Unique games conjecture - Revision history

2001:638:403:5050:224:1DFF:FEDE:83A3: formatting of citation

2015-01-06T14:39:54Z

formatting of citation

← Older revision		Revision as of 16:39, 6 January 2015
Line 1:		Line 1:
	The ~~'''Huntington–Hill method''' of apportionment assigns seats by finding a modified divisor ''D'' such that each constituency's priority quotient (population divided~~ by ~~''D'' ), using~~ the ~~[[geometric mean]]~~ of ~~the lower and upper quota for the divisor, yields the correct number of seats that minimizes the percentage differences~~ in ~~the size of the congressional districts~~.~~<ref>{{cite web \| title = Congressional Apportionment \| publisher = NationalAtlas~~.gov \| url = http://www.nationalatlas.gov/articles/boundaries/a_conApport.html#six \| accessdate = 2009-02-14}}</ref> When envisioned as a [[Proportional representation\|proportional]] [[voting system]], this is ~~effectively~~ a ~~[[highest averages method]] in which the divisors are given by~~ <~~math~~>~~\scriptstyle D=\sqrt{n(n+1)}~~<~~/math~~>, ''n'' being the number of seats a state is currently allocated in the apportionment process (the lower quota) and ''n''+1 is the number of seats the state ''would'' have if it is assigned to this state (the upper quota).		The author is recognized by the title of Numbers Lint. Her family lives in Minnesota. What I love doing is playing baseball but I haven't made a dime with it. He utilized to be unemployed but now he is a computer operator but his marketing never arrives.<br><br>Also visit my blog post ... [http://www.gaysphere.net/user/Z5147 www.gaysphere.net]

	~~The [[United States House of Representatives]] uses this method of apportionment to assign the number of representative seats to each state~~.

	~~The method is credited to [~~[~~Edward Vermilye Huntington]] and [[Joseph Adna Hill]].<ref>{{cite web \| title = The History of Apportionment in America \| publisher = American Mathematical Society \| url =~~ http://www.~~ams~~.~~org~~/~~featurecolumn~~/~~archive/apportion2~~.~~html \| accessdate = 2009-02-15}}</ref>~~

	~~==Examples==~~
	~~The U~~.S. House of Representatives guarantees one seat for each state. So, each state starts off with a divisor D of 1.41 (the square root of the product of ''one'', the number seats currently assigned, and ''two'', the number of seats that would next be assigned). Each state's census population is divided by its D, to produce a priority value for each state. Since all of the D's are equal for this first seat, the state with the largest population would win (California).

	Now, California's D would be changed to 2.45 (the square root of ''two'' times ''three''), and we would repeat this process. Unless California has about twice the population of any other state, the next largest state would win this second seat. In this case Texas would win the next seat because its population (24 million) divided by its current D (still 1.41) is greater than California's similarly calculated priority value (37 million/2.45) for priority values of 17 million and 15 million, respectively).

	This process is repeated until all empty house seats have been exhausted. If the number of U.S. House of Representatives seats were equal in size to the population of the United States, this method would guarantee that the appointments would equal the populations of each state.

	Although the U.S. House of Representatives currently uses the Equal Proportions method, Congress has not always used it. In fact, George Washington used the presidential [[Veto#United States\|veto]] power for the very first time in order to block apportionment legislation less favorable to his home state of [[Virginia]]. Had Congress used the Equal Proportionment Method (with a divisor of 34,800) to apportion House seats according to state population following the 1790 [[United States Census\|census]], the 105 seats in the [[3rd United States Congress]] the House of Representatives would have been apportioned as follows:

