Why decision by committee often fails
Facing a tough choice, my boss set up a committee to decide. The committee spent days arguing and eventually came up with a horrendous recommendation. Sound familiar to you?
image credit: dandechiaro
I’ve wondered why committees often fail and make terrible decisions. Recently I came across a mathematical illustration that helps explain this phenomenon.
A simple decision question
Imagine you face a very difficult decision and there is a low probability of making the right choice.
What would you rather do: ask a single person to decide or instead send it to a three-person group where the majority choice wins?
Let us explore the math.
Solution
The situation can be modeled using probability. We can say that each person has an independent probability p of making the right choice. Since the problem is difficult, we will say p < 0.5. (Imagine each person is equally likely to choose among three or more possible alternatives).
What’s the success of the individual versus the group?
The individual is easy: the probability of making the right decision is p.
The three-person group is a little harder. The group will find the right answer whenever two or more of the people vote for the right option. Since each person can vote “right” or “wrong,” there are 8 possible ways to vote:
RRR
RRW
RWR
RWW
WRR
WRW
WWR
WWW
The bolded choices are the 4 ways the group can come to the right decision. Adding the probabilities for these events gives the chance the group will come to the correct decision.
When all three are right, RRR, that is p3. When two are right, say RRW, that is p2(1-p) and there are three such events like this.
The probability of therefore p3 +3p2(1-p) = 3p2 – 2p3
Since p < 0.5, we can see this final expression is less than p :
Generated from WolframAlpha
The moral: committees may not be the best for making touch choices!
That’s not to say committees are useless. They will of course exist to diffuse risk and for the purpose of brainstorming (which may increase the odds of success over an individual). But this does show committees are ill-suited for the type of hard problem they are meant to address.
Discussion questions
1. What happens with a group of 5 people?
2. What happens if the right choice is easier to find, say p > 0.5?
3. Explore the connection with the solution to the hat puzzle.
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One Response to “Why decision by committee often fails”
Nice!
Of course, the follow-up is: if they are so prone to failure, then why are they so ubiquitous?
It’s fun to joke about this in an office setting but gets scary when you remember that this is how trial by jury operates.
Let’s go back to the above scenario:
“Imagine you face a very difficult decision and there is a low probability of making the right choice.
What would you rather do: ask a single person to decide or instead send it to a three-person group where the majority choice wins?”
And compare to this variation:
“Imagine you face a very difficult decision and there is a low probability of making the right choice.
What would you rather do: ask a single person to decide or instead send it to three people individually and use whatever a majority of those people decide?”
Mathematically these two scenarios work out the same, but in reality are drastically different. Asking three people, independently, is a whole different game than asking three people together.
What’s missing from the math here is exchange of information.
The probabilities represented here are static when, in reality, they are dynamic, changing based upon the available information (ideal) or based upon other factors (peer pressure, convincing rhetoric – not ideal).
Thus the purpose of committees: The goal is to put a group of people who, collectively, have all the relevant information. The hope is that said information will diffuse to everyone thus resulting in a majority decision that is most likely correct.
Let’s say that for a given decision there are three relevant facts such that a person’s probability of making the right decision is equal to the proportion of facts they are in possession of.
So if you have three people, each in possession of one fact, they each have a probability of 1/3. Ask them each individually to make a decision and take the majority, and you have the same problems you listed above.
But if you put them together, and they exchange information, they each are now in possession of all the facts and now each have a probability of 1.
Why committees often fail are because things never work ideally.
A) You can’t guarantee that any group of people will collectively be in possession of all the relevant facts.
B) People may not divulge the relevant facts they are aware of.
C) People may not be receptive to the relevant facts they aren’t aware of.
D) People are often more receptive to irrelevant things such as politics, rivalries, articulate (but flawed) arguments.
E) The fundamental axiom – that given the same information people will come to the same conclusion – is clearly not absolute.
By Scott on May 6, 2010