## Definition

Arrow’s Impossibility Theorem is a social-choice paradox illustrating the impossibility of having a decision-making process that meets all desirable criteria. Developed by economist Kenneth Arrow, it stipulates that no system can simultaneously satisfy fairness, rationality, determinacy, and independence from irrelevant alternatives. Essentially, it asserts that it’s impossible to devise a ‘perfect’ voting system, underlining a fundamental challenge in collective decision-making.

### Phonetic

**The phonetic transcription of “Arrow’s Impossibility Theorem” is /ˈæroʊz ɪmˌpɑːsəˈbɪlɪti θɪˈrɛm/.**

## Key Takeaways

- Arrow’s Impossibility Theorem is a significant concept in the field of social choice theory which proves that no voting system can be perfect. That is, there is no voting system that can accurately transform the ranked preferences of individuals into a community-wide or global ranked preference.
- The theorem expresses the difficulty of making collective decisions that meet a set of logical criteria. These criteria include unrestricted domain, non-dictatorship, Pareto efficiency, and independence of irrelevant alternatives. According to Arrow, it is impossible for a voting procedure to meet these criteria all at once.
- Arrow’s theorem has profound implications for democratic decision making and the study of political science, economics, and philosophy. It raises important questions about the nature and possibility of democratic governance, and whether any voting system can truly reflect the will of the people.

## Importance

Arrow’s Impossibility Theorem is a pivotal concept in the field of economics and social choice theory that highlights the inherent difficulty in fairly aggregating individual preferences to reflect collective ones. Named after economist Kenneth Arrow, the theorem stipulates that it is impossible to devise a voting system that accurately captures individuals’ preferences without violating some fundamental democratic criteria. This includes non-dictatorship (no single voter should decide the collective preference), unanimity rule (if everyone prefers A over B, then the group should too), and independence of irrelevant alternatives (ranking of A over B should not be affected by changes in ranking with respect to any other alternatives). Therefore, the importance of Arrow’s theorem lies in its profound implications for democratic decision-making and economic welfare theories, providing an understanding of the limitations and potential flaws within voting and decision-making systems.

## Explanation

Arrow’s Impossibility Theorem, also known as the General Possibility Theorem, is a significant contribution to the field of social choice theory, which seeks to understand how individual preferences can be aggregated to form collective decisions. The theorem, named after Nobel laureate Kenneth Arrow, provides a perspective on the challenges entailed in designing a social welfare function, a mechanism that translates a set of individual preferences into a single, collective decision. The purpose of the theorem is to reveal the inherent complexities associated with reaching fair decisions in group settings or societies, emphasizing the difficulties in fulfilling everyone’s preferences simultaneously while ensuring fairness and efficiency.Arrow’s Impossibility Theorem essentially dictates that no voting method can meet all of the fair and reasonable conditions Arrow outlined, which makes achieving absolute social choice fairness impossible under his stipulated conditions. These conditions include a commitment to universality, whereby all individual preferences are accounted for; respect for individual sovereignty, signifying that an individual’s preference should not be disregarded; avoidance of dictatorial decision-making; and monotonicity, ensuring that if an individual raises the rank of an option, the group ranking of that option doesn’t decrease. The theorem is widely used for understanding and analyzing the limitations and trade-offs of various decision-making and voting methods, providing us with valuable insights on how collective decisions might be either empowering or limiting towards constituents’ preferences.

## Examples

Arrow’s Impossibility Theorem, proposed by economist Kenneth Arrow, states that it is impossible to create a social voting system that will always result in a fair and reconcilable outcome. Here are three approximate real-world examples of how it’s applied:1. Election Voting Systems: In any nation with more than two political parties, decisions about who should lead can often be difficult to make and can result in unintended consequences. For example, in a three-party system, voters may rank their preferences, expecting that their second choice will be considered if their first choice is not the majority’s choice. However, according to Arrow’s theorem, there’s no guarantee that these second-preference votes will result in a universally satisfactory outcome.2. Corporate Decision Making: In a corporation where decisions are made by a board of directors, Arrow’s theorem may also apply. If each board member has different preferences about a critical decision – such as the hiring of a CEO – there’s no guarantee that collective decision-making will lead to the optimal result. The outcome can often be swayed by the power dynamics within the board, rather than reaching a universally accepted decision.3. Market Economies: In this context, the theorem may imply that there’s no such thing as concisely defining public interest, as it’s impossible to aggregate individuals’ preferences into a community’s given various preferences about investments, spending, taxes and so forth. This could be seen in a democratic society’s debate over the budget spending for a particular year. Different groups will have different thoughts on how to allocate funds, and arriving at a decision that satisfies everyone would be impossible according to Arrow’s theorem.

## Frequently Asked Questions(FAQ)

## What is Arrow’s Impossibility Theorem?

Arrow’s Impossibility Theorem is a principle developed by economist Kenneth Arrow, which suggests that it is impossible to create a perfect voting system that accurately represents the preferences of every individual voter.

## What do you mean by a ‘perfect’ voting system according to this theorem?

A perfect voting system, as assumed in Arrow’s theorem, is one where the collective decision-making process meets a range of criteria including unrestricted domain, non-dictatorship, Pareto efficiency, and independence of irrelevant alternatives.

## Can you briefly explain these criteria used in Arrow’s Theorem?

Sure, unrestricted domain means voters can order their preferences in any way they like. Non-dictatorship means no single voter can dictate the entire outcome. Pareto efficiency means if every individual prefers a certain option then so should society. Independence of irrelevant alternatives means ranking of two options should not be affected by introduction or removal of other options.

## What are some implications of Arrow’s Impossibility Theorem in the field of finance and business?

The theorem is primarily used in the realm of social choice and voting systems, but it can also be applied to fields like finance and business in situations where collective decision-making is important. For example, it shows the limitations of attempts to derive market demand from individual demand, with implications for understanding market behavior and economic policy.

## What was the intention behind the creation of the Arrow’s Impossibility Theorem?

Kenneth Arrow created his theorem with the intention of finding a flaw in democratic decision making by putting the idea of an ‘ideal’ voting system to the test. He found that no system could satisfy all the criteria, which fundamentally challenged the concept of democratic fairness.

## Is there any real-world application of Arrow’s Impossibility Theorem?

The theorem provides a theoretical framework used to understand the limitations of collective decision-making processes. While the strict requirements of Arrow’s Theorem mean it has limited direct application, the insights it offers can be valuable in designing and evaluating electoral systems and other forms of group decision-making.

## Can Arrow’s Impossibility Theorem be disputed or disproved?

Arrow’s Impossibility Theorem is a mathematical theorem, and as such, it can’t be disproved. However, some argue that its assumptions do not perfectly apply to real-world scenarios or that some of its criteria can be relaxed to make way for ‘almost perfect’ voting systems.

## Related Finance Terms

- Social Welfare Function
- Voting Paradox
- Collective Decision-Making
- Preference Ranking
- Unanimity Rule