	~~{\| class="wikitable"~~
	\|-
	~~! State !! Population !! Quotas !! Lower !! Upper !! G. Mean !! Rnd. Dir. !! Seats~~
	~~\|- align="right"~~
	~~\| align="left" \|Connecticut \|\| 236,841 \|\| 6.81 \|\| 6 \|\| 7 \|\| 6.48 \|\| align="center" \| up \|\| 7~~
	~~\|- align="right"~~
	~~\| align="left" \|Delaware \|\| 55,540 \|\| 1.60 \|\| 1 \|\| 2 \|\| 1.41 \|\| align="center" \| up \|\| 2~~
	~~\|- align="right"~~
	~~\| align="left" \|Georgia \|\| 70,835 \|\| 2.04 \|\| 2 \|\| 3 \|\| 2.45 \|\| align="center" \| down \|\| 2~~
	~~\|- align="right"~~
	~~\| align="left" \|Kentucky \|\| 68,705 \|\| 1.97 \|\| 1 \|\| 2 \|\| 1.41 \|\| align="center" \| up \|\| 2~~
	~~\|- align="right"~~
	~~\| align="left" \|Maryland \|\| 278,514 \|\| 8.00 \|\| 8 \|\| 9 \|\| 8.49 \|\| align="center" \| down \|\| 8~~
	~~\|- align="right"~~
	~~\| align="left" \|Massachusetts \|\| 475,327 \|\| 13.66 \|\| 13 \|\| 14 \|\| 13.49 \|\| align="center" \| up \|\| 14~~
	~~\|- align="right"~~
	~~\| align="left" \|New Hampshire \|\| 141,822 \|\| 4.08 \|\| 4 \|\| 5 \|\| 4.47 \|\| align="center" \| down \|\| 4~~
	~~\|- align="right"~~
	~~\| align="left" \|New Jersey \|\| 179,570 \|\| 5.16 \|\| 5 \|\| 6 \|\| 5.48 \|\| align="center" \| down \|\| 5~~
	~~\|- align="right"~~
	~~\| align="left" \|New York \|\| 331,589 \|\| 9.53 \|\| 9 \|\| 10 \|\| 9.49 \|\| align="center" \| up \|\| 10~~
	~~\|- align="right"~~
	~~\| align="left" \|North Carolina \|\| 353,523 \|\| 10.16 \|\| 10 \|\| 11 \|\| 10.49 \|\| align="center" \| down \|\| 10~~
	~~\|- align="right"~~
	~~\| align="left" \|Pennsylvania \|\| 432,879 \|\| 12.44 \|\| 12 \|\| 13 \|\| 12.49 \|\| align="center" \| down \|\| 12~~
	~~\|- align="right"~~
	~~\| align="left" \|Rhode Island \|\| 68,446 \|\| 1.97 \|\| 1 \|\| 2 \|\| 1.41 \|\| align="center" \| up \|\| 2~~
	~~\|- align="right"~~
	~~\| align="left" \|South Carolina \|\| 206,236 \|\| 5.93 \|\| 5 \|\| 6 \|\| 5.48 \|\| align="center" \| up \|\| 6~~
	~~\|- align="right"~~
	~~\| align="left" \|Vermont \|\| 85,533 \|\| 2.46 \|\| 2 \|\| 3 \|\| 2.45 \|\| align="center" \| up \|\| 3~~
	~~\|- align="right"~~
	~~\| align="left" \|Virginia \|\| 630,560 \|\| 18.12 \|\| 18 \|\| 19 \|\| 18.49 \|\| align="center" \| down \|\| 18~~
	\|}

	~~Compared with the actual apportionment, [[Pennsylvania]] and [[Virginia]] would have lost one seat each, while [[Delaware]] and [[Vermont]] would have gained one seat each.~~

	~~{{reflist}}~~

	~~{{DEFAULTSORT:Huntington-Hill Method}}~~
	~~[[Category:Voting systems]~~]

2001:6B0:1:1E00:680A:453E:9EC1:D014: Minor edits to the approximability table, e.g., "UGC Hardness" to "UG hardness".

2013-08-01T13:35:51Z

Minor edits to the approximability table, e.g., "UGC Hardness" to "UG hardness".

