Sen’s Theorem: Overview and Analysis

Sens Theorem Overview and AnalysisTable of Contents (Jump to)1. Introduction2. A Review of Sens Theorem3. The Rise of New recital4. Merits of the New Interpretation5. ConclusionReferences1. IntroductionThe Sens theorem has an important impact on the decisiveness and social choice theory. In the Nobel Prize lecture of 1998, Sen said that discovering the societal detecting regularises will be the main objective 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 states that it is impossible to achieve the minimal aspect of liberalism when it is combined with the P arto condition. harmonise to the theorem of Sen, it seems that on that point is a sound conflict between the Pareto welfare concepts and the liberalism. After this argument, there is a pooling of studies that focus on the idiosyncratic rights and there are in any case studies that find new comment for the theorem of Sen.According to Saari and his collaborators, the cyclic decision outcomes established by heater theorem describe a transitional, dysfunctional state of family. This raise will mainly explain how this interpretation arises and discuss its merits relative to the original interpretation offered by Sen. The essay will be structured as follow in the second session, the essay will briefly introduce the Sens Theorem regarding to the conflicting results between Pareto optimal and Liberalism. Examples will also be used to snap off illustrate the choice decisions. In the third session, the essay will how and wherefore there will be new interpretations of the theorem of Sen. Particularly, the essay will base its argument on the research 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 Sen himself. In the last session, a brief conclusion will be do based on th e analysis in the previous session.2. A Review of Sens TheoremThe Sens impossibility of a paretian libertarian theorem or Sens paradox Paratian liberal states that weak Pareto criterion and liberalism whitethorn have conflicts on the fundamental level, which indicated that the Pareto criterion is flawed. On whizz hand, it shows that the Pareto criteria only consider aspects of difference in efficiency among relevant states while ignoring the individual utility conflicts arising because of these states. On the other hand, the theorem also shows the in addition to considering some reasonable internal conditions, one also needs to consider issues such(prenominal) as liberalism for social order decision making. According to Sen, there are some choices that are stringently of personal nature, such as the state (x) means everything else in the confederation as , when A is quiescence unresisting, state (y) means everything else in society as , when A is sleeping prostrate. If A has a taste perception of y than x, while many others in the society prefer the opposite, then it move be considered that social choice between x and y is a purely personal thing, because A is the only a real person that is related to the choice while other people are just nosy person. It can also be considered that one can choose 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 attention to the study of individual rights and other issues affecting the social choice order and decision making. The new welfare economics and welfare economics research before the new welfare economics are consciously or unconsciously distract these problems.Sen (1970) found that the Pareto criterion is incompatible with liberalism. Pareto optimality is used by the economists and other social scientists to measure the efficiency of society, which is also the the most common and widespread, even the only indicator. It refers to such a state that we are good as it gets, no one can make an additional welfare without compromising the welfare of others. And the principles of individual independence are the relentless pursuit of mankind, both of which are on the intuition that people can fully accept and understand. However, Sens theorem shows that these cardinal attractive standards are contradictory and cannot be simultaneously true.3. The Rise of New Interpretation there are three assumptions that Sens theorem is based on and the realistic of these assumptions 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 open area principleThe Pareto principleThe minimum principles of liberalism (ML), which states society should give at to the lowest degree two people the right to choose between at least a pair of s ocial status. If one thinks that A better than B, then society should not interfere and should agree with the preference.With Sens words, if you want 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 satisfy these above three conditions because there will be the similar results of cyclical Condorcet voting paradox revealed by arrow Impossibility Theorem when Pareto optimal is in combination with a minimum principle of liberalism.Sens theorem on freedom of the Pareto impossibility can be accurately depict as there does not exist the collective decision rule that meets the following conditions.The first condition is a sort of rational conditions. The sort is reflexive, relevance, and the preference relation is not circulating. Reflexive means for any choice x has xRx, which indicates that any choice is at least as good as its own. relevance 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 better 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 sho uld 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 matrix is similar to game theory, for example a state in the famous 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 basically based on the assumption that there are conflicts between the Pareto Conditions and the 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 originative 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 elicit the transitivity of individual preferences. Therefore, it is not the conflicts between societal need and individual rights that undermine the assumption of individual rationality it is the concentration of pairs that leads to the ignorance of individual rationality. And Saari also made geometric 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 derive t he closing 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 reason that the cyclic decision outcomes established by Sens theorem describe a transitional, dysfunctional state of society.Thirdly, the new interpretation has pointed a new direction for the movements of individual rights. Compared with th e interpretation by Sen, the new interpretation focus more on the intensity minimal liberalism, which will leads to social decision procedures without cyclic outcomes and at the like 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, individual preferences may or may not be transitive. Therefore, they conclude that Minimal Liberalism makes transitivity information irrelevant and this happens for any pos sible example of Sens cycles. They find a way to work this problem and the response to this is to modify Minimal Liberalism in a way that is sensitive to transitivity information. They use the Intensity Minimal Liberalism (IML), which is a decisive that constituent can impose 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 set aside 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, Social Choice and Welfare 31 393-413. Focus oddly on pages 393-401.Petron, A and D.G. Saari 2006. Negative externalities and Sens liberalism theorem,Economic Theory 28 265-281. Read Sections 1 to 4.Saari, D. G. (1995). Basic G eometry of Voting, Springer-Verlag, New YorkSaari, D. G. (1998). Connecting and resolving Sens and Arrows Theorems, Social 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 parts 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 Theorem 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 o f a Paretian Liberal, The journal of Political Economy, 78(1), 152-57.Sen, A. K. (1976). Liberty, unity 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