Fitness Landscapes and Probability Distributions

Imagine trying to solve a problem of unknown complexity. You have to start somewhere, so you try a solution more or less at random. If you’re lucky, you know enough about the situation to start with an educated guess.

Regardless of how successful – or unsuccessful – your attempt was, you learn something about the best way to tackle the problem.

Next time you do a little bit better.

Perhaps there are other people around you trying to solve the same or similar problems. You can learn from their efforts as well.

Eventually you converge on what seems like the best possible solution, and then, problem solved, you keep deploying the same solution.

In several disciplines, this process can be described as exploring a fitness landscape. There are optimal solutions, really bad solutions, and everything in-between. Some combination of a priori knowledge and learned exploration gives you an intuition of what the fitness looks like.

Imagine the quick calculations you do in your head when trying to figure out how long it will take you to get somewhere. If you’ve gone there before, you might have a sense of the average length of travel. If you’re familiar with an areas traffic patterns you might have a sense of how much traffic to expect, or what routes to avoid. You may also have a sense of whether it would be more socially proper to arrive a little bit late or a little bit early.

You almost effortlessly predict an optimal solution to a complex problem.

There’s a great deal of interesting research being done to understand how individuals and groups explore or exploit these complex landscapes. As a matter of simplicity in an already challenging problem, it is common to study problems for which an optimal solution is universally an optimal solution.

That is – if every person had perfect knowledge of the fitness landscape, they would each make the same normative judgements about what solutions are “good.”

For my own research interests, this is an important piece of the challenge. One’s definition of “good” or “optimal” is a crucial piece of what policy solutions one might seek – or, more generally, how one might interpret the “fitness landscape.”

If two or more people are exploring the same landscape but have different normative judgements as to what is optimal, this poses a huge challenge.

One solution to this challenge is to hope for the convergence of opinion – so a group may not start with normative agreement on the fitness landscape, but with good deliberation they will come to collective agreement eventually.

There’s a great deal of social science research looking at how consensus forms in groups, with an eye towards possible biases and poorly-formed consensus. Does a group agree with the loudest voice in the room? Does it converge on whatever idea was most popular before discussion began? Did it give full attention and weight to all possible alternative before a final decision was reached?

Yet, on top of all the things that could go wrong in consensus forming, one of the most disconcerting thoughts is that such ideal consensus is not possible at all.

Examining such a question means understanding just what causes a person’s opinion to form in they first place – an understanding, I’m afraid, we are quite far from.

Some opinions may be formed on the spot, with no clear reason why. Other opinions may have cemented through some past series of experiences.

But here’s a thought experiment – imagine dozens of clones of the same person, each starting their life in an identical setting. With every event they encounter – on whatever time scale you prefer – the effect of that experience on them is given by some probability distribution.

If one were so inclined, you could build your favorite sense of nature vs. nurture into this probability distribution.

After some series of n events, the people produced…would be different?

If that were to be the case – even among a starting group with all the same initial conditions, it would pose a significant challenge to the idea of consensus, and ultimately would require some method to make sense of overlapping conceptions of a similar fitness landscape.

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