← Older revision		Revision as of 15:35, 1 August 2013
Line 1:		Line 1:
	~~Nice to meet you, my name is Refugia. For years he~~'s ~~been residing~~ in ~~North Dakota and his family members enjoys it. One~~ of the ~~very best things~~ in the ~~globe for me~~ is ~~to do aerobics~~ and I'~~ve been performing~~ it ~~for fairly a while~~. ~~Bookkeeping~~ is ~~her working day occupation now~~.<br>~~<br>Here is my site: home std test ([~~http://www.~~videoworld~~.~~com~~/~~user~~/~~SMaloney visit~~ this ~~site~~ right ~~here~~])		The '''Huntington–Hill method''' of apportionment assigns seats by finding a modified divisor ''D'' such that each constituency's priority quotient (population divided by ''D'' ), using the [[geometric mean]] of the lower and upper quota for the divisor, yields the correct number of seats that minimizes the percentage differences in the size of the congressional districts.<ref>{{cite web \| title = Congressional Apportionment \| publisher = NationalAtlas.gov \| url = http://www.nationalatlas.gov/articles/boundaries/a_conApport.html#six \| accessdate = 2009-02-14}}</ref> When envisioned as a [[Proportional representation\|proportional]] [[voting system]], this is effectively a [[highest averages method]] in which the divisors are given by <math>\scriptstyle D=\sqrt{n(n+1)}</math>, ''n'' being the number of seats a state is currently allocated in the apportionment process (the lower quota) and ''n''+1 is the number of seats the state ''would'' have if it is assigned to this state (the upper quota).

			The [[United States House of Representatives]] uses this method of apportionment to assign the number of representative seats to each state.

			The method is credited to [[Edward Vermilye Huntington]] and [[Joseph Adna Hill]].<ref>{{cite web \| title = The History of Apportionment in America \| publisher = American Mathematical Society \| url = http://www.ams.org/featurecolumn/archive/apportion2.html \| accessdate = 2009-02-15}}</ref>

			==Examples==
			The U.S. House of Representatives guarantees one seat for each state. So, each state starts off with a divisor D of 1.41 (the square root of the product of ''one'', the number seats currently assigned, and ''two'', the number of seats that would next be assigned). Each state's census population is divided by its D, to produce a priority value for each state. Since all of the D's are equal for this first seat, the state with the largest population would win (California).

			Now, California's D would be changed to 2.45 (the square root of ''two'' times ''three''), and we would repeat this process. Unless California has about twice the population of any other state, the next largest state would win this second seat. In this case Texas would win the next seat because its population (24 million) divided by its current D (still 1.41) is greater than California's similarly calculated priority value (37 million/2.45) for priority values of 17 million and 15 million, respectively).

			This process is repeated until all empty house seats have been exhausted. If the number of U.S. House of Representatives seats were equal in size to the population of the United States, this method would guarantee that the appointments would equal the populations of each state.

			Although the U.S. House of Representatives currently uses the Equal Proportions method, Congress has not always used it. In fact, George Washington used the presidential [[Veto#United States\|veto]] power for the very first time in order to block apportionment legislation less favorable to his home state of [[Virginia]]. Had Congress used the Equal Proportionment Method (with a divisor of 34,800) to apportion House seats according to state population following the 1790 [[United States Census\|census]], the 105 seats in the [[3rd United States Congress]] the House of Representatives would have been apportioned as follows:

