Saturday, September 28, 2013

Complex Problems: The Multiplication of Doubt

In my last two posts which build the foundation of my epistemological framework, I have described how the complexity of problems can be defined through building a hierarchy of constructs and relationships in the order of their complexity. There, I briefly describe the most basic elements with a rudimentary explanation for its complexity ranking as a standalone element. To follow, I described the most basic element, existence, and the general concept of abstraction, which allows us to discuss doubt as a concept which is the abstraction of certainty.

Let us build on the previous discussion here of the nature of knowledge as being inherently probabilistic. Let the certainty of the truth of any given proposition X be represented as Pr(X) in standard statistical notation. Suppose X is some basic proposition with the lowest level of complexity: "The spoon exists," for example, where a spoon is observed on a table in front of you. Having experienced the spoon in front of you, and indeed, currently experiencing it in front of you, you would have supreme confidence in the existence of the spoon. You could not provide a logical proof of the spoon's existence, but you could say that you are as close to absolute certainty in this proposition as one may be; in other words, the limit of Pr(X) approaches 1 in this case. For ease of demonstration, let's suppose Pr(X) = 0.9999.

Tuesday, September 24, 2013

S*** My Future Fed Chair Said

In honor of Janet Yellen, the former President of the San Francisco Federal Reserve, being recently elevated to "frontrunner" status for the chair of the Federal Reserve Board, I present a list of past quotations from Mrs. Yellen here. All emphasis is my own.
"While a tightening of credit to the subprime sector and foreclosures on existing properties have the potential to deepen the housing downturn, I do not consider it very likely that such developments will have a big effect on overall U.S. economic performance." - Speech to the Money Marketeers of New York University, April 26, 2007 (link
Of course, these events very much did have an impact on overall economic performance, and continue to do so today, some 6 years later.

Friday, September 20, 2013

Existence, Abstraction, and Doubt

A proposition expressing existence takes the form "X is". This form of proposition is the most basic form and can serve as a building block from which other, more complex propositions can be constructed. Let us examine more closely the nature of existence and the implications for the use of existence as the lowest-order proposition.

Any animate being can be shown to demonstrate the awareness of existence. Animals, though they are not self-aware and thus may not be cognizant of the concept of existence, will nevertheless react to stimuli in a manner consistent with the awareness of this concept. A dog, for example, will not attempt to run through a wall; it recognizes the existence of the wall and can understand that its efforts would be in vain. It, perhaps, does not know this innately, but through experience it becomes highly confident that the wall exists. Similarly, its eyes will follow an object that it is interested in, such as a ball or a morsel of food; this action directly represents the recognition of the existence of those objects.

Tuesday, September 17, 2013

Incentive and Investment: The Future of Crowdfunding and Venture Capital

Over the course of the last year, Kickstarter has risen to prominence as one of the easiest and most effective ways to fund projects and ideas. By relying on the collective wisdom of crowds, Kickstarter tends to fund projects which are generally recognized by would-be investors as good ideas. The market forces at work here are generally no different than those which govern the more established, more institutional market for venture capital. It's no secret that financial incentive is a great motivator for producing discerning analysis and careful decision-making. 

However, there are several variables that separate Kickstarter projects from venture capital investing. Most of these involve reducing the barriers to entry for small-time investors. An analogy to political fundraising is appropriate: large institutions may dominate funding in federal elections (particularly for the presidency), but it would be impractical for these institutions to devote time and resources supporting candidates for state and local offices. Nevertheless, funding is no less important for those candidates - and in fact, campaign dollars spent there have a much greater impact on the race.

Friday, September 13, 2013

Orders of Complexity

If we assume that we, as humans, have no knowledge a priori from our creation, and that we instead are only more or less certain about any given proposition, then we must start to examine the most basic propositions in our world. The goal, in so doing, is not to determine some empirical probability that we have for any specific proposition or type of proposition, on average. Nor should we be naive enough to believe that we might be able to order our confidence in any two specific propositions. Although confidence can be expressed on a continuum from 0 to 1, we resign our practical ability to fall short of precisely determining our internal confidence in any given proposition, much less a strict comparison between two propositions in which we have similar confidence.

Rather, by examining some propositions, we can perhaps discover how our brains operate in practice, by producing a rough classification which distinguishes certain problems from others. Then, we might generally say that we are naturally inclined to be more confident in the truth of some propositions than others. Another way of stating our goal is that we might classify the order of complexity of a given proposition, based on the constituent elements of that proposition - much in the same way as a grammar teacher might be able to evaluate the complexity of a sentence based on the parts of speech, syntax, and vocabulary of which it is comprised.

Tuesday, September 10, 2013

Universal Life Insurance: Imperfect Competition

How do life insurance markets operate within the classic textbook framework? Is the market perfectly competitive, or do some frictions exist that cause macro-level inefficiencies? The answer depends on what type of insurance product you are looking at, as term insurance and universal life insurance markets have drastically different competitive elements.1

Term life insurance is, all things considered, a very simple form of insurance which is consistent with other lines of insurance such as health or auto. Assuming, for example, that a 35 year old male will need coverage for 10 years, a fixed cost payable annually can cover that risk. When shopping competitively for rates, this individual has one primary element to consider: the amount of the premium. Because of the simplicity of the insurance, consumers can fairly easily compare rates to find the lowest cost policy. This is as close to a perfectly competitive market as exists in financial markets, on par with bonds and other "plain vanilla" assets.

Friday, September 6, 2013

Determinism, Laplace's Demon, and the Statistical Divide

The concept of ex post determinism, which I have referred to here as scientific determinism, is not a new concept by any stretch. Various forms of determinism have been proposed and debated over the last several centuries, and while the boundaries I have laid out may differ, the idea that events are deterministic is well trodden ground.

Perhaps one of the most extreme, or pure, forms of determinism is represented by Laplace's demon. "Laplace's demon" is the name given to the ideas posited in a passage late in Laplace's life on probability (available here). In simple terms, Laplace expressed the idea of pure determinism: If the position and speed of all particles in the universe are known at a time t=0, then the state of the world at a later time t=1 can be perfectly calculated. Laplace, an early statistician, perhaps most clearly demonstrates the divide between frequentist (or probabilist) and Bayesian modes of thought: You may notice that Laplace's demon seems to have nothing at all to do with statistics as we know it today.

Tuesday, September 3, 2013

What Can Monopoly Teach Us About Economics?

Monopoly is a game made familiar to many of us as children; and, as a game of property and trade, it is natural to consider what economic lessons it might teach. It is fairly evident that the objective of the game - to own all property on the board by raising rents on captive, choiceless consumers - does not represent any sort of market economy. This has been well-documented elsewhere, and for a more complete discussion of the economic faults of the game, I would direct you to those sources. 

However, this is not to say that there are no elements of the game that can teach us valid economic lessons, whether directly or indirectly. Economists should not disregard these lessons simply because the broader game economy is unrealistic or does not align with their views. Here are a few things Monopoly can teach us.