“The Arrow impossibility theorem and its implications for voting and elections”

Arrow’s impossibility theorem represents a fascinating problem in the philosophy of economics, widely discussed for insinuating doubt on commonly accepted beliefs towards collective decision making procedures. This essay will introduce its fundamental assumptions, explain its meaning, explore some of the solutions available to escape its predictions and finally discuss its implications for political voting and elections. I will begin by giving some definitions and presenting the fundamental issue of social choice theory, consisting of the identification of an “ideal” device for preference aggregation, capable of converting individual rankings into collective ones, reflecting each individual’s preference into an optimal societal choice.

Given a finite set of voters having to choose between a finite set of candidates, we call a voting system the function taking as input the voting preferences of each voter and returning as output a collectively valid ranking of the candidates. Majority voting is the voting system requiring that given two alternative options X and Y, X is preferred to Y by the group if the number of group members prefering X to Y exceeds that of members prefering Y to X. When group preferences are rational and transitive, for every pairwise comparison between two options, the group-wide valid outcome obtained applying majority voting is a unique winning alternative, which is said to be the “Condorcet winner”. Sometimes though, group preferences are not rational and for each pairwise comparison a different winner emerges. In such case there is said to be a cycling majority and the situation represents a “Condorcet paradox”.

Named after the distinguished economist and nobel laureate Kenneth Arrow, the “Arrow Impossibility Theorem” was first proposed and demonstrated in his book “Social Choice and Individual Values”, published in 1951. The...

...Courtney Thompson
The Impossibility of Social Choice
Introduction
Social choice theory depends on individual preferences. Kenneth Arrow wrote a book exploring the properties of social choice functions. This book focuses on problems of aggregating individual preferences to maximize social choice functions, or to satisfy some kind of normative criteria given the preferences of the individual voters. This research on optimal methods of aggregation has spurred interest in properties of actual procedures for aggregating preferences via voting rules. The problem is finding a social choice function that satisfies normative criteria and establishing equilibrium under voting rules. (Mueller, 3, 1989) Arrow’s ImpossibilityTheorem set out to prove that democratic social choice processes were inherently flawed and had no way to be fixed. In order for a person to vote there must be a social welfare function that satisfies unrestricted domain, positive association, independence of irrelevant alternatives, non-dictatorship, and ordering simultaneously. It says that liberalism is flawed. In order to continue with social choice one of the liberal conditions has to give.
Kenneth Arrow made the first and most important attempt to define a social choice function in terms of a few, basic ethical axioms. (Mueller, 385, 1989) He was born in New York on August 23, 1921. He received his undergraduate education at the City...

...Original year 11 Advanced English short story written by Aisha Akhtar - copyright users will face severe consequences
The Wrong Arrow (c)
That’s weird thought cupid, ‘I’ve never hit the wrong person like that before’, he sat on a fluffy white cloud and stared down at the world. ‘How’, he thought with a bedazzled look on his face, ‘I was concentrating’. He slightly shuddered and squared his shoulders in an attempt to pull himself back together. ‘Hmm, better go talk to mom about this’, his blue eyes sparkled with confusion, a hint of worry and a little bit of hurt. Only Venus could fix this, God of beauty and Fertility, also known as Cupids mother.
He was beautiful. A light yellowish halo sat on his golden brown curls that lay perfectly at shoulder length, one short curl escaping the twirled bunch and resting on his smooth pale forehead. Thick blonde eyelashes with high outlined cheekbones, a protruding jaw line and a slim mouth. Golden runes in the shapes of arrows, crossbows and hearts engraved in his toned bare chest. It was like wearing a shirt for cupid was forbidden.
‘Now I’ll never get my wings’, he said through mumbles while slowly sinking back into the cloud.
Yesterday
Wholemeal bread, cheese slices, salmon pieces, lettuce and tomatoes. ‘Oh yummy’ thought Jace. ‘Tastiest sandwich ever’ he said between mouthfuls of his deliciously fresh breakfast. With a beep followed by a gangster beat, his phone rang. ‘Really? Now?’ annoyed...

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Arrow Electonics - distributor of electronic components.
The thing
They recently adquired Eagle semiconductor division, and in the negoatiation they made a deal that Eagle will keep its autonomy when it comes to management.
Concerns to this deal: low inventory accuracy levels reported for Eagle warehouses. (Niveles de precision baja de inventario)
Decicions: allow them to keep operating with several regional warehouses or move the inventory to Arrow´s large (PDC) Primary Distribution Centers.
Ella se da cuenta de lo importante que es el cumplimiento del sistema y la precisión en los records del inventario y como ha defendido la causa en la compañía. Started as inventory Clerk, he passion was ensuring that inventory data ( stored in manual system) was accurate as posible.
Physical audit revealed accuracy in inventory records. With time arrow´s operating process se acostumbro a los altos niveles de cumplimiento del Sistema y no dudaban de la precision del sistema al tomar decisiones.
Creció en 35 años de 10 millones a 10 billones en ventas, la necesidad de compartir info y mejorar el rendimiento operativo aumento. Entonces el cumplimiento del sistema y pricion en los datos del inventario nunca habían sido mas importantes.
Industy
2002 Distribution of electronic was a 30B industry worldwide and 12B in NA. Growth from 1970-2000 has been strong 13%. Annual. 1970 the top 5 distributors had 25% of industry revenue, in 1990 the...

