd party voting. Moreover, the stakes are high in terms of people's personal histories with sexual trauma, and their ongoing dealings with abusers. Those experiences will impact an specific individual’s action set, as I’ll discuss later.

As a modeler and an engineer, the best practice is to build the basic workflow first. Once it is working, I can expand it to grapple with the complexity of reality. So in this essay, I keep things simple, hoping this mental model can help people grapple with the complexity.

Weighing evidence of explanations

(1) Make a binary set of explanations. For simplicity, let's consider one piece of evidence (she alleges the assault happened). The evidence has several explanations. However, we start with a simple binary breakdown. 

  1. The sexual assault happened & she's truthful.

  2. The sexual assault didn't happen & she's untruthful.  

Let’s sketch it on a whiteboard.

I'm leaving out the evidence that he denies the allegation because it won't add much. If he is lying, the implications of lying seem trivial compared to the implications of having done the sexual assault. If he's telling the truth, he shouldn't get any browny points for not sexually assaulting anyone.

Expand the binary decision into a tree.  From here, you can parse the explanations into a tree, such as the following.

Why might have Reid come forward if she’s truthful? I reason that it could be altruism, or revenge against the person who victimized her. Even if she’s truthful there could be some element of gain, as in feeling like she is owed something for having been victimized.

Consider explanations where Reid is untruthful tends to spark my imagination a bit more.

If she’s lying, then why? If it is for gain, then what kind of gain? Perhaps the goal would be to gain money (e.g., through speaking engagements), or to gain fame, or for the sake of her political tribe. Money for what? It could be desperation, or does she simply want a bigger boat?

The trick in building out the tree is to choose nodes that split the world into small sets of discrete possibilities. Follow the 80/20 rule, explicitly model choices that capture 80% of possible events, and shunt the rest in an "other" bucket.

Stop adding depth when the details don't matter. For example, if Tara Reid is untruthful because of desperation, the source of desperation could be that someone close to her is uninsured and need surgery, or to pay off a debt, or pay off a blackmailer, or ransomer. But in my view, the flavor for desperation doesn't matter, so I omit them from consideration.

Make your biases evident. You are a biased person, stop pretending you aren't. Embrace your biases by making them explicit in this tree. Building the tree forces a kind of introspection. If you find yourself spending significant time diagramming Dan Brown-style explanations where Reid is a bit player in a vast conspiracy, then perhaps you should call yourself on your bullshit. Devote a comparable of time to hashing out explanations that go against your prejudices.

Avoid cop-outs. An example of a cop-out explanation are ones that require Tara Reid to be crazy.

Female Hysteria during Victorian Era: Its Symptoms ...

You can do better than that.

Evaluate the likelihood of each explanation. Given the tree, there is a quantitative way of evaluating the likelihood that involves assigning probabilities and chaining them together. You should definitely do this in technical applications.

However, as a mental model for widespread use, we should go for a mental heuristic. The more we exercise decision-making with such heuristics, the better our decisions get in the long run.

At this stage, we've already visualized our mental narratives in the form of a tree. Now we can ask ourselves what the tree tells us.

The next step is to weigh these explanations of the evidence by how likely they are. Here, Bayes Ockham's razor should come into play. 

The gist behind Bayes Ockham's razor is the following. The more complicated the explanation, the more low-probability events had to happen for it to have been true. Therefore, simpler explanations should be seen as more likely.

Note that in my case, while my imagination was more active on the Reid is lying side, the simplest explanations are on the “she’s telling the truth” side.

Bayes Ockham's razor leads me to want to soften the dogmatic rule of "believe women", to something like "the accuser’s story is usually among the most likely of explanations, because they wouldn’t have bothered to come forward otherwise." But that’s less catchy.

However, our goal here IS NOT to conclude what is true.

From likelihood to decision

This is where people get stuck. The goal of the previous step wasn't to conclude which explanation to believe. Concluding in favor of one explanation over another is a decision, and in our case, it is not the decision we care about.

For example, consider the justice system. In a jury trial, the jury's job is not to simply pick "guilty" or "innocent" based on which explanation is more likely. Instead, its job is to decide to "convict" or "acquit." Further, the jury should pick "convict" only if "guilty beyond a reasonable doubt", i.e., the likelihood of the guilty explanation strongly outweighs the likelihood of innocence.

