】 【Glossary Arrow Impossibility Theorem is that if many members of society have different preferences, and the community have a variety of options, then under the system of democracy that all people can not get satisfactory results. Theorem is the 1972 Nobel laureate in economics U.S. economist Kenneth Arrow j · proposed. Practice】 【Operation As we all know, the majority principle is widely accepted in modern society in decision-making methods. Locke believed that "according to the laws of nature and reason, the majority has all the power, so most of the acts are considered acts of all, of course, the power to decide." But many in the natural right of jurists there is something taken for granted in social choice theory to be proven. The so-called social choice, expressed as a mathematically based on the preferences of all individuals on the function (or mapping), the nature of the function represents the value of certain norms, such as sovereign citizens, all, anonymity, the target neutral, Pa Rectorite optimality, non-authoritarian and so on. The most important question of social choice is between these values is a logical specification of coordination. Arrow proved that there is no meet the following four basic axioms of social choice functions: ① unlimited personal preferences, that is possible for a society for all states, any logically possible preference should not be a priori exclusion; ② Pareto principle that a program is the best means for all relative to the social preference ordering is optimal; ③ the independence of non-related objectives, namely, a pair of social goals on the social preference ordering from other the impact of changes in target sequence preferences; ④ non-authoritarian social preferences. 】 【Classic case Suppose A, B, C three, from China, Japan and the United States, but were good friends for many years. Three long-awaited reunion, excitedly decided to eat together to renew old friendships. However, the formation of different cultural backgrounds of their different eating habits, food requirements vary with different styles A: Chinese food> Western> Japanese meal B: Japanese cuisine> Chinese cuisine> Western C: Western> Japanese cuisine> Chinese food If a democratic majority vote, the results are as follows: First, _select_ Chinese and Western, A, B like Chinese food, western food like C; Then, in the Western and Japanese dishes in the _select_ion, A, C like the Western, B like Japanese food; Finally, in Chinese and Japanese cuisine in the _select_ion, B, C like Japanese food, a favorite Chinese food. Three of the final voting results are as follows: Chinese food> Western, Western> Japanese cuisine, Japanese cuisine> Chinese food Therefore, the use of majority voting mechanism, so that everyone will not produce a satisfactory conclusion, this is the famous "voting paradox" (paradox of voting). Voting paradox was first introduced by Kandel race (marquis de coudorcet) in the 18th century and, therefore, the paradox is also known as "Kandel race effect" [③], and its use of mathematical argument is Kenneth Arrow. Arrow believes that the two axioms on social choice and democracy can not meet the requirements of the various conditions. He said that the following axioms: Axiom 1: coherence (connectedness) Two options in the x and y co-exist, the following permanent establishment of a situation: x is greater than or equal to y; y greater than or equal to x. Axiom 2: transitivity (transitivity) Where x, y, z three options, there will be several situations like: x is greater than or equal to y; y is greater than or equal to z; then x is greater than or equal to z. Arrow pointed out, laid the foundation of these two axioms of social welfare function and his so-called democracy is not commensurate with the various conditions. Various conditions of democracy are as follows: (1) Condition 1: the order of the ordinary individual tolerance intervals. As a personal sense, how to _select_ their choice for the value of sequence problem is irrelevant. For example, in the face of x, y, z three options, either x> y> z, or z> y> x, or y> z> x ,...... All in all, will allow individuals according to their own Arrange the value of the order of _select_ion. (2) Condition 2: social assessment and individual evaluation of normal correlation. If there are five to choose x, y, when the three of them as x> y, the other two for the xy, and, even if there is a minority in the party to change his mind, x> y the time, x> y the majority vote of all the results of social will remain as before, will not change. (3) Condition 3: _Select_ the object has nothing to do with the independence of irrelevant. In the x, y, z values between the three options, assuming the _select_ion order for the x> y> z, then _select_ a value even if the y have ceased to exist, the remaining x and z, x> z