Parsenn

Parsenn, renowned ski area near Davos, Switzerland. The recently updated red Parsenn railway covers the difference of 1100 meters to the Weissfluhjoch ridge. Ski runs from here run up to 17 kilometres into the Prättigau valley, one of them used in the Parsenn Derby Race. The Parsenn area is the largest and most modern of Davos' five mountains.

Davos, Switzerland

Davos (population 13,000) is a town in eastern Switzerland, in the canton of Graubünden, on the Landwasser River. Davos is mostly known as a winter sports town (where the annual Spengler Cup ice hockey tournament is played, hosted by local hockey team HC Davos), but it is also host to the annual meetings of the World Economic Forum (WEF), an annual meeting of global political and business elites, which is often referred to as simply Davos. Its claim to fame derives from the fact that the microclimate in the high valley was deemed excellent by doctors and recommended for lung disease patients. Arthur Conan Doyle wrote an article about skiing in Davos in 1899. Davos is also the setting of Thomas Mann's novel Der Zauberberg (The Magic Mountain), which takes place at a sanatorium. Subsequently, Davos became famous as a ski resort, especially with citizens from the United Kingdom and the Netherlands. After a peak in the 1970s and 1980s, the two-part city has re-established itself as a leading, yet less high-profile, tourist attraction. It is claimed to be the highest city in Switzerland and Europe. Europe The five main ski areas are:
- Parsenn / Gotschna
- Jakobshorn
- Pischa
- Rinerhorn
- Schatzalp Category:Cities in Switzerland

Congressional apportionment

The membership of the United States House of Representatives changes each decade following the decennial United States Census. Each state is apportioned a number of members of Congress based upon its population. This number also determines the state's number of electors in presidential elections, which equals the size of their congressional delegation (House plus Senate).

House size

In 1911, Public Law 62-5 set the membership of the U.S. House at 433; with the subsequent admission of Arizona and New Mexico as states, membership increased to 435, where it has remained (except for a brief period from 1959 to 1963 following the admission of Alaska and Hawaii, during which House membership was 437).

Apportionment methods

Apart from the fact that the number of delegates is at least one for each state, as required by the Constitution, this number is in principle proportional to population (equalizing the size of congressional districts nationwide). To arrive at whole numbers, the Method of Equal Proportions is used. The method first assigns one seat to each state, and then assigns each additional seat successively to the state with the highest "priority value", a value for the population per seat. For the latter the question would arise whether the current number of seats or one more should be taken. This is solved by taking an intermediate value, the geometric mean of the two. The resulting priority value is the geometric mean of the current population per seat and the population per seat in the case the state gets the extra seat. Computing for every state and any number of seats the priority value, and sorting the list in descending order of the resulting values, the first 385 are applicable (seats 51-435) (see [http://www.census.gov/population/censusdata/apportionment/00pvalues.txt Census 2000 Ranking of Priority Values]). The Equal Proportions method has been the fifth distinct method of determining congressional apportionment since the adoption of the United States Constitution. The size of the Congressional delegations from the thirteen original states were assigned by the Constitution for use until the completion of the first U.S. Census. Legislation admitting new states into the union has also designated the number of representatives of states until the time of the next census.

The Equal Proportions Method

Reapportionment of the United States House of Representatives (the lower house of the U.S. Congress) occurs every year ending in "1", the year after the U.S. Census Bureau performs the decennial census mandated by the U.S. Constitution. Once seats have been reapportioned to the various states, each state creates districts of approximately equal population, a process called redistricting. The United States authorizes there to be 435 members of Congress to be divided up between the 50 states. The seats are "apportioned" out to each state. Apportionment is done each time a new census is taken and they figure out how many people live in a particular state. So the total number of representatives is 435, and they are apportioned out to each state based on the state's population. Apportionment is done through the Equal Proportions Method. First, each state is automatically guaranteed at least one seat in Congress. That means there are a total of 385 seats left to hand out. The remaining seats are handed out one at a time, to the state that "deserves" another seat the most. Thus, the 51st seat always goes to the largest state (currently California). Now who gets the 52nd? We need to somehow take into acount the fact that California already has a second seat, and so "deserves" a third one less. That is, we need a mathematical formula that expresses the priority formula that a state should have for getting another seat. The formula used by the method of equal proportions is :

A=\frac

where P is the population of the state, and n is the number of seats it currently has. When all states have 1 seat, the largest value of A corresponds to the largest state. But now that California has 2 seats, its priority value decreases, and it has to take a step back in line. The 52nd seat goes to Texas, the 2nd largest state, but the 53rd goes back to California, and so on until all the seats have been handed out. Each time a state gets a seat, its priority drops and another state comes to the top of the list. The Census 2000 Ranking of Priority Values (see link above) shows the order in which seats 51-435 were apportioned after the 2000 Census, with additional listings for the next five priorities. North Carolina was allocated the final (435th) seat. Utah (priority list 436) missed a fourth seat by only 857 residents. Legal action by Utah to amend the results, citing irregularities in North Carolina and undercounting of Utah's overseas population, was unsuccessful.

State Congressional Delegation Size

1789-1910

1920-present

Notes

Delegate counts in italics represent temporary counts assigned by Congress until the next decennial census or by the U.S. Constitution in 1789 until the first U.S. Census. Elections held in the year of a census use the apportionment determined by the previous census. ^- The state of Maine was formed out of portions of Massachusetts in 1820. ^- The state of West Virginia was formed out of portions of Virginia in 1863.

External links

- [http://www.census.gov/population/www/censusdata/apportionment.html Congressional Apportionment by the U.S. Census Bureau]
- Cut-the-knot.org: :
- [http://www.cut-the-knot.org/ctk/Democracy.shtml The Constitution and Paradoxes] :
- [http://www.cut-the-knot.org/Curriculum/SocialScience/Adams.shtml A Java Simulation of Adams' method] :
- [http://www.cut-the-knot.org/Curriculum/SocialScience/AHamilton.shtml A Java Simulation of Hamilton's method] :
- [http://www.cut-the-knot.org/Curriculum/SocialScience/HH.shtml A Java Simulation of the Huntington-Hill method] :
- [http://www.cut-the-knot.org/Curriculum/SocialScience/Jefferson.shtml A Java Simulation of Jefferson's method] :
- [http://www.cut-the-knot.org/Curriculum/SocialScience/Webster.shtml A Java Simulation of Webster's method]
- Thirty-thousand.org: :
- [http://www.thirty-thousand.org/pages/Apportionment.htm A Brief History of Apportionment] :
- [http://www.thirty-thousand.org/pages/section_I#A.htm Forty or Thirty Thousand?] :
- [http://www.thirty-thousand.org/pages/QHA-02.htm The Size of the U. S. House of Representatives and its Constituent State Delegations Authorized Number of Seats by Year and by Congress 1789 to 2006] :
- [http://www.thirty-thousand.org/pages/Neubauer-Zeitlin.htm Outcomes of Presidential Elections and the House Size] Congressional apportionment Congressional apportionment Congressional apportionment

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