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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  • Scott

    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.

  • http://www.mrieck.com/ Mikael

    I hate committees. I find that they are the reason for most of countries deficits. Very seldom those they result in anything useful and if they do there are probably some politician that disregards the conclusion anyway.

    /Mikael

  • http://www.toprankconsultants.com Brandon

    I think Scott makes some valid points. I think the idea of a committee is to open discussions.

    Just one person might have a certain idea in his head of how things should work or should be.

    When you open different minds to the same information, that will form different opinions within each. This could possibly lead to one of the opinions being the “best decision.”

    I’m not sure if this can correctly be determined with a mathematical equation, because as Scott said, information is dynamic.

    My two cents,
    Brandon

  • Mark

    Great article, interesting and educational.

    Committees may not be great at making decisions, but they tend to be ok at proofreading ;-)

  • Pingback: Brand Building: Fear Decisions By Committee | Oasis Creative

  • Thoughts

    This assumes that the decision space is only made up of two options: right and wrong. While this decision space is true in many instances, it may not be true in the instance of committees. Generally, if a decision space is made up of only two answers (right & wrong), you wouldn’t even go to a committee; one person can make this decision equally as well as a committee, so there is no benefit in bringing in a committee. However, if the decision space is made up of multiple graded decisions, each carrying with it some trade off, a committee might be a better place to explore the possibilities. In any case, the point being made is, your solution is only valid in the case of right and wrong. Real decisions often don’t boil down to right and wrong.

  • http://www.lanudensikkerhed.dk Peter

    I agree with committees not always beeing the best way. You could spend quite som time with a lot of people holding meetings in a room without getting anywhere. But once in a while a committee actually brings value. Some things are just easier to talk about face to face.





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