			{\| class="wikitable"
			\|-
			! State !! Population !! Quotas !! Lower !! Upper !! G. Mean !! Rnd. Dir. !! Seats
			\|- align="right"
			\| align="left" \|Connecticut \|\| 236,841 \|\| 6.81 \|\| 6 \|\| 7 \|\| 6.48 \|\| align="center" \| up \|\| 7
			\|- align="right"
			\| align="left" \|Delaware \|\| 55,540 \|\| 1.60 \|\| 1 \|\| 2 \|\| 1.41 \|\| align="center" \| up \|\| 2
			\|- align="right"
			\| align="left" \|Georgia \|\| 70,835 \|\| 2.04 \|\| 2 \|\| 3 \|\| 2.45 \|\| align="center" \| down \|\| 2
			\|- align="right"
			\| align="left" \|Kentucky \|\| 68,705 \|\| 1.97 \|\| 1 \|\| 2 \|\| 1.41 \|\| align="center" \| up \|\| 2
			\|- align="right"
			\| align="left" \|Maryland \|\| 278,514 \|\| 8.00 \|\| 8 \|\| 9 \|\| 8.49 \|\| align="center" \| down \|\| 8
			\|- align="right"
			\| align="left" \|Massachusetts \|\| 475,327 \|\| 13.66 \|\| 13 \|\| 14 \|\| 13.49 \|\| align="center" \| up \|\| 14
			\|- align="right"
			\| align="left" \|New Hampshire \|\| 141,822 \|\| 4.08 \|\| 4 \|\| 5 \|\| 4.47 \|\| align="center" \| down \|\| 4
			\|- align="right"
			\| align="left" \|New Jersey \|\| 179,570 \|\| 5.16 \|\| 5 \|\| 6 \|\| 5.48 \|\| align="center" \| down \|\| 5
			\|- align="right"
			\| align="left" \|New York \|\| 331,589 \|\| 9.53 \|\| 9 \|\| 10 \|\| 9.49 \|\| align="center" \| up \|\| 10
			\|- align="right"
			\| align="left" \|North Carolina \|\| 353,523 \|\| 10.16 \|\| 10 \|\| 11 \|\| 10.49 \|\| align="center" \| down \|\| 10
			\|- align="right"
			\| align="left" \|Pennsylvania \|\| 432,879 \|\| 12.44 \|\| 12 \|\| 13 \|\| 12.49 \|\| align="center" \| down \|\| 12
			\|- align="right"
			\| align="left" \|Rhode Island \|\| 68,446 \|\| 1.97 \|\| 1 \|\| 2 \|\| 1.41 \|\| align="center" \| up \|\| 2
			\|- align="right"
			\| align="left" \|South Carolina \|\| 206,236 \|\| 5.93 \|\| 5 \|\| 6 \|\| 5.48 \|\| align="center" \| up \|\| 6
			\|- align="right"
			\| align="left" \|Vermont \|\| 85,533 \|\| 2.46 \|\| 2 \|\| 3 \|\| 2.45 \|\| align="center" \| up \|\| 3
			\|- align="right"
			\| align="left" \|Virginia \|\| 630,560 \|\| 18.12 \|\| 18 \|\| 19 \|\| 18.49 \|\| align="center" \| down \|\| 18
			\|}

			Compared with the actual apportionment, [[Pennsylvania]] and [[Virginia]] would have lost one seat each, while [[Delaware]] and [[Vermont]] would have gained one seat each.

			{{reflist}}

			{{DEFAULTSORT:Huntington-Hill Method}}
			[[Category:Voting systems]]

en>A3 nm: /* Relevance */ add left margin to table

2012-04-08T08:37:45Z

Relevance: add left margin to table

New page

Nice to meet you, my name is Refugia. For years he's been residing in North Dakota and his family members enjoys it. One of the very best things in the globe for me is to do aerobics and I've been performing it for fairly a while. Bookkeeping is her working day occupation now.<br><br>Here is my site: home std test ([http://www.videoworld.com/user/SMaloney visit this site right here])

← Older revision		Revision as of 16:39, 6 January 2015
Line 1:		Line 1:
	The ~~'''Huntington–Hill method''' of apportionment assigns seats by finding a modified divisor ''D'' such that each constituency's priority quotient (population divided~~ by ~~''D'' ), using~~ the ~~[[geometric mean]]~~ of ~~the lower and upper quota for the divisor, yields the correct number of seats that minimizes the percentage differences~~ in ~~the size of the congressional districts~~.~~<ref>{{cite web \| title = Congressional Apportionment \| publisher = NationalAtlas~~.gov \| url = http://www.nationalatlas.gov/articles/boundaries/a_conApport.html#six \| accessdate = 2009-02-14}}</ref> When envisioned as a [[Proportional representation\|proportional]] [[voting system]], this is ~~effectively~~ a ~~[[highest averages method]] in which the divisors are given by~~ <~~math~~>~~\scriptstyle D=\sqrt{n(n+1)}~~<~~/math~~>, ''n'' being the number of seats a state is currently allocated in the apportionment process (the lower quota) and ''n''+1 is the number of seats the state ''would'' have if it is assigned to this state (the upper quota).		The author is recognized by the title of Numbers Lint. Her family lives in Minnesota. What I love doing is playing baseball but I haven't made a dime with it. He utilized to be unemployed but now he is a computer operator but his marketing never arrives.<br><br>Also visit my blog post ... [http://www.gaysphere.net/user/Z5147 www.gaysphere.net]

	~~The [[United States House of Representatives]] uses this method of apportionment to assign the number of representative seats to each state~~.