Presumption of Innocence | Stern Albert Shapray

But that doesn't mean acquittal is equivalent to innocence or that conviction is equivalent to guilt. Even if all the myriad problems of the legal system were magically fixed and it was working ideally, there would still be wrongful convictions (and wrongful acquittals). Just like in statistical classification or any other evidence-based decision problem, there is an irreducible rate of error.  

What this means is that, the evidence of guilt vs. innocence drives the decision outcome of the trial, but the decision outcome of the trial is not proof of guilt or innocence. Conflating these ideas is a common error. Of course, the fact that courts literally use the terms "guilty" and "not guilty" instead of "decide to convict" and "decide to acquit" makes the confusion that much worse.

Consider what R. Kelly said in his infamous interview with Gayle King. In the interview, King notes that "the past is relevant with you with underage girls.Kelly denies that, saying, "Absolutely no it's not. … Because, for one, I beat my case… You can't double-jeopardy me like that... When you beat your case, you beat your case." Kelly is using the assumption that "decide to acquit" is equal to "conclude he is innocent" to argue that past evidence cannot be used in reasoning about more recent allegations against him. However, this flies in the face of common sense. The reason he was acquitted because the underaged girl who allegedly appeared on a sex tape refused to testify. But the tape itself is pretty damning as far as evidence goes, it makes sense to consider it as part of a long term pattern of abuse by Kelly.

Understanding the difference between the acquit/convict decision and the guilt/innocence conclusion is a nuance that is highly relevant to sexual misconduct cases because in such cases it is notoriously hard to get a conviction. Acknowledging the difference allows us to hold two distinct ideas in our heads; "the accused likely did it" and "the likelihood they did do it does not exceed the reasonable doubt threshold". These are not mutually exclusive, but in our culture of moral certitude, most people think they are. Most people think that if it is likely someone committed a crime and that person goes free then the system failed. It fact it may have been operating to spec.

But, but, but… Remember that our decision task is neither concluding guilt/innocence nor convicting/acquitting. It is to decide between (1) vote for Biden, (2) vote for Trump, and (3) don't vote.  

Again, this subtly is lost in the public discourse. Biden supporters are saying that he deserves "due process", while Trump supporters call hypocrisy, saying they were less generous with Trump. “Due process” is moot; this controversy isn't a criminal trial. Our role is not to be a jury member but to be a voter. The distinction matters, because a “beyond a reasonable doubt” might be an appropriate standard for the court but be inappropriate for the voting booth.

Minimizing risk

According to my basic breakdown, we have the following possible outcomes.

  1. Reid is truthful and vote for Biden.

  2. Reid is untruthful and vote for Biden.

  3. Reid is truthful and vote for Trump.

  4. Reid is untruthful and vote for Trump.

  5. Reid is truthful and don't vote.

  6. Reid is untruthful and don't vote.

Statistical decision theory would have us assign a cost function to each of these outcomes, then multiply each cost by the likelihood Tara Reid is truthful/untruthful. The resulting value is called "risk" or "expected cost". One would then choose the decision with the lowest "risk" value.

But math aside, we can see how focusing on the end decision outcomes could simplify the problem. You might reason that in the worst case where Tara Reid is truthful, Biden is the better choice since Trump has even more credible allegations against him (3 has more risk than 1). Or that no matter if Reid is truthful or not, Biden is the better choice given all the political issues at stake (1 and 2 both have less risk than all others). Or you might conclude that you cannot in good conscience support any candidate with a credible accusation (risk of 5 and 6 are lower than all other actions).  

How you decide depends on how you weigh the costs for each outcome, and the likelihood you assign for each outcome. But note that this decision does not require you to conclusively decide on Biden's guilt or innocence, or equivalently, Reid's truthfulness.

Let costs be complex

Obviously, things are not as simple as I've made them out. But now we can start to compartmentalize the complexity. Coming up with varied explanations that support the evidence is hard, particularly if more evidence comes out and we have to reevaluate.

But I think the hardest issue is deciding on how to assign costs to those outcomes. It is also highly personal. In real life, this controversy is bringing sexual assault victims’ traumas to the surface, and those victims (not the voting public at large) are the ones who have to carry that burden. The controversy also affects the ongoing battles some individuals are having with sexual abusers; for example, how members of an HR office or corporate committee judges an allegation. It is affecting children, who see role models of success and leadership being connected to heinous acts. Parents must factor that in.

We must also consider the costs of how this controversy impacts the culture we all live in. For example, regardless of what is true or not, sexual predators will use this controversy as a shield for their misconduct, just as R. Kelly compared his case to "an attempted lynching of a black man." What decisions can we make to make that harder to do?