William Baumol's Fairness Assumption

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Definitions

For convenience, the below definitions assume a world with two individuals, A and B, and two goods, X and Y

• Envy:

If A prefers to his own bundle, the bundle of goods held by B, A is said to envy B.

• Fairness:

The distribution of goods X and Y is fair if no envy is involved.

• Superfairness:

If the bundles held by both A and B can be reduced without giving rise to envy, then the distribution is superfair.

Who cares about fairness?

• If preferences are strictly selfish, then why does fairness matter?
  

Selfish people are selfishly worried about others treating them unfairly. As a result, it is often times these innately selfish individuals who insist on rules of fairness. Fairness rules are accepted by selfish individuals as an insurance arrangement to make sure that they will not be mistreated. They pay for this insurance by guaranteeing others that they too will not be mistreated.

Properties of Fariness

• The divide-and-choose game
  
  • In the divide-and-choose game, each player can insure that he does not envy the other.
    
    

Strategy #1

• The "divider" (D):
  • divides the goods so that he is indifferent to the chooser's choice. That is, he divides the bundle so that he himself is indifferent between the resultant bundles.
    
    
• The "chooser" (C):
  • After D establishes the bundles, C need only choose his most preferred bundle.
    
    

Strategy #2

If the divider is certain of the chooser's preferences...

• The "divider" (D):
  • divides the goods so that the chooser is indifferent between the resultant bundles.
    
    
• The "chooser" (C):
  • Can be counted on to choose the bundle that D would prefer him to choose.

Properties of Superfairness