Are two heads better than one?

I was listening to NPR the other day and heard the word “constult”. This word is in Oxford English Dictionary (I checked). It is a verb that means “To play the fool together.” Both examples in the OED are from the 17th century:

1630 J. TAYLOR (Water P.) World's eighth Wonder Wks. II. 67/1 Some English Gentlemen with him consulted And he as nat'rally with them constulted. 1659 GAUDEN Slight Healers (1660) 91 What do they meet, and sit, and consult (or rather constult) together?

So, this brings up the question (posed on the Car Talk web site); “Do two people who don’t know what they are talking about know more or less than one?” This is worth asking since most hard decisions are plagued by a lack of knowledge. In fact, this was this question (not so well articulated) that led me to start thinking about decision making in the mid 1990s.

When I am designing a new product, I don’t know much about the new details of it. Designing is learning. Often I will enlist others to help on the functions and features I know the least about. Are these colleagues consulting or constulting, and if the latter, why do I seek their help?

I think I know the answer. If I know absolutely nothing about something and my response is a wild guess, then the probability of my being right is 50%. If another person is added to my team and they too know nothing then she is truly constulting, together we know nothing and the probability is still 50%. However, if I know a little and what I know is correct, then my probability is greater than 50%. And, if I add a colleague and she knows a little then the probability of us together being correct is greater still.

As a numerical example (taken from “Making Robust Decisions” page 231), say that I know enough that the probability that I am right is 68%. If another person is added to the team and they independently also have a probability of being correct of 68%, then our fused probability is 82%. If there are three of us, it raises to 91%. The theory behind these numbers is in the book, but they do make intuitive sense.

This also supports the examples in the book “Wisdom of Crowds” (a good read). Obviously there are some limitations. What if members of the team disagree on the answer? What about Group Think? What is the level of knowledge is less than estimated? All of these can lead to constulting.

So to answer the question:

• Two people who know nothing know as much as one person who knows nothing.
• Two people who know a little independently (no group think or peer influence) and their meager knowledge is correct, know more than one person. This is how we get to the wisdom of crowds. If their knowledge is conflicting, they still know more, just that answer is still in doubt.
• Two people who know a little and they have influenced each other through peer pressure (think alpha males), group think or other mechanism, or one or more of them knows less than they think they do; together they may actually know less and be constulting.
  

The goals then are to know when you know nothing and how to avoid the pitfalls that lead to constulting. I have been struggling with these goals for about ten years.