2. What is Arrow's Impossibility Theorem?
Arrow's impossibility theorem is a social-choice paradox illustrating
the flaws of ranked voting systems. It states that a clear order of
preferences cannot be determined while adhering to mandatory
principles of fair voting procedures.
Arrow's impossibility theorem, named after economist Kenneth J.
Arrow, is also known as the general impossibility theorem.
3. KEY TAKEAWAYS
•Arrow's impossibility theorem is a social-choice paradox illustrating
the impossibility of having an ideal voting structure.
•It states that a clear order of preferences cannot be determined
while adhering to mandatory principles of fair voting procedures.
•Kenneth J. Arrow won a Nobel Memorial Prize in Economic
Sciences for his findings.
4. Arrow's impossibility theorem,
the general possibility theorem or Arrow's paradox is an impossibility theorem in social
choice theory that states that when voters have three or more distinct alternatives
(options), no ranked voting electoral system can convert the ranked preferences of
individuals into a community-wide (complete and transitive) ranking while also meeting the
specified set of criteria: unrestricted domain, non-dictatorship, Pareto efficiency,
and independence of irrelevant alternatives
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13. • In other words, social choice is inconsistent or undemocratic because no
voting system allows these five conditions to be satisfied. This has come to
be known as the Arrow Impossibility Theorem. To illustrate Arrow’s general
impossibility theorem, suppose there are three individuals A, B and C in a
society. They are asked to rank three alternative situations X, Yand Z They
vote by writing number 3 for their first choice, 2 for their second choice and
1 for their third choice. Suppose the voting pattern is as shown in Table 1
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15. • Two individuals A and C prefer X to Y
.Two individuals Aand B prefer Yto
Z. Nonetheless, B and C prefer Z to X. Hence the majority prefers X to Y
and Y to Z, but it also prefers Z to X. This is illustrated in Figure 5 which
shows a multiple-peaked pattern. This explains the paradox of the majority
rule which is inconsistent with those of individuals composing the majority.
16. • Thus Arrow shows that the use of the democratic process of voting leads to
a contradictory welfare criterion. “This ‘voting paradox’explored by Prof.
Arrow, comes as a shock to one’s faith in electoral democracy,” according to
Prof. Musgrave. “Fortunately the paradox does not imply that majority rule
cannot work.
• Rather, the conclusion is that for majority rule to give non-arbitrary results,
the preference structure of individuals must be typically single-peaked.” By
single-peaked preference patterns, Musgrave means, where there is an
absence of voters with “extremist” preference patterns.
17. Criticism
• 1. Not related to Social Welfare Function
• 2. No Solution of Interpersonal Comparisons
• 3. Mathematical Politics
• 4. Social Choice not the only Alternative.
• 5. Majority Voting Pattern Unrealistic:
