The Math Of Trust - Or: How To Judge Opinions With A Few Questions

Introducing the BCI decision model

Not all opinions need to be treated as equals.

Yes, that’s an often controversial statement. But it shouldn’t be.

Simply because not all opinions are in fact equal.

This is true both in our personal and professional lives. Whether it’s a discussion with friends around the Corona virus or a strategic planning session with managers and co-workers about which features to develop.

Not all opinions matter equally. There, I said it again.

Intuitively, we understand that my dermatologist’s opinion about the two large moles on my neck (that I actually have in reality) matters somewhat more — a lot more — than my personal opinion about them based on how “they make me feel” (or something like that).

But why is that and how can we look at this when it’s not so intuitively obvious?

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The Math of Trust

A systematic approach to understanding which opinions to take into account to what degree and which views to ignore is the BCI, or Believability-Credibility-Intention, model. I know, it’s a clunky term but I just invented it on the fly — bear with me please.

In its basic version, it says that:

Someone’s opinion is more believable the more credible they are and the more they have aligned intentions.

In more analytical terms, a formula looks something like this:

Believability (B) = Credibility (C) x Intentions (I)

Now, what I say about the spread of or political measures against the Coronavirus can either be completely believable (B=1), completely unbelievable (B=0), or, as it’s usually the case, something in between (say B=0.4).

Two Questions to Assess Opinions

To which degree you should take my opinion seriously hinges on two questions:

Q1: What’s the Credibility (C) of my formed opinion?

Q2: What’s the Intention (I) behind my reasoning?

Re: Credibility

My Credibility further depends on my expertise (e) in the field and my ability to apply logic (l) to my construction of arguments.

Credibility (C) = expertise (e) x logic (l)

If I have a lot of expertise (e.g., e=0.95) and am a very logical thinker (e.g., l=0.9), my Credibility will be close to 1. Think of a well-trained virologist with a math and statistics background.

If, however, I have only very little idea of what I am talking about (e.g., e=0.1) — even though I am a logical thinker maybe (e.g., l=0.8) — my Credibility is way below 1, closer to 0. Think of the intelligent uncle at the dinner table who just read a few Facebook headlines.

The same applies when I do in fact know my shit, but I am really bad at constructing logical arguments. Again, my Credibility is low. Think of the well-read tinkerer who struggles with putting one and one together.

Generally, Credibility (C) can be anything between 1 (very high credibility) and 0 (very low credibility).

Re: Intention

Apart from the credibility I might have (or not), the intentions behind my reasoning matter a lot.

In the best case, my intention is to simply find the truth — ar at least understand the problem properly (I=1).

In the worst case, my intention is completely decoupled from truth-finding and understanding and it’s based on some other motive (I=0).

For example, if I try to convince you of something I benefit from (like when I try to convince you to assign more budget to my department), my intentions might be questionable. Incentives (i) matter.

Likewise, if I hold a deeper religious belief that’s incompatible with another opinion (e.g. if I am a hardcore Catholic physicist arguing for Creationism instead of the big bang), my intention is also questionable. Beliefs (b) matter.

Intention (I) = incentives (i) x beliefs (b)

Generally, Intention (I) can also be anything between 1 (well-aligned intentions) and 0 (misaligned intentions).

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Don’t Use A Calculator

Now, bringing all of this together; there exists a space in which our Believability (B) can go into many different directions as a result of a few different reasons.

While it’s important to respect that other people think differently about a particular topic, it’s equally important to understand that not all of these differing opinions have the same weight when it comes to finding the truth (if there is one to be found).

Practically, we will never apply math formulas to judge whether or not to trust someone (or ourselves — pro game!).

However, we can use the BCI model to add vigor to our assessing and using opinions when it matters.

To which degree we should believe someone’s opinion (B) depends on their Credibility (C), in turn depending on how much they know the subject matter they are talking about (e) and how good they are at formulating logical conclusions (l). People’s believability is also impacted by their Intention (I), in turn built from the true underlying incentives of having a particular opinion (i) as well as the beliefs they might hold to motivate a particular reasoning (b).

A few of these can usually be identified to a sufficient degree without taking out the calculator and by asking questions.

As a result, our ability to weigh opinions properly goes through the roof.

To opinions,
Phil