A Little Logic Puzzle

Consider the following syllogism.

Premise 1: All living things need water.
Premise 2: Roses need water.
Therefore: Roses are living things.

Is the conclusion logically valid or invalid? Try to answer before reading on.

About 70 percent of university students who have been given this problem think that the conclusion is valid. They were wrong, probably by confusing truth and logical validity. The syllogism's form is as follows.

Premise 1: All S is P.
Premise 2: Q is P.
Therefore: Q is S.

This is more likely judged as invalid, since true/false doesn't interfere.

The following with the same form is more obviously invalid.

Premise 1: All cows breathe air.
Premise 2: My cat breathes air.
Therefore: My cat is a cow.

If the conclusion and Premise 2 of any syllogism above were reversed, it would be logically valid. Of course, 'my cat is a cow' would remain false.

Lotto Probabilities

Is the probability of drawing six consecutive lotto numbers, e.g. the first set following, different than the probability of getting six random numbers, e.g. the second set following?
     5, 6, 7, 8, 9, 10          1, 13, 15, 29, 49, 32

They are equal, but many people believe the second set is more likely to be drawn. I guess they believe that because random numbers are more likely to be drawn. Indeed, that is true in aggregate. But to impute that to one combination commits the fallacy of division. Suppose  there are Z possible combinations and N is the number of consecutive combinations. Then the probability of drawing one consecutive combination is (1/N) * (N/Z) = 1/Z. The probability of drawing one non-consecutive combination is (1/(Z-N)) * ((Z-N)/Z) = 1/Z.

Constructivist and Ecological Rationality #5

A market in which lenders can measure and monitor each borrower's risk will charge more/less for more/less risk. Lenders will also deny loans to risks that are too high. Pooling customers into different classes -- short-term loans to businesses, longer-term loans to businesses, loans to states/municipalities for various purposes, car loans, mortgages, loans for college, and so on -- may be the best practical market solution to attenuate the problems of adverse selection and asymmetric information. "The non-existence of certain markets that are not self-sustainable, or their failure to serve all potential customers, or that otherwise encounter incentive compatibility problems that fail to align prices with individual costs and benefits, is evidence of market success, not market failure" (p. 97, my bold).

Capitalism-Socialism Debate

At FreedomFest2016 there was a debate about capitalism versus socialism. The debaters were John Mackey for capitalism and John Roemer for socialism. Mackey is the CEO and co-founder of Whole Foods Markets (link). Roemer is a Marxist professor of political science and economics at Yale University (link).

Mackey argued that capitalism offers the profit incentive that motivates entrepreneurs to build businesses and create new products. Roemer argued for redistribution of income from people with high incomes to people with low incomes via taxes, also wealth from rich to poor via inheritance (or estate) taxes. He argued that high taxes would not demotivate high-achieving entrepreneurs, because such people are self-driven to accomplish their goals for reasons beyond only money. He may have given Steve Jobs as an example; I can’t recall. He seemed to approve of having competitive markets -- he has advocated a species of market socialism (link).    

He said nothing about redistribution altering the incentives for other people – most people – who aren’t entrepreneurs, self-driven, and ambitious for other than only money. If they don’t have the need to earn a living, work hard to get a raise or promotion or even keep their jobs, and yet receive a comfortable income regardless of how little they produce, how would that affect the level of production in their society?

He said nothing about redistribution altering opportunities for other people. Money taken by the government as taxes from a profitable business is money the business can’t use to produce more and hire more people.

Professor Roemer probably believes his intentions are glorious, but the road to serfdom and misery is paved with the unintended consequences of ideas like his. Venezuela is a great example.

Constructivist and Ecological Rationality #4

It is commonly believed that monopoly means one supplier and such a supplier will raise prices and gouge customers.  Vernon Smith used what happened after airline deregulation to show suppliers not acting that way.  “With low entry and exits cost, passenger rates on any route were highly competitive [ ], even if the numbers serving those routes were very small. “Small” includes one. Yes, a route served by only one airline might well charge little above a competitive price; otherwise, the airline would soon find itself facing other airlines operating on the same route. Hence if the route passenger demand were such that it was a “natural monopoly,” with only one firm needed to serve the route at lowest cost, this implied not a monopoly price, but a price that would limit the entry of a second competitor. There is no way that any single airline thinking that it had a monopoly on a particular route could charge more than the opportunity cost of a second entrant. Such a price is a competitive equilibrium price: The market clears with one firm scheduling, say, one flight a day to serve all those willing to pay at least the clearing price, with no firm finding it profitable to schedule a second flight” (p. 86-7).  

He adds that neoclassical economics had relied on the mistaken notion that any competitive equilibrium requires a large number of buyers and sellers actively serving a market, rather than on the opportunity costs of potential suppliers. This is another example of the significance of knowing what is not (an absence of other actual suppliers) in order to understand what is (only one supplier).

Constructivist and Ecological Rationality #3

In the chapter Asymmetric Information, Smith critiques the ideas of Joseph Stiglitz. Stiglitz is another Nobel Prize winning economist, who got the prize for work on markets with asymmetric information.  These are markets that don’t meet the assumptions for "perfect competition". Stiglitz’s early work focused on markets where the participants are "imperfectly" informed and unequally informed. Smith takes Stiglitz to task for jumping to the unwarranted conclusion that such markets are “imperfect”, inefficient, and thus need governmental constructivist intervention.  Stiglitz is a vocal critic of Adam Smith’s “invisible hand” and free markets. Vernon Smith defends Adam Smith’s ideas. Stiglitz has become a prominent leftist. 

Constructivist and Ecological Rationality #2

My first post gave the essences of the two concepts. In the next paragraph Smith describes their relationship.

"Again, individuals and groups invent products, ideas, policies, and such, but whether they endure or are copied is subject to forces of selection and filtering that are well beyond the control of the initiators. Every business decision is someone’s constructivist idea of a best or appropriate action, but whether that decision is ecologically fit is up to socioeconomic forces far beyond the originator. Ecological rationality, however, always has an empirical, evolutionary, and/or historical basis; constructivist rationality need have little, and where its specific abstract propositions lead to some form of implementation, it must survive tests of acceptability, fitness, and/or modification”  (p. 25).

"Reason is good at providing variation, but poor at selection; that is, construcivism is a powerful engine for generating variation, but it is too far narrowly limited and inflexible in its ability to comprehend and apply all the relevant facts in order to serve the process of selection, which is better left to to ecological processes that implicitly weights more versus less important influences" (p. 38).

Constructivist ideas are also used for political action, advocacy and influence. Smith doesn’t say a lot about that on or near page 25, except Hayek criticizing some constructivist ideas of John Stuart Mill. It seems he will later in connection with U.S. airline deregulation (1978-yy) and the California energy crises (2000-01). Hayek strongly criticized constructivist ideas in politics, and Smith is an admirer of Hayek.

As an aside, the middle paragraph reminded me why there is beta testing and other forms of testing for computer programs (link).