is still the choice of relationship does not change. (4) Condition 4: citizens sovereignty Order of personal choice has nothing to do with the social structure, that everyone in society according to their values, the freedom to choose the alternative object. (5) Condition 5: Non-authoritarian In all the members, when only a specific individual choice x> y, the other people choose to xy. [④] In summary, all five conditions that should have become a democratic society. Arrow believes that if at the same time recognize the first two axioms and the five conditions, it will contribute to the voting paradox effect. This is Arrow's impossibility theorem. Next, I take a simple example Minge Luo justice and democracy in the so-called two of the five conditions of social contradictions. According to Arrow's theory, assuming that there are seven people ready to go to dinner together. The seven individual food preferences in the following order: 1: Chinese> Western> Japanese meal 2 3 Japanese cuisine> Chinese cuisine> Western 4 5 6 Western> Japanese cuisine> Chinese food 7 Arrow involved in this issue of great representative. Arrow illustrates the decision taken by the so-called majority voting rules for the phenomenon of dictatorship is bound to be there. We usually think majority voting is the decision to promote the principles of democracy, but in reality, it did not play this role. To a democratic society, the Arrow-called principle-based expression of the majority of the voting results can sometimes lead to the paradox of voting effect, quite important for their views. Arrow believes that the voting paradox not happen often, but has some chance. If this probability is negligible, then the meaning of Arrow's impossibility theorem will be eclipsed. Paradox of voting to produce mathematical method to calculate the probability of a Camp Bull (c. campbell) and Tullock (g. tullock). Camp, who use Monte Carl Boolean method to calculate the probability of voting paradox generated, and that voters _select_ the value of the increase in the quantity or more, resulting in the paradox more likely. For example, in 3 voters who choose the case is 3 points, resulting paradox is about 5.7% probability of effect; when voters increased to 15, _select_ the value increased to 11, the resulting paradox effect probability increased to 50%. [⑤] That is, there is a paradox of voting two phenomena. Thus, for every day in frequent meetings and gatherings of all kinds of democratic society at large, can never be on such a high percentage lightly. In addition, Niemi and Davis Berg also greatly push forward the Camp, who Boolean calculations. They pointed out that more than ten people in the case of voters, the probability of more of the voting paradox occurs almost no change, and choose how much value there is a considerable probability of the paradox effect. [⑥] Can be seen, in this scenario, the use of majority voting mechanism, so that everyone will not produce a satisfactory conclusion.
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Glossary
Arrow Impossibility Theorem is that if many members of society have different preferences, and the community have a variety of options, then under the system of democracy that all people can not get satisfactory results. Theorem of 1972 Nobel Laureate in Economics J · American economist Kenneth Arrow proposed.
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Operating Practices
As we all know, the majority principle is widely accepted in modern society in decision-making methods. Locke believed that "according to the laws of nature and reason, the majority has all the power, so most of the acts are considered acts of all, of course, the power to decide." But many in the natural right of jurists there is something taken for granted in social choice theory to be proven. The so-called social choice, expressed as a mathematically based on the preferences of all individuals on the function (or mapping), the nature of the function represents the value of certain norms, such as sovereign citizens, all, anonymity, the target neutral, Pa Rectorite optimality, non-authoritarian and so on. The most important question of social choice is between these values is a logical specification of coordination. Arrow proved that there is no meet the following four basic axioms of social choice functions: ① unlimited personal preferences, that is possible for a society for all states, any logically possible preference should not be a priori exclusion; ② Pareto principle that a program is the best means for all relative to the social preference ordering is optimal; ③ the independence of non-related objectives, namely, a pair of social goals on the social preference ordering from other the impact of changes in target sequence preferences; ④ non-authoritarian social preferences.
