The Barber Paradox

October 31, 2011

I recently listened to the Radiolab podcast on Loops that has a segment on The Barber’s Paradox:

The barber shaves only those men in town who do not shave themselves.

Who shaves the barber?

Apparently this paradox was a big issue for set theory. The following SQL works quite nicely to describe the statement “all people either shave themselves, are shaved by someone else, or don’t shave at all”:

CREATE TABLE Person(
name VARCHAR(40) NOT NULL PRIMARY KEY,
shavedBy VARCHAR(40) REFERENCES Person(name)
);

INSERT INTO Person(name, shavedBy) VALUES(‘Floyd’, ‘Floyd’);
INSERT INTO Person(name, shavedBy) VALUES(‘Andy’, ‘Floyd’);
INSERT INTO Person(name, shavedBy) VALUES(‘Goober’, ‘Floyd’);
INSERT INTO Person(name, shavedBy) VALUES(‘Gomer’, ‘Gomer’);
INSERT INTO Person(name, shavedBy) VALUES(‘Opie’, NULL);

SELECT DISTINCT shavedBy AS barber FROM Person
WHERE shavedBy IS NOT NULL
AND shavedBy != name;

The result is:

barber
——–
Floyd

The relational model defines Entities and Attributes on those Entities. So is the issue with the Barber’s Paradox that the language does not make a distinction between Entities and Attributes or is the self-referencing part problematic? Creating a Barber TABLE to go with the Person TABLE is the wrong approach but I think it is only wrong if a self-referencing Attribute exists. We could define a patient-doctor relationship with either a doctor Attribute or a Doctor Entity and both approaches would work fine.

The SQL solution to the Barber Paradox nicely handles additional cases like a new barber moves to Mayberry or Aunt Bee shaves some men in her spare time.

Q.E.D.?

The Brother’s Keeper Bill

October 30, 2011

Bryan Caplan on the EconLog blog writes:

Suppose someone proposed a “Brother’s Keeper Bill.” According to this BKB, people earning at least double the poverty line would be financially obliged to give 20% of their income to any sibling earning less than the poverty line.

Caplan doubts that many people would support this bill and provides several potential responses that fall into the following nine types: 1) atomic individualist, 2) libertarian, 3) moral hazard, 4) donor incentive, 5) work ethic, 6) meritocratic, 7) Puritanical, 8) evasive, and 9) debt.

You wouldn’t want to pay 20% to your brother who you know so why would you pay 20% to a total stranger? The answer is that you are not paying “a” stranger, you are entering into an agreement with a very large group of strangers. It is the same idea behind car/home insurance but applied to income.

The issue with Caplan’s argument is that it equates Responsibility-for-an-Individual with Obligations-to-a-Collective.

I think it is perfectly valid to question whether it is the role of government to provide income insurance but “The Brother’s Keeper Bill” is a sophism.