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Theorems from social choice theory

by Bipolarity
Tags: choice, social, theorems, theory
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Nov8-12, 04:08 PM
P: 783
I thought I would share some interesting theorems from economics.

1) Arrow's Impossibiliy Theorem:
This theorem states that in voting that involves 3 or more candidates, no rank ordered voting system can simultaneously satisfy the following set of criteria:
- If every voter prefers candidate X to candidate Y, the group will prefer X to Y
- If every voter's preference between X and Y is constant, then the group's preference between X and Y is a constant
- No single voter possesses the power to always dictate the outcome of the vote

A proof is provided here:

2) Coase' Theorem:
The allocation of resources is invariant to the assignment of private property rights under zero transaction cost and zero income effect.
What this theorem essentially says is that no matter what legal system you apply to a group of parties, the parties will always find a way to trade with one anoter so as to produce the most efficient outcome possible for them, provided that the costs of any transactions they make is 0, and that the income effect is 0.

The theorem has yet to be proved formally.

3) Marriage tax theorem (from Mankiw's Principles of Microeconomics):
There is no taxation system that simultaneously satisfies the four properties listed below:
- Two married couples with the same total income should pay the same tax.
- When two people get married, their total tax bill should not change.
- A person or family with no income should pay no taxes.
- High-income taxpayers should pay a higher fraction of their incomes than
low-income taxpayers.

This is an interesting result, its proof established in the following paper:

I invite you all to discuss the three theorems, and their implications in real life.

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