arrowsimpossibilitytheorem-220603081823-4733ec7f (1).pptx

economist

1. Arrow’s Impossibility Theorem

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

5. 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, Y and 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

6. Two individuals A and C prefer X to Y. Two individuals A and B prefer Y to 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.

7. 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.

8. 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:

9. Amartya”s sen capability approach for well being……

10. Conclsion ..