The probability that democracy works

We are told that a large number of people opting for a certain choice(ex. a candidate in an election) represents near-certainty that this choice meets necessary and sufficient criteria. No particular person needs to understand how a country works if a lot of people who understand different functions of a country cast a vote on the matter…the aggregate decision represents the closest thing to a complete picture. 

Let’s make the following assumptions:
1. The ideal candidate must satisfy  n equally important criteria and we assume that this candidate is present among the existing candidates. 

2. There are  N voters where  N \gg n and each voter has partial knowledge of the  n necessary criteria. In particular, we assume that each voter is aware of at least one criterion and their knowledge of these criteria is given by a uniform distribution.

From the above assumptions it follows that the probability that the correct candidate is chosen is approximately 1-\sum_{k=1}^{n-1} {n \choose k} (\frac{k}{n})^N .  In theory this is good. However, there are some problems with our theory. 

The first problem is that ‘choice’ of criteria is highly correlated within social groups. Second, the definition of equally-important criteria is problematic. Some criteria like the role of government in tech innovation are more complex than others which means that knowledge of criteria is probably given by a gamma distribution rather than a uniform distribution. Finally, the appropriate candidate might not exist among the set of available candidates.

Now, I think the only way for society to move closer to a system where voting works is to change the current education system. Using uniform grading requirements, students are taught to attain knowledge by consensus which merely encourages groupthink. The necessary alternative is to encourage inquiry-driven learning.

This could come in the form of open-ended competitions, like the Harvard Soft Robotics competition that I’m participating in, or working on projects within Fab Labs/Hacker Spaces. In any case, society will have to shift from skill-based employment to innovation-driven employment due to the growing number of tasks that can be automated. People will be paid for their imagination rather than their time and I believe that in 15 years time sheets will all but disappear. 

If we want a democracy that works and not merely the theatrical nonsense that passes for democracy today, radical changes to the education system will be required at all levels. 

Note 1: The probability calculation can be much more complicated depending upon your assumptions.

Note 2: For the reader that’s interested in my opinion on Hacker Spaces, you may read more here

The world we understand

A regular problem I encounter is that people create false dichotomies and use this to guide their reasoning as well as influence the reasoning of others. The problem is that we live in an increasingly complex world with lots of tuneable parameters. Some of them are known, most of them are unknown and almost all of them behave in a highly non-linear manner. 

If a project is ineffective that doesn’t mean that the original idea was inherently bad nor does it mean that the particular implementation of that idea wasn’t carefully thought out. It could have failed for any number of reasons. My guess is that many of us reason in a simplistic manner in order to maintain the belief that we live in a world we understand. 

Let me give some examples of nonsense I often hear:

  1. “curiosity-driven education doesn’t work
  2. “foreign aid is a terrible idea”
  3. “renewables are the future and always will be”
  4. “Mars-bound rockets can’t be built by a company”

In every case the educated person in question will point me to a list of experimental or empirical studies and then try to convince me that the particular idea is lousy. However, what many don’t seem to realise is that in many cases it’s difficult to separate the conclusion of a study and its design. Moreover, what is particularly pernicious about this sloppy method of reasoning is that it often targets unconventional ideas. 

In many cases enterprising ideas aren’t inherently more risky than conventional methods. Very often the unusual idea is more carefully thought out whereas the conventional approach merely relies on tradition for justification. If you should take an unusual path there’s less social support in the event of failure and that’s an important reason why many people judge that it’s safer to fit in. There might be a greater chance of succeeding with approach X but if people are guaranteed to say “I told you so” in the event of failure you wouldn’t be irrational to choose conventional methods.  

This might seem like a fuzzy cultural problem but I think that this is one of the most important problems facing our society today. We may not be one technology away from utopia but if our society doesn’t become more adaptive I don’t see how we’ll collectively overcome the biggest problems facing us in the 21st century. Tradition should not be the default answer. 

However, modern society’s collective desire to be accepted means that even the truth surrounding historically important innovators gets distorted. Paul Graham touches this topic very succinctly in his essay, The Risk of Discovery:

Biographies of Newton, for example, understandably focus more on physics than alchemy or theology. The impression we get is that his unerring judgment led him straight to truths no one else had noticed. How to explain all the time he spent on alchemy and theology?

In Newton’s day the three problems seemed roughly equally promising. No one knew yet what the payoff would be for inventing what we now call physics; if they had, more people would have been working on it.

Now, among those people who are aware that Newton spent a considerable amount of time on things other than physics almost all tend to interpret it by saying that he was a bit crazy like all geniuses. This is simply a careful attempt to recast an important innovator to someone more conventional so we can maintain an illusion that comforts us rather than rationalise unusual and possibly risky projects. 

In reality we aren’t safer by collectively walking off the side of a cliff. We need important innovation in the areas of energy, education and government. For this to happen we need to encourage people that take calculated risks and if they should fail instead of saying “I told you so” we should say “It was worth a try”.