Sen’s Theorem: Overview and Analysis

Sens Theorem Overview and digestTable of Contents (Jump to)1. Introduction2. A f completely over of Sens Theorem3. The jump out of recent Interpretation4. Merits of the unfermented Interpretation5. mop upReferences1. IntroductionThe Sens theorem has an important impact on the purpose and social choice theory. In the Nobel Prize lecture of 1998, Sen said that discovering the societal decision rules go out be the main accusing of the choice theory. However, Sen found it is difficult to achieve this objective in his paper of Impossibility of a P betian Liberal (Sen, 1970a, b, 1976c). Sens theorem subjects that it is out of the question to achieve the negligible aspect of liberalism when it is combined with the P arto feel out. According to the theorem of Sen, it seems that on that point is a fundamental frequency conflict between the P areto public assistance concepts and the liberalism. After this argument, there is a pooling of studies that focus on the case-by-case rights and there are overly studies that become wise indication for the theorem of Sen.According to Saari and his collaborators, the cyclic decision outcomes established by Sens theorem describe a transitional, dysfunctional state of comp either. This taste entrust mainly explain how this adaptation arises and discuss its merits relative to the original commentary offered by Sen. The essay will be structured as cost in the second session, the essay will briefly introduce the Sens Theorem regarding to the conflicting results between Pareto Optimal and Liberalism. Examples will in addition be utilise to remedy illustrate the choice decisions. In the third session, the essay will how and why there will be sore descriptions of the theorem of Sen. Particularly, the essay will base its argument on the investigate results of Saari and his collaborators. In the fourth session, the essay will discuss the merits of the new interpretation compared with the interpretation by Se n himself. In the last session, a brief conclusion will be do based on the analysis in the previous session.2. A Review of Sens TheoremThe Sens impossibility of a paretian libertarian theorem or Sens conundrum Paratian liberal states that weak Pareto criterion and liberalism may have conflicts on the fundamental level, which indicated that the Pareto criterion is flawed. On unitary hand, it shows that the Pareto criteria only consider aspects of difference in efficiency among relevant states while ignoring the idiosyncratic utility conflicts arising beca apply of these states. On the early(a) hand, the theorem also shows the in addition to considering close to reasonable internal conditions, adept also require to consider issues such as liberalism for social night club decision making. According to Sen, there are some choices that are sternly of psycheal nature, such as the state (x) means everything else in the ordination as , when A is sleeping supine, state (y) means everything else in society as , when A is sleeping prostrate. If A has a preference of y than x, while many others in the society prefer the opposite, then(prenominal) it bottomland be considered that social choice between x and y is a purely soulfulnessal thing, because A is the only a real person that is related to the choice while other people are meet nosy person. It can also be considered that hotshot can favor one such a collective choice rule where As preference should be accurately reflected by social preferences in this purely personal nature choices (Sen, 1970). Based on this point, Sen emphasizes that people should pay perplexity to the study of individual rights and other issues affecting the social choice range and decision making. The new welfare economics and welfare economics research before the new welfare economics are consciously or unconsciously avoid these problems.Sen (1970) found that the Pareto criterion is incompatible with liberalism. Pareto optim ality is used by the economists and other social scientists to measure the efficiency of society, which is also the the most plebeian and widespread, even the only indicator. It refers to such a state that we are wide-cut as it gets, no one can make an additional welfare without compromising the welfare of others. And the principles of individual granting immunity are the relentless hunting of mankind, both of which are on the intuition that people can to the full accept and understand. However, Sens theorem shows that these dickens attractive standards are contradictory and can non be simultaneously true.3. The Rise of New InterpretationThere are trinity preconditions that Sens theorem is based on and the realistic of these self-assertions will be one reason why there will be new interpretations for the Sens theorem. First, the essay will briefly introduce the assumptions related to the Sens theorem.An unrestricted area principleThe Pareto principleThe minimum principles of liberalism (ML), which states society should give at least two people the right to choose between at least a pair of social status. If one thinks that A conk out than B, then society should not interfere and should keep with the preference.With Sens words, if you sine qua non sleeping supine and did not want to sleep prostrate, the society should agree with it. However, Sen also prove that for two or more people in the society, there exist no social choice functions that simultaneously run into these above three conditions because there will be the similar results of cyclic Condorcet voting paradox revealed by Arrow Impossibility Theorem when Pareto optimal is in combination with a minimum principle of liberalism.Sens theorem on foregodom of the Pareto impossibility can be accurately described as there does not exist the collective decision rule that meets the following conditions.The introductory condition is a sort of rational conditions. The sort is reflexive, relevance , and the preference analogy is not circulating. Reflexive means for any choice x has xRx, which indicates that any choice is at least as good as its own. relevancy means for any two options, there must be xRy or yRx or both. The second condition is weak Pareto criterion. For any choice of x and y, if everyone i think xPiy, then the society also thinks that xPy. The third condition is the minimal liberalism. In this condition, there are two non-empty, disjoint subsets L1 and L2, two different options for the (a, b) and (c, d), if everyone in L1 considers a is let on than b, then the society also thinks that a is better than b if everyone in L1 thinks that b is better than a, then b is also better than a for the society. Similarly, if everyone in L2 believes that c is better