What is 'Arrow's Impossibility Theorem'

Arrow's impossibility theorem is a social-choice paradox illustrating the impossibility of having an ideal voting structure that is reflective of specific fairness criteria, such as Pareto efficiency. Arrow's impossibility theorem states that a clear order of preferences cannot be determined while adhering to mandatory principles of fair voting procedures.

BREAKING DOWN 'Arrow's Impossibility Theorem'

For example, the following shows the type of problem typical of an election. Consider the following example, where voters are asked to rank their preference of candidates A, B and C:

• 45 votes A > B > C (45 people prefer A over B and prefer B over C)
• 40 votes B > C > A (40 people prefer B over C and prefer C over A)
• 30 votes C > A > B (30 people prefer C over A and prefer A over B)

Candidate A has the most votes, so he/she would be the winner. However, if B was not running, C would be the winner, as more people prefer C over A. (A would have 45 votes and C would have 70). This result is a demonstration of Arrow's theorem.

Who Developed the Theorem?

Kenneth J. Arrow (1921-2017) was an American economist who had a long teaching career at Harvard University and Stanford University. Arrow's impossibility theorem, published in 1950, earned him a Nobel Prize in Economics in 1972.

  1. Bayes' Theorem

    Bayes' theorem is a mathematical formula for determining conditional ...
  2. Mutual Fund Theorem

    The mutual fund theorem is an investing theory suggesting the ...
  3. C Corporation

    A legal structure that businesses can choose to organize themselves ...
  4. Posterior Probability

    Posterior probability is the revised probability of an event ...
  5. Cumulative Voting

    The procedure of voting for a company's directors; each shareholder ...
  6. Contingent Voting Power

    A provision granting voting rights to preferred shareholders ...
Related Articles
  1. Investing

    Understanding the Modigliani-Miller Theorem

    The Modigliani-Miller (M&M) theorem is used in financial and economic studies to analyze the value of a firm, such as a business or a corporation.
  2. Small Business

    How Zuckerberg Will Control Facebook Forever (FB, GOOG)

    Zuckerberg has pledged his wealth for charity, which includes his Facebook stock ownership. Here's how he will still control the Facebook business forever.
  3. Personal Finance

    Quiz: How Do Your Finances Measure Up?

    We look at average American debt, credit scores and much more so you can find out how you stack up.
  4. Investing

    A Primer On Preferred Stocks

    Offering both income and relative security, these uncommon shares may work for you.
  5. Investing

    Explaining the Coase Theorem

    The Coase theorem states when there are competitive markets and no transaction costs, bargaining will lead to a mutually beneficial outcome.
  6. Investing

    Efficient Market Hypothesis

    An investment theory that states it is impossible to "beat the market".
  7. Managing Wealth

    What You Need To Know About Preferred Stock

    Curious about preferred shares? Here's what you should know about these bond-like instruments.
  8. Trading

    Trading Wave "C" In Stocks

    Stock corrections typically unfold in three major waves: A, B and C. It is highly likely B, is underway, and any slide in prices over the coming weeks is likely to trigger wave C in many stocks.
  9. Trading

    J. C. Penney Reports as a Retail Mall Survivor

    J. C. Penney reports earnings with an elevated P/E ratio of 52.63, but the stock is recovering as a successful "option on survival."
  10. Investing

    What are Class B Shares?

    Class B shares are one classification of common stock issued by corporations.
  1. What is Fisher's separation theorem?

    Fisher's separation theorem stipulates that the goal of any firm is to increase its value to the fullest extent, regardless ... Read Answer >>
Hot Definitions
  1. Entrepreneur

    An Entrepreneur is an individual who founds and runs a small business and assumes all the risk and reward of the venture. ...
  2. Money Market

    The money market is a segment of the financial market in which financial instruments with high liquidity and very short maturities ...
  3. Perfect Competition

    Pure or perfect competition is a theoretical market structure in which a number of criteria such as perfect information and ...
  4. Compound Interest

    Compound Interest is interest calculated on the initial principal and also on the accumulated interest of previous periods ...
  5. Income Statement

    A financial statement that measures a company's financial performance over a specific accounting period. Financial performance ...
  6. Leverage Ratio

    A leverage ratio is any one of several financial measurements that look at how much capital comes in the form of debt, or ...
Trading Center