Learning vs memorizing

The other day the feasibility of AI came up in casual conversation. Somebody argued that machines can only do what they’re told to, that they just follow a pre-programmed set of rules or commands, and so on.

In response to this I normally cite the field of machine learning as an example of computers doing things (I’ll use classification here) they were not explicitly programmed to do. When recognizing characters, for instance, the computer is not explicitly given a set of rules to determine what letter a given handwritten element corresponds to. Rather it learns from a training set, which for classification is a set of elements together with their correct labels (classifications).

An objection was made to my response: that the process is supervised; even though the programming is not explicit, it is nonetheless programming in the form of example-classification pairs. In effect, the computer is just being fed rules, even if we call that process learning. Now, I could have gone on about unsupervised learning, but there’s a better point to make.

The supervised/unsupervised aspect is not the key to whether learning occurs or not. What is the defining characteristic of learning is the fact that the computer can correctly classify examples it has not seen before.

An agent that only memorizes the training set can correctly identify previously seen elements, but it cannot deal with unseen ones, its memorized knowledge has nothing to say about them. A learning agent, in contrast, manages to extract some knowledge from the training set that can be used to classify new unseen elements. The key to learning is the thus the ability to generalize from examples. It is the acquisition of knowledge from specific cases that is applicable in general.

However, this is not the end of the story. An agent may have the ability to learn, but that is not enough to guarantee that learning does in fact take place [1]. The extra necessary ingredient is that the target of learning must be learnable. If no “explanation” exists that reproduces the data, then there is nothing to be learned [2], the data is just “noise” [3].  This is why a phone book cannot be learned, it can only be memorized.


Notes

[1] This is another statement of the problem of induction

[2] Alternative formulations of this are: that  the data has no internal structure; the data cannot be compressed; the data’s constituent elements have zero mutual information

[3] Unfortunately there is no way to tell whether an “explanation” exists or not, short of finding it. Hence the uncomputability of Kolmogorov complexity.

Direct democracy: Spinning its wheels?

When I first contemplated the possibility of direct democracy channeled through the internet, the idea seemed to me obviously brilliant. The old concept of direct democracy exercised by millions of people just seemed like a perfect match for the internet. Add to this the mechanism of liquid democracy, that is, a hybrid system that allows both representative and direct voting, and the idea made even more sense. The convenience and knowledge specialization of representation together with the control and purity of direct vote.

In an ideal world, the delegation graph would tend towards optimality in the sense of processing information efficiently and reliably. Efficiently in the sense that those with the best knowledge necessary to cast votes accumulate delegated votes. Reliably in the sense that those that best represent voter’s interests accumulate delegated votes. Hence optimal: combining transparent goal representation, the what, with the best means of achieving those goals, the how.

For these reasons I began researching the mathematics, algorithms and in general technologies necessary to create a secure platform to enable liquid democracy through the internet. This research was done on behalf of a local spanish political party whose aim was solely to establish a direct democracy channel within the current political system, that is, without having to make any changes to existing law.

But despite it’s apparent great potential, direct democracy remains a fringe idea that few people take seriously. Until recently, the great difficulty in implementing it practically would have been a good candidate to explain why. But with the development of enabling technology, i.e. the internet, one could expect the concept to take off instead of just spinning its wheels. Now, I’m not going to pretend to believe that the world is the ideal place I’ve sketched above. Direct democracy has many potential drawbacks, and so does its electronic incarnation; I’m aware of many of the sound criticisms that can be made.

However, the point I am trying to make here is that electronic direct democracy fails to attract the population at large for different reasons.

In fact, for a different reason, singular. And that is related to my previous post on politics as rationality catastrophe. If politics can be understood from the vantage point of evolutionary psychology, and political attitudes therefore framed in terms of identity and tribe, then it becomes immediately clear why direct democracy has not had a greater following.

The concept of direct democracy exists at the system level, whereas ideologies normally reside at the policy level. Put simply, direct democracy seems for most people ideologically empty. There is nothing to identify with, no hooks, no content to be part of, and thus tribal adaptations leading to allegiance and group forming are not triggered. Political affiliation is not driven by an intellectual response about what can technically work, but by an emotional one about what one identifies with on a gut level.

Why vote? The so called Paradox of Voting

Someone asked me to formalize an argument I made some time ago about how voting is an irrational act. The essence of the argument is as follows. Given that hundreds of thousands of people vote, the chance of a tie is minuscule. So the chances that an individual’s vote decides the election is equally minuscule. Hence it is almost certain that the act of voting has no consequences. So why vote?

At first glance, it seems like an infantile argument to make, most people would reply: if everybody thought/did that no one would vote. And truth be told, the first time I heard that reply I was fooled. But of course, that reply is wholly irrelevant to the matter. It’s an example of argumentum ad consequentiam, and on top of that, something being true does not imply people believe it. So the bottom line stands, and you can readily formulate it in decision-theoretic terms. As follows:

Expected Utility of Voting = (Probability of Deciding * Utility of Deciding) – Cost of voting

Because the probability of deciding is so small the term in parentheses vanishes, and the utility of voting is negative, the cost of voting, which includes explicit costs of going to vote plus opportunity costs of what you could have done otherwise.