than d, then the society also thinks that c is better than d if everyone in L2 thinks d is better than c, then the society thinks also that d is better than c. The two groups were decisive on the choice between the two groups. Anyone is free to do what he likes to do, which means there are some choices that are entirely personal, personal preferences should not be affected by some other people.How to walk out of Sens paradox? Mueller has proposed two solutions in the public choice theory . One is to let the Pareto principle in some cases to comply with the right to liberalism. The other is through Pareto transactions. As Mueller noted, the ground substance is similar to game theory, for example a state in the notable prisoners dilemma, and the Pareto inferior results are due to the independent exercise of each person in his own right, regardless of the damage to others such externalities.The results of Sens theorem are established mainly through examples. There are no rigorous proofs on the results why there will be inconsistency of minimal liberalism and Pareto conditions. The results are basicall(a)y based on the assumption that there are conflicts between the Pareto Conditions and th e minimal Liberalism. There are questions keep asking whether the assumption is true and what if the cyclic societal rankings are not due to these conditions?In fact, in 1998 and 2001, Saari argues that the real reason of the seminal result of Sens theorem is not related to the nature of the Pareto condition and the Minimal Liberalism. The reason is that Pareto conditions and Minimal Liberalism needs the societal rankings to be made over pairs, which dismiss the transitivity of individual preferences. Therefore, it is not the conflicts between societal need and individual rights that undermine the assumption of individual moderateness it is the concentration of pairs that leads to the ignorance of individual rationality. And Saari also made nonrepresentational proof on this argument, which provides a new interpretation for the Sens theorem.4. Merits of the New InterpretationThere are several advantages of the new interpretation compared to the one that Sen present in the original version. First of all, the theorem carried out by Saari and his collaborates are proved using geometric proof, instead of using only examples and assumptions to get the final results. In addition, the new interpretation can explain all the examples used by Sen in his prior papers and the new interpretation also supports Sens own interpretation that the three conditions in Sens theorem force the decisions to be made by ignoring the individual rationality. The new interpretation also thinks that the decision rule also wants to meet the demand in the cyclic preference (Saari 2001 Saari and Petron, 2004).Secondly, the geometric proof of the new interpretations has identified all possible profiles that support any examples of Sens model. In addition, Saari and his collaborates have also significantly expanded on earlier observations by providing a new statistical interpretation for Sens Theorem. And they also conclude that the cyclic decision outcomes established by Sens theorem describ e a transitional, dysfunctional state of society.Thirdly, the new interpretation has pointed a new guidance for the movements of individual rights. Compared with the interpretation by Sen, the new interpretation focus more on the forcefulness minimal liberalism, which will leads to social decision procedures without cyclic outcomes and at the akin time satisfy weak Pareto conditions. They pointed out the deeper reason of the ignorance of individual rationality instead of concluding that the reason is because of the inconsistency of the Pareto condition and the Minimal Liberalism.5. ConclusionAs discussed in the previous session, the Sens theorem provides a good direction for the research of individual rights. And there are many researchers working on the topic to find new interpretation for the seminal results of Sens theory. Saari and his collaborates find that Minimal Liberalism makes some of the information in the society irrelevant. However, depending on that information, ind ividual preferences may or may not be transitive. Therefore, they conclude that Minimal Liberalism makes transitivity information irrelevant and this happens for any possible example of Sens cycles. They find a way to solve this problem and the response to this is to veer Minimal Liberalism in a way that is sensitive to transitivity information. They use the Intensity Minimal Liberalism (IML), which is a decisive that agent can gossip his preferences only when the choice does not create a strong negative externality for some other agent. And they finally find that there are social decision procedures without cyclic outcomes that satisfy weak Pareto and IML, which provides a new interpretation for the Sens theorem. The new interpretation finds a more trance way to proof Sens theorem and expends Sens theorem in several aspects.ReferencesLi, I. and D.G. Saari 2008. Sens theorem geometric proof, new interpretations, fond Choice and Welfare 31 393-413. reduce especially on pages 39 3-401.Petron, A and D.G. Saari 2006. blackball externalities and Sens liberalism theorem, economic opening 28 265-281. Read Sections 1 to 4.Saari, D. G. (1995). Basic Geometry of Voting, Springer-Verlag, New YorkSaari, D. G. (1998). Connecting and resolving Sens and Arrows Theorems, affectionate Choice Welfare 15, 239-261Saari, D. G. (2001). Decisions and Elections Explaining the Unexpected, Cambridge University Press, New YorkSaari, D. G., and Petron, A. (2004). (April), Negative Externalities and Sens Liberalism Theorem, IMBS working papers, University of California, Irvine, to appear in Economic Theory,June, 2006.Saari, D. G. and Sieberg, K. (2001). The sum of the split can violate the whole, American Political Science Review 95, 415-433.Salles, M. (1997). On Modelling Individual Rights Some Conceptual Issues Discussion p 129-133 in Social Choice Re-examined, Vol. 2 Ed. by K. J. Arrow, A. K. Sen, and K. Suzumura,St Martins Press New York.Sen, A. K. (1966). A Possibility Theo rem on Majority Decisions, Econometrica, 34(2), 491-09.Sen, A. K. (1970a). Collective Choice and Social Welfare, Holden-Day, San Francisco.Sen, A. K. (1970b). The Impossibility of a Paretian Liberal, The journal of Political Economy, 78(1), 152-57.Sen, A. K. (1976). Liberty, Unanimity and Rights, Economica 43(171), 217-45.Sen, A. K., Liberty and Social Choice, Journal of Philosophy, 80(1), 5-28.Sen, A. K. (1992) Minimal Liberty, Economica, 59 (234), 139-60.Sen, A. K. (1999) The possibility of social choice. The American Economic Review 89 (3), 349-378