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

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