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Classic Case
Suppose A, B, C three, from China, Japan and the United States, but were good friends for many years. Three long-awaited reunion, excitedly decided to eat together to renew old friendships. However, the formation of different cultural backgrounds of their different eating habits, food requirements vary with different styles A: Chinese food> Western> Japanese meal B: Japanese cuisine> Chinese cuisine> Western C: Western> Japanese cuisine> Chinese food If a democratic majority vote, the results are as follows: First, _select_ Chinese and Western, A, B like Chinese food, western food like C; Then, in the Western and Japanese dishes in the _select_ion, A, C like the Western, B like Japanese food; Finally, in Chinese and Japanese cuisine in the _select_ion, B, C like Japanese food, a favorite Chinese food. Three of the final voting results are as follows: Chinese food> Western, Western> Japanese cuisine, Japanese cuisine> Chinese food Therefore, the use of majority voting mechanism, so that everyone will not produce a satisfactory conclusion, this is the famous "voting paradox" (paradox of voting). Voting paradox was first introduced by Kandel season (Marquis de Coudorcet) in the 18th century and, therefore, the paradox is also known as "Kandel race effect" [③], and its use of mathematical argument is Kenneth Arrow. Arrow believes that the two axioms on social choice and democracy can not meet the requirements of the various conditions. He said that the following axioms: Axiom 1: coherence (connectedness) Two options in the x and y co-exist, the following permanent establishment of a situation: x is greater than or equal to y; y greater than or equal to x. Axiom 2: transitivity (transitivity) Where x, y, z three options, there will be several situations like: x is greater than or equal to y; y is greater than or equal to z; then x is greater than or equal to z. Arrow pointed out, laid the foundation of these two axioms of social welfare function and his so-called democracy is not commensurate with the various conditions. Various conditions of democracy are as follows: (1) Condition 1: the order of the ordinary individual tolerance intervals. As a personal sense, how to _select_ their choice for the value of sequence problem is irrelevant. For example, in the face of x, y, z three options, either x> y> z, or z> y> x, or y> z> x ,...... All in all, will allow individuals according to their own Arrange the value of the order of _select_ion. (2) Condition 2: social assessment and individual evaluation of normal correlation. If there are five to choose x, y, when the three of them as x> y, the other two for the xy, and, even if there is a minority in the party to change his mind, x> y the time, x> y the majority vote of all the results of social will remain as before, will not change. (3) Condition 3: _Select_ the object has nothing to do with the independence of irrelevant. In the x, y, z values between the three options, assuming the _select_ion order for the x> y> z, then _select_ a value even if the y have ceased to exist, the remaining x and z, x> z is still the choice of relationship does not change. (4) Condition 4: citizens sovereignty Order of personal choice has nothing to do with the social structure, that everyone in society according to their values, the freedom to choose the alternative object. (5) Condition 5: Non-authoritarian In all the members, when only a specific individual choice x> y, the other people choose to xy. [④] In summary, all five conditions that should have become a democratic society. Arrow believes that if at the same time recognize the first two axioms and the five conditions, it will contribute to the voting paradox effect. This is Arrow's impossibility theorem. Next, I take a simple example Minge Luo justice and democracy in the so-called two of the five conditions of social contradictions. According to Arrow's theory, assuming that there are seven people ready to go to dinner together. The seven individual food preferences in the following order: 1: Chinese> Western> Japanese meal The 2nd Japanese cuisine> Chinese cuisine> Western 3 Japanese cuisine> Chinese cuisine> Western 4 Japanese cuisine> lunch> Western 5, Western> Japanese cuisine> Chinese food 6 Western> Japanese cuisine> Chinese food 7 Western> Japanese cuisine> Chinese food Arrow involved in this issue of great representative. Arrow illustrates the decision taken by the so-called majority voting rules for the phenomenon of dictatorship is bound to be there. We usually think majority voting is the decision to promote the principles of democracy, but in reality, it did not play this role. To a democratic society, the Arrow-called principle-based expression of the majority of the voting results can sometimes lead to the paradox of voting effect, quite important for their views. Arrow believes that the voting paradox not happen often, but has some chance. If this probability is negligible, then the meaning of Arrow's impossibility theorem will be eclipsed. Paradox of voting to take the probability of generating mathematical method to calculate the Camp Boolean (C. Campbell) and Tullock (G. Tullock). Camp, who use Monte Carl Boolean method to calculate the probability of voting paradox generated, and that voters _select_ the value of the increase in the quantity or more, resulting in the paradox more likely. For example, in 3 voters who choose the case is 3 points, resulting paradox is about 5.7% probability of effect; when voters increased to 15, _select_ the value to 11 points, resulting paradox effect probability increased to 50%. [⑤] That is, there is a paradox of voting two phenomena. Thus, for every day in frequent meetings and gatherings of all kinds of democratic society at large, can never be on such a high percentage lightly. In addition, Niemi and Davis Berg also greatly push forward the Camp, who Boolean calculations. They pointed out that more than ten people in the case of voters, the probability of more of the voting paradox occurs almost no change, and choose how much value there is a considerable probability of the paradox effect. [⑥] Can be seen, in this scenario, the use of majority voting mechanism, so that everyone will not produce a satisfactory conclusion.