Decision-making paradoxes

Apportionment paradox

An apportionment paradox exists when the rules for apportionment in a political system produce results which are unexpected or seem to violate common sense. To apportion is to divide into parts according to some rule, the rule typically being one of proportion. Certain quantities, like milk, can be divided in any proportion whatsoever; others, such as horses, cannot—only whole numbers will do. In the latter case, there is an inherent tension between the desire to obey the rule of proportion as closely as possible and the constraint restricting the size of each portion to discrete values. This results, at times, in unintuitive observations, or paradoxes. Several paradoxes related to apportionment, also called fair division, have been identified. In some cases, simple post facto adjustments, if allowed, to an apportionment methodology can resolve observed paradoxes. However, as shown by examples relating to the United States House of Representatives, and subsequently proven by the Balinski–Young theorem, mathematics alone cannot always provide a single, fair resolution to the apportionment of remaining fractions into discrete equal whole-number parts, while complying fully with all the competing fairness elements. (Wikipedia).

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Introduction to Apportionment

This video provides an introduction to apportionment. Site: http://mathispower4u.com

From playlist Apportionment

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Apportionment: The Population Paradox

The video explains the population paradox and provides an example of the population paradox. Site: http://mathispower4u.com

From playlist Apportionment

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Apportionment: The Alabama Paradox

This video explains and provides an example of the Alabama paradox. Site: http://mathispower4u.com

From playlist Apportionment

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Apportionment: The New States Paradox

The video explains the new states paradox and provides an example of the population paradox. Site: http://mathispower4u.com

From playlist Apportionment

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Apportionment: Hamilton's Method

This video explains and provides an example of the Hamilton's method of apportionment.. Site: http://mathispower4u.com

From playlist Apportionment

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Math for Liberal Studies - Lecture 2.7.2 Hamilton's Method and Apportionment Paradoxes

This is the second video lecture for Math for Liberal Studies Section 2.7: Apportionment. In this video, we learn how to use Hamilton's Method to assign a whole number of seats to each state based on their population. We also discuss several "paradoxes" that result from this method.

From playlist Math for Liberal Studies Lectures

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Apportionment: Webster's Method

This video explains Webster's method of apportionment. Site: http://mathispower4u.com

From playlist Apportionment

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Math for Liberal Studies - Lecture 2.7.3 The Standard Divisor

This is the third video lecture for Math for Liberal Studies Section 2.7: Apportionment. In this video, I discuss alternatives to Hamilton's Method that avoid the paradoxes that we learned in the previous lecture. Specifically, we talk about Jefferson's method: a "guess and check" method o

From playlist Math for Liberal Studies Lectures

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Math for Liberal Studies - Lecture 2.7.1 The Apportionment Problem

This is the first video lecture for Math for Liberal Studies Section 2.7: Apportionment. In this video, I give an overview of the apportionment problem: assigning representatives to states based on their population.

From playlist Math for Liberal Studies Lectures

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Examples of removable and non removable discontinuities to find limits

👉 Learn how to classify the discontinuity of a function. A function is said to be discontinuos if there is a gap in the graph of the function. Some discontinuities are removable while others are non-removable. There is also jump discontinuity. A discontinuity is removable when the denomin

From playlist Holes and Asymptotes of Rational Functions

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The Importance of Atonement

The idea of ‘atonement’ sounds very old-fashioned and is deeply rooted in religious tradition. To atone means, in essence, to acknowledge one’s capacity for wrongness and one’s readiness for apology and desire for change. It’s a concept that every society needs at its center. For gifts and

From playlist RELATIONSHIPS

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How to use the LCD to help us solve a rational equation

👉 Learn how to solve proportions. Two ratios are said to be proportional when the two ratios are equal. Thus, proportion problems are problems involving the equality of two ratios. When given a proportion problem with an unknown, we usually cross-multiply the two ratios and then solve for

From playlist How to Solve Rational Equations

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Understanding Apportionment

This video explains the properties of the most commenly used apportionment methods. 00:00 Introduction 02:22 Largest Remainder 09:15 Adams 13:54 Jefferson 17:25 Divisormethods 24:28 Divisormethod Adams 25:56 Webster 30:23 Summary 33:55 Outro

From playlist Summer of Math Exposition Youtube Videos

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Solving an Absolute Value Equation and Checking for Extraneous Solutions

Learn how to solve absolute value equations with extraneous solutions. Absolute value of a number is the positive value of the number. For instance, the absolute value of 2 is 2 and the absolute value of -2 is also 2. To solve an absolute value problem, we first isolate the absolute value

From playlist Solve Absolute Value Equations

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Tutorial lesson for solving a rational expression by multiplying by the LCD

👉 Learn how to solve proportions. Two ratios are said to be proportional when the two ratios are equal. Thus, proportion problems are problems involving the equality of two ratios. When given a proportion problem with an unknown, we usually cross-multiply the two ratios and then solve for

From playlist How to Solve Rational Equations

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Learn how to find and classify the discontinuity of the function

👉 Learn how to classify the discontinuity of a function. A function is said to be discontinuous if there is a gap in the graph of the function. Some discontinuities are removable while others are non-removable. There is also jump discontinuity. A discontinuity is removable when the denomi

From playlist Holes and Asymptotes of Rational Functions

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Injective, Surjective and Bijective Functions (continued)

This video is the second part of an introduction to the basic concepts of functions. It looks at the different ways of representing injective, surjective and bijective functions. Along the way I describe a neat way to arrive at the graphical representation of a function.

From playlist Foundational Math

Related pages

Huntington–Hill method | Proportionality (mathematics) | Mathematics | Proof of impossibility | Largest remainder method | Highest averages method | House monotonicity | Coherence (fairness)