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Network Theory:

Computational Phenomena and

Processes

Institutions

Institutions

A set of rules and norms that guide collective action.

E.g: The stock exchange

Consider Braess’s Paradox

• Braess Researched road traffic and found

counter intuitive results. Consider the following

routes

X= number of cars traveling the path

C

A

D

B

X/

X/

45

45

Exogenous vs. Endogenous factors

Unknown desirability of alternatives

• Exogenous : Value Independent of others
• Endogenous : Value dependent on others choices

Exogenous events in Markets

Prediction markets create a collective opinion by coalescing opinions of a group about a future event.

E.g : Iowa electronic markets to forecast 2008 presidential election results.

Price= Average of beliefs about a event probability. Market= An institution that aggregates positions of its consistent

members

Voting Systems

• Voting Systems produce collection action
• We must aggregate subjective preferences

among a group.

Majority Rule

• Assume an odd number of voters and for a pair

of alternatives, sum votes for each and the maximum votes selects its fair choice.

Condorcet Paradox

• A voting paradox noted by the Marquis de Condorcet in an essay published in 1785. For example, suppose there are three candidates, A, B, and C, and three voters whose preferences are as follows:
• Preference
• First Second Third
• Voter 1: A B C
• Voter 2: B C A
• Voter 3: C A B
• A is preferred to B by a majority of voters and B is preferred to C by a majority. However, it is also the case that C is preferred to A by a majority.

Borda Count

• With k alternatives, voter i gives k-1 to her

prior choice, k-2 to her 2nd, and so on. Alternatives are ordered based on sum of this weights gives by voters

• Borda Count suffers from pathological as well
• Arrow’s impossibility theorem: Proves there

isn’t a voting system free from pathology.

Single peaked preference

• A preference that clearly identifies top

candidate at the peak.

Top candidate ranking

alternatives

Median Favorite

• Let’s have individual voters each have an

ordered list of candidates. Find the candidate that is at the median of all ordered lists.

• Theorem: the median candidate defeats every

other alternatives in pairwise majority vote.

The following holds in a market equilibrium:

1. The value of consumer good > the cost of consumer good
2. Goods are assigned to consumers who value them the most. This is evident in prices paid for goods.
3. Total consumer good value -Total good cost = Social surplus from property rights.

Markets as Institutions

• Consider a restaurant as an example:
• A consumer buy $5 smokes a cigar.
• Another consumer suffers $10. If benefit beyond cost is $5;
• benefit=$
• surplus=$15-$10=$

Markets as Institutions

There are several alternative for compensation. There are problems arising from each.

1. Pay the consumer for her suffering
2. Convert “smoke free air” in the restaurant into a commodity to be traded
3. Pass a law prohibiting public smoking.

Markets as Institutions

John Coase’s Theorem using on example:

• Consider a baker and a doctor who share an office building.
• Problem: baker’s machinery disturbs the doctor’s medical practice who is responsible for externalities.

Markets as Institutions

• Baker can buy quieter machinery for $50. Doctor can sound proof for $100.
• Scenarios:

1. Town assigns property rights of noise to doctor so he forces baker to spend $50.
2. Town assigns prop rights if noise to baker. So doctor pays 50$ to baker to buy machinery.

Markets as Institutions