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Pythagorean Theorem
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a relation in Euclidean geometry among the three sides of a right triangle (right-angled triangle). In terms of areas, it states:
In any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).
The theorem can be written as an equation relating the lengths of the sides a, b and c, often called the Pythagorean equation:[1]
where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides.
These two formulations show two fundamental aspects of this theorem: it is both a statement about areas and about lengths. Tobias Dantzig refers to these as areal and metric interpretations.[2][3] Some proofs of the theorem are based on one interpretation, some upon the other. Thus, Pythagoras' theorem stands with one foot in geometry and the other in algebra, a connection made clear originally byDescartes in his work La Géométrie, and extending today into other branches of mathematics.[4]
The Pythagorean theorem has been modified to apply outside its original domain. A number of these generalizations are described below, including...

...bernoulli's theorem
ABSTRACT / SUMMARY
The main purpose of this experiment is to investigate the validity of the Bernoulli equation when applied to the steady flow of water in a tape red duct and to measure the flow rate and both static and total pressure heads in a rigid convergent/divergent tube of known geometry for a range of steady flow rates. The apparatus used is Bernoulli’s Theorem Demonstration Apparatus, F1-15. In this experiment, the pressure difference taken is from h1- h5. The time to collect 3 L water in the tank was determined. Lastly the flow rate, velocity, dynamic head, and total head were calculated using the readings we got from the experiment and from the data given for both convergent and divergent flow. Based on the results taken, it has been analysed that the velocity of convergent flow is increasing, whereas the velocity of divergent flow is the opposite, whereby the velocity decreased, since the water flow from a narrow areato a wider area. Therefore, Bernoulli’s principle is valid for a steady flow in rigid convergent and divergent tube of known geometry for a range of steady flow rates, and the flow rates, static heads and total heads pressure are as well calculated. The experiment was completed and successfully conducted.
INTRODUCTION
In fluid dynamics, Bernoulli’s principle is best explained in the application that involves in viscid flow, whereby the speed of the moving fluid is increased...

...Negative Externalities and the Coase Theorem
As Adam Smith explained, selfishness leads markets to produce whatever people want. To get rich, you have to sell what the public wants to buy. Voluntary exchange will only take place if both parties perceive that they are better off. Positive externalities result in beneficial outcomes for others, whereas negative externalities impose costs on others. The Coase Theorem is most easily explained via an example
This paper addresses a classic example of a negative externality (pollution), and describes three possible solutions for the problem: government regulation, taxation and property right – a better solution to overcome the externality as described by economist Ronald Coase.
Imagine being a corn farmer and growing corn. What are the private costs that you face that help you determine production? Things like fuel, seed, fertilizer; these are your private costs. But it turns out that every spring and summer when you lay down the fertilizer some of this flows into the stream nearby and flows into a lake downstream, oftentimes resulting in large fish kills. All those downstream, the fisherman, the recreationist, and the landowners all incur a negative externality.
There are three ways in which we can address these externalities:
1- Government Regulation:
a) First, direct regulation is applied through technology-specific methods. This is where the government requires producers to use a...

...In mathematics, the Pythagorean theorem — or Pythagoras' theorem — is a relation in Euclidean geometry among the three sides of a right triangle (right-angled triangle). In terms of areas, it states:
In any right-angled triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).
The theorem can be written as an equation relating the lengths of the sides a, b and c, often called the Pythagorean equation:[1]
where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides.
The Pythagorean theorem is named after the Greek mathematician Pythagoras (ca. 570 BC—ca. 495 BC), who by tradition is credited with its discovery and proof,[2][3] although it is often argued that knowledge of the theorem predates him. There is evidence that Babylonian mathematicians understood the formula, although there is little surviving evidence that they used it in a mathematical framework.[4][5]
The theorem has numerous proofs, possibly the most of any mathematical theorem. These are very diverse, including both geometric proofs and algebraic proofs, with some dating back thousands of years. The theorem can be generalized in various ways, including higher-dimensional spaces, to spaces that...

...BINOMIAL THEOREM :
AKSHAY MISHRA
XI A , K V 2 , GWALIOR
In elementary algebra, the binomial theorem describes the algebraic expansion of powers of a binomial. According to the theorem, it is possible to expand the power (x + y)n into a sum involving terms of the form axbyc, where the coefficient of each term is a positive integer, and the sum of the exponents of x and y in each term is n. For example: The coefficients appearing in the binomial expansion are known as binomial coefficients. They are the same as the entries of Pascal's triangle, and can be determined by a simple formula involving factorials. These numbers also arise in combinatorics, where the coefficient of xn−kyk is equal to the number of different combinations of k elements that can be chosen from an n-element set.
HISTORY :
HISTORY This formula and the triangular arrangement of the binomial coefficients are often attributed to Blaise Pascal, who described them in the 17th century, but they were known to many mathematicians who preceded him. The 4th century B.C. Greek mathematician Euclid mentioned the special case of the binomial theorem for exponent 2 as did the 3rd century B.C. Indian mathematician Pingala to higher orders. A more general binomial theorem and the so-called "Pascal's triangle" were known in the 10th-century A.D. to Indian mathematician Halayudha and Persian mathematician Al-Karaji, and in the 13th century...