When numbers fail

William Easterly has an absolutely bizarre reader survey on his blog:

Please tell me which you think is more probable:

  1. a country succeeds at economic development, or
  2. a country succeeds at economic development with a wise and capable leadership.

Since the probability of ‘wise and capable leadership’ is less than 1, the probability of option (2) is P(option 1) x P(wise and capable leadership) < P(option 1). Can this survey tell us about anything other than the mathematical savvy of his readership?
I suppose what it can tell us, if option (2) is preferred, is that making truthful statements (like (1) being more probable than (2)) isn’t always the best way to persuade people that your plan’s a good idea. As Eliezer puts it in explaining the conjunction fallacy:

Adding detail can make a scenario sound more plausible, even though the event necessarily becomes less probable.

So, when you want to persuade people your explanation’s better just add lots of plausible sounding detail to the causality and they’ll think the outcome’s more likely than if you left it out. Words to live by.

ht: Anti-Dismal

  • Dave

    the probability of option (2) is P(option 1) x P(wise and capable leadership) < P(option 1).

    Only if the two probabilities are independent, but you can’t assume independence here. So if you think a wise and capable leadership has significant influence on successful economic development you might choose option 2, or if you believe that countries succeed in spite of governments you might choose option 1.

  • @Dave
    The way I interpret the question it doesn’t matter. I read the options as
    1) P(succeed) | wise) + P(succeed | not wise)
    2) P(succeed | wise)
    so
    P(1) >= P(2) and the equals bit requires a zero probability of success without wise leadership, which is implausible so I left it out.

    If you read the first option as P(succeed | not wise) then you’re right, but then I think the question would be very badly phrased.

  • ben

    @rauparaha

    Rauparaha, you take the same formulation as Crampton on AntiDismal, but I disagree with you both.

    On my reading Option 1 contains an implicit reference to average leadership.

    This reading leads to the intuitively plausible (to me) possibility that wise and capable leadership reduces the likelihood of economic growth.

    Under your formulation, that is impossible.

    On my reading, the correct comparison is between:

    1) P(succeed | average leader (or random leader, take your pick)); or
    2) P(succeed | wise leader)

    Since wise and capable is not defined wrt economic development, its possible there is a negative relationship between the two. It took some seriously unwise leadership to produce Magna Carta, and that turned out to be a ripper.

  • @ben
    Hmmmm, I’m not convinced of that interpretation for two reasons:

    1) Option 2 contains a specific reference to leadership while option 1 has none. If a reference were intended then why include it in one but not the other.

    2) I think any question in which you ask ‘is good stuff more likely with smart leaders’ is going to produce an obvious answer.

    I can accept that Easterly wrote a quick blog post and didn’t think too hard about his phrasing of the question, so anything plausible is possible. However, whichever way you interpret it I doubt the answer will be either enlightening or interesting.

  • I’m with Rauparaha. The first is an unconditional, the second conditional.

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  • My bet: Easterly’s just checking whether his readers are familiar with the conjunction fallacy.

  • I think it is possible to read the question as saying – do you think it is more likely that a country succeeds at economic development when they have wise and capable leadership. As I think it is possible to read the second question as “when the country has wise and capable leadership will it succeed at economic growth”.

    If this is the case it is looking at only a subset and asking if the probability of economic growth is greater in this subset than in every possible state of the world.

    Now I can also read it the way you guys are saying it – which implies to me that the problem is that the question is written a bit ambiguously.

    If the question said “a country succeeds at economic development AND HAS wise and capable leadership” instead of with a I would definitely read it the same way you guys have – but the “with a” statement points me to this being a question about the probability in a specific state (namely that the leadership is hot) vs the probability in all states of the world.

  • @rauparaha

    “I think any question in which you ask ‘is good stuff more likely with smart leaders’ is going to produce an obvious answer.”

    Not necessarily – if you think that government is always and everywhere interested in their own wellbeing and not that of society then you may want dumber leaders 🙂

  • I actually have an article on that last point arguing that to the extent that the calculation problem makes planning more difficult, it improved the lives of folks under Stalin. :>

  • @Matt Nolan
    Haha, yes, I failed to consider that Easterly may have meant a wise, capable leader who has no care for the success of his nation. Given the alternative interpretations I guess that’s no more implausible than any other reading 😛