Disambiguating expected likelihood of discrete outcomes

I’ve been writing about disambiguation techniques. Here’s another one. This one applies when the question cannot be disambiguated into a continual variable.

Suppose Adam and Bob and a bunch of friends live in a house together. They all enjoy living together and hope to continue for a long time to come. But a complication has emerged. Adam is allergic to dogs, and Bob’s girlfriend has a dog. Bob would like to have his girlfriend come over more — and maybe even move in some day — but it’s hard for her to do that because she has to leave her dog at home.

This poses a risk to Adam and Bob’s goals of living in the house together. If Bob can’t have his girlfriend over, he might have to move out. Or Bob might not move out, but might someday find that his relationship with his girlfriend has been strangled by the fact that she doesn’t spend much time at his house. Or if Bob brings his girlfriend’s dog over anyway, it may cause Adam to have constant allergies, and Adam might have to move out.

There’s also a possibility that some happy compromise can be found — perhaps if the dog is bathed regularly it won’t produce an allergic reaction. Or maybe the dog can be limited to certain areas of the house that Adam doesn’t care to spend time in.

But Adam and Bob find themselves having a hard time talking about the issue. If they were to disambiguate using this technique, they might find out why.

The first step is to list the possible outcomes. They agree that there are 4 possible outcomes worth discussing. Next, they each record their likelihood estimate for each outcome.

Here’s what they come up with.

OutcomeAdam’s expected likelihood of this outcomeBob’s expected likelihood of this outcome
Bob moves out25%10%
Bob stays but his relationship with his girlfriend is strangled50%35%
Adam moves out20%5%
A happy solution is found whereby all of the above are false5%50%

Finally, they compare results. Looking at the last row, they see a huge delta on their expected likelihood of a happy solution. Now it makes sense to both of them that Bob has been excited to talk about solutions, while to Adam this has felt wrong.

From here, with a greater understanding of one another’s point of view, they can further disambiguate to find out why they have such different likelihood estimates for this outcome. They’re doing productive disagreement.