Social Choice Theory

What Is Social Choice Theory?

Social choice theory is an economic theory that considers whether a society can be ordered in a way that reflects individual preferences. The theory was developed by economist Kenneth Arrow and published in his book Social Choice and Individual Values in 1951.

Understanding Social Choice Theory

Frenchman Nicolas de Condorcet laid the groundwork for social choice theory in a 1785 essay. The essay included the jury theorem. In the theorem, each member of a jury has an equal and independent chance of making the correct judgment on whether a defendant is guilty.

Condorcet showed that the majority of jurors are more likely to be correct than each individual juror, thereby making the case for collective decision-making. Condorcet's paradox builds upon his previous theorem and proposes that majority preferences can be irrational. Thus, Condorcet showed that while collective decision-making is preferable to individual decisions, there are still problems associated with it.

In the 20th century, Arrow broadened the theory of social choice beyond the investigation of the properties of majority rule. Arrow's generalization of the theory of social choice asks whether it is possible to find a rule that aggregates individual preferences, judgments, votes, and decisions in a way that satisfies minimal criteria for what should be considered a good rule.

Arrow's social choice theory considers all sorts of individual choices, not just political choices, and all sorts of possible rules for reaching collective decisions beyond a simple majority voting rule.

Arrow's Five Conditions

Ordering society in a way that reflects these many and varied individual preferences is difficult. Arrow specified five conditions that a society's choices must meet in order to fully reflect the choices of its individuals. They are:

Using these conditions, Arrow developed his Impossibility Theorem. Arrow's Impossibility Theorem states that it is impossible to order society in a way that reflects individual preferences without violating one of the five conditions. Therefore, selecting a social choice rule will always involve sacrificing or compromising among Arrow's five axiomatic conditions.

Special Considerations

Another notable contributor to social choice theory is Jean Charles de Bourda, a contemporary of Condorcet, who developed an alternative voting system known as Borda Count. Other contributors to the theory include Charles Dodgson (better known as Lewis Carroll) and Indian economist Amartya Sen.

Example of Social Choice Theory

To consider a political example, under a dictatorship, decisions about social choices and the ordering of society are made by a single individual. Meanwhile, in an open democratic society, each individual has an opinion about how society should best be ordered. Both of these systems violate Arrow's Impossibility Theorem and are thus flawed methods for reaching social decisions that reflect the preferences of society.

A dictatorship obviously violates the non-dictatorship condition. A majoritarian democracy, on the other hand, violates the conditions of independence of irrelevant alternatives. This is because in majority voting, cycling (an endless loop of alternatives with no preferred solution) of preferences is possible, which makes the order and selection of alternatives presented a deciding factor in which alternative will be preferred.

For example, consider three voters voting for three alternatives:

All voters prefer A over B, B over C, and C over A, and a majority of voters will always vote against each of the possible options. Only if one of the options is excluded can a majority vote reach a decision in this situation, which means that the social rank order is dependent on the presence (or rather absence) of an irrelevant alternative.

In practice what this means is that in democracy, the outcome of majority voting may often be a function of the allowable alternatives that voters are permitted to consider and not a reflection of the voters' true preferences.