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# Social Choice Math MGF 1107

FIU

GPA 3.96

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###### Study Guide

##### STA 3123- Statistics for Behavioral and Social Sciences

###### Sheyla Moliner

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This 4 page Study Guide was uploaded by Yoshiko Ankunding Sr. on Monday October 12, 2015. The Study Guide belongs to MGF 1107 at Florida International University taught by Robert Storfer in Fall. Since its upload, it has received 137 views. For similar materials see /class/221792/mgf-1107-florida-international-university in Mathematics (M) at Florida International University.

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Date Created: 10/12/15

MGF 1107 Short Answer Questions 1 Which apportionment methods are susceptible to the Alabama Paradox 2 List all apportionment methods known as divisor methods 3 Which apportionment methods isare biased towards states with large populations 4 Which apportionment method is are biased towards states with small populations 5 Name the apportionment method that contains the least amount of bias towards states with small or large populations and explain why 6 State the Quota Condition and all apportionment methods that could violate that condition 7 State the Population Paradox and all apportionment methods that are susceptible to that paradox 8 Which apportionment method was never used to apportion the House of Representatives 9 Name the apportionment method in use today for the House of Representatives 10 Name the two apportionment methods which guarantee that every state subdivision receives at least one sea item 11 The RinkyDink Academy in Elon AZ apportioned 7 history teachers among 150 students Mr Flagg s original quota 18568 and he ended up with 20 students in his class Which apportionment methods could have been used 12 If district populations are used to decide how well an apportionment method works then out of the ones we have studied which method is best Multiple Choice Select the best answer 13 Consider the nation with the five Provinces Sandy Stormy Humid Dry and Windy Suppose Sandy s apportionment went down from 28 to 26 in the National Assembly and Humid s apportionment had increased from 10 to 11 even though Humid s population grew at a slower rate than Sandy s The number of seats to be apportioned was the same as the last time What has de nitely occurred a A Quota Condition violation b The Alabama Paradox c The Population Paradox d The Large State Paradox e There was no violation or Paradox 15 The country of Comapistan decided to increase its House size from 282 to 296 As a result of the new apportionment the state of Condorcetia lost a seat What apportionment method must have been used a Adams b Jefferson s c Hamilton s d HuntingtonHill e Webster s f There is not enough information to tell g None of these 16 Which apportionment method violates the Quota Condition the most a Webster s b Adams c Jefferson s d Both a and b equally e Both b and c equally f All do so equally g None violate the quota condition h None of these 17 Which apportionment is best a Hamilton s b Jefferson s c Adams d Webster s e HuntingtonHill f none of these 18 Suppose that the lower and upper quotas for a certain state are 12 and 13 and the state s initial apportionment was 12 Which two methods could have been used Show work for all problems 19 Round the four numbers in the table by using the HuntingtonHill method cutoffs 2022 Suppose that we have 25 seats to distribute on a regional board in the given cities of South Carolina Apportion the 25 seats using each one of the five methods we have studied For the divisor methods use divisors within 4000 of the standard divisor Consider problems 2022 23 Did any quota violations occur Why or why not 24 Suppose that Hamilton s method was used in the apportionment immediately proceeding the HH apportionment Back then 23 seats were apportioned and Cowpits received 8 of them Which if any paradoxes occurred Explain your answer 25 Refer back to problem 23 Suppose Nastonia received 8 seats in the previous apportionment and again Hamilton s was used Also assume that Nastonia s population grew twice as fast as Cowpits s did Did a paradox occur If so which ones Explain your answer 2628 The manager of West Miami Sushi and Thai a busy restaurant is working on a schedule for the restaurant s 35 food servers There are three shifts as given below Use the Adams Webster s and HuntingtonHill method to determine how many food servers should be scheduled for each shift Try divisors from 35 to 40 29 A province of Epsilonia has three districts with the populations shown below Apportion the 11 seats among the districts using Webster s Method Try divisors within 1000 of the standard divisor 30 Seven course sections are to be scheduled for a total of 217 students at Cowpits HS in Cowpits SC Enrollments are 109 in Calculus One 79 in Calculus Two and 29 in Advanced Calculus Find the apportionment for each course using the HuntingtonHill Method Try divisors from 25 to 45 31 Circle all the numbers which cannot be probabilities there could be more than one a 0250 b 0999 c 1001 d 1000 e 0100 f 23 g 54 h 12 32 Suppose that you are 5 times as likely to vote for a certain candidate for the city council of Schmataburg SC as you are not to vote for that candidate What is the probability that you do vote for that candidate 33 A white Christmas occurring in Tallahassee FL is 115 as likely to occur as it is not to occur What is the probability of a white Christmas in Tallahassee this problem is based on meteorological data Use the information in the table below for problems 3436 City Population County Commission Seats Daffey 14 589 24 Spitoonenburg 51290 85 34 Find the representative shares for each city 35 Find the district populations for each city 36 Name the apportionment method which minimizes the absolute difference in representative shares

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