I decided to briefly google the subject and it turns out it’s actually a controversial issue in rational choice theory. It was initially formulated exactly as above by Anthony Downs in 1957[1][2]. Nope, it wasn’t just something of an anecdote anymore, but an open “problem” as of today. Here are some example calculations from [3] including probability estimates

Consider an election in which 5 million voters are expected to cast ballots and candidate 1’s expected vote share is 50.1 percent, while candidate 2 is expected to receive 49.9 percent ofthe votes cast. Myerson (2000) develops a formula in which the number of people who vote is a random number drawn from a Poisson distribution with mean n. According to Myerson’s formula, the probability a vote is pivotal for candidate 2 is 8.1079 x 10^-9. Thus, the benefit to a voter who prefers candidate 2 must be more than 8 billion times greater than the cost to vote. For example, if voting costs $.01, then the expected benefit of electing one’s favored candidate must be greater than $80 million dollars. Expected benefits at such levels seem unreasonable.

Because rational choice theory has the pretense of describing actual human behavior, and because in fact millions of people do vote, there is an apparent contradiction. It’s called the Paradox of Voting, and has been described as “the paradox that ate rational choice theory” [4].

I haven’t looked extensively into the literature at how attempts are made to resolve the “paradox”. I’m pretty sure one can invoke all sorts of technical wizardry to get the desired empirical results (game theory and Nash equilibrium come to mind). But to be frank, I presume it’s just ad-hockery to arrive where you were trying to get to initially.

It’s much simpler to just accept that people are either not rational (surprise surprise) or that there are motivations besides those related to the act of deciding itself (surprise surprise). People may go to vote because they have nothing else to do, out of a sense of duty, because it’s amusing, because it’s what everyone else does [5], or simply because they are outright irrational in estimating cost/benefit. What’s that? Do I hear anybody crying heresy at this scandalous violation of democracy’s sanctitude?

As I said previously, this matter has been debated extensively since 1957. But it seems to me that it’s just as simple as I’m making it out to be; there is no Paradox of Voting just as there is no Paradox of Buying Lottery.


References

[1] Downs, Anthony. 1957.  An Economic Theory of Democracy.

[2] Riker, William and Peter Ordeshook. 1968. “A Theory of the Calculus of Voting.”

[3] Feddersen (2004) Rational Choice Theory and the Paradox of Not Voting

[4] Fiorina, Morris (1990). Information and rationality in elections.

[5] These motivations for voting can be modeled as a consumption benefit in Riker and Ordeshook (1968):

Riker and Ordeshook (1968) modify the calculus of voting by assuming that, in addition to a cost to vote, voters get a consumption benefit D > 0 from the act of voting.

 

 

Politics as rationality catastrophe

One of the spinoffs of my short research into epistemic rationality is the realization that politics is a rationality catastrophe. When a person engages in thought, or even worse, debate, about politics, they will most probably deviate strongly from the standards of rational thinking and distort reality. Put differently, politics is a trigger for a large battery of cognitive biases; confirmation bias as usual gets honorable mention.

Ok, so this doesn’t really count as a new realization, I’ve been making analogies between politics and sports for a long time. But nailing down vague or half-baked ideas into precise explicit form feels like a novelty, even if most of the information was already there.

Some quotes that illustrate the matter.

People go funny in the head when talking about politics.  The evolutionary reasons for this are so obvious as to be worth belaboring: In the ancestral environment, politics was a matter of life and death.  And sex, and wealth, and allies, and reputation…  When, today, you get into an argument about whether “we” ought to raise the minimum wage, you’re executing adaptations for an ancestral environment where being on the wrong side of the argument could get you killed. – Eliezer Yudkowsky

The typical citizen drops down to a lower level of mental performance as soon as he enters the political field. He argues and analyzes in a way which he would readily recognize as infantile within the sphere of his real interests. He becomes primitive again. – Joseph A. Schumpeter

The proposition here is that the human brain is, in large part, a machine for winning arguments, a machine for convincing others that its owner is in the right – and thus a machine for convincing its owner of the same thing. The brain is like a good lawyer: given any set of interests to defend, it sets about convincing the world of their moral and logical worth, regardless of whether they in fact have any of either. Like a lawyer, the human brain wants victory, not truth; and, like a lawyer, it is sometimes more admirable for skill than for virtue. – Robert Wright, The Moral Animal

If people can’t think clearly about anything that has become part of their identity, then all other things being equal, the best plan is to let as few things into your identity as possible. – Paul Graham

Yudkowsky’s point is that irrationality is best understood as a fact of evolutionary psychology, especially in politics. Another interesting insight is the framing of political thinking in terms of identity, self-defense/self-esteem, us vs them (sports anyone?), as Graham suggests.

Now the remaining question is, does thinking rationally let you “get ahead”? Is there an advantage to it? Or could it be a handicap? A rational person could be unable to establish strong ties and membership inside cohesive groups precisely because of his/her clear detached thinking.  And this seems a strong disadvantage in society where groups can exert power for the benefit of their individuals.

So ironically, it could be that nature is still right! Those evolutionary adaptations that worked in the ancestral environment are still “winning” today, even if from the standards of correct thinking they are aberrations. It could be one of those funny cases where epistemic and instrumental rationality are not aligned.