	~~The method is credited to [~~[~~Edward Vermilye Huntington]] and [[Joseph Adna Hill]].<ref>{{cite web \| title = The History of Apportionment in America \| publisher = American Mathematical Society \| url =~~ http://www.~~ams~~.~~org~~/~~featurecolumn~~/~~archive/apportion2~~.~~html \| accessdate = 2009-02-15}}</ref>~~

	~~==Examples==~~
	~~The U~~.S. House of Representatives guarantees one seat for each state. So, each state starts off with a divisor D of 1.41 (the square root of the product of ''one'', the number seats currently assigned, and ''two'', the number of seats that would next be assigned). Each state's census population is divided by its D, to produce a priority value for each state. Since all of the D's are equal for this first seat, the state with the largest population would win (California).

	Now, California's D would be changed to 2.45 (the square root of ''two'' times ''three''), and we would repeat this process. Unless California has about twice the population of any other state, the next largest state would win this second seat. In this case Texas would win the next seat because its population (24 million) divided by its current D (still 1.41) is greater than California's similarly calculated priority value (37 million/2.45) for priority values of 17 million and 15 million, respectively).

	This process is repeated until all empty house seats have been exhausted. If the number of U.S. House of Representatives seats were equal in size to the population of the United States, this method would guarantee that the appointments would equal the populations of each state.

	Although the U.S. House of Representatives currently uses the Equal Proportions method, Congress has not always used it. In fact, George Washington used the presidential [[Veto#United States\|veto]] power for the very first time in order to block apportionment legislation less favorable to his home state of [[Virginia]]. Had Congress used the Equal Proportionment Method (with a divisor of 34,800) to apportion House seats according to state population following the 1790 [[United States Census\|census]], the 105 seats in the [[3rd United States Congress]] the House of Representatives would have been apportioned as follows:

	~~{\| class="wikitable"~~
	\|-
	~~! State !! Population !! Quotas !! Lower !! Upper !! G. Mean !! Rnd. Dir. !! Seats~~
	~~\|- align="right"~~
	~~\| align="left" \|Connecticut \|\| 236,841 \|\| 6.81 \|\| 6 \|\| 7 \|\| 6.48 \|\| align="center" \| up \|\| 7~~
	~~\|- align="right"~~
	~~\| align="left" \|Delaware \|\| 55,540 \|\| 1.60 \|\| 1 \|\| 2 \|\| 1.41 \|\| align="center" \| up \|\| 2~~
	~~\|- align="right"~~
	~~\| align="left" \|Georgia \|\| 70,835 \|\| 2.04 \|\| 2 \|\| 3 \|\| 2.45 \|\| align="center" \| down \|\| 2~~
	~~\|- align="right"~~
	~~\| align="left" \|Kentucky \|\| 68,705 \|\| 1.97 \|\| 1 \|\| 2 \|\| 1.41 \|\| align="center" \| up \|\| 2~~
	~~\|- align="right"~~
	~~\| align="left" \|Maryland \|\| 278,514 \|\| 8.00 \|\| 8 \|\| 9 \|\| 8.49 \|\| align="center" \| down \|\| 8~~
	~~\|- align="right"~~
	~~\| align="left" \|Massachusetts \|\| 475,327 \|\| 13.66 \|\| 13 \|\| 14 \|\| 13.49 \|\| align="center" \| up \|\| 14~~
	~~\|- align="right"~~
	~~\| align="left" \|New Hampshire \|\| 141,822 \|\| 4.08 \|\| 4 \|\| 5 \|\| 4.47 \|\| align="center" \| down \|\| 4~~
	~~\|- align="right"~~
	~~\| align="left" \|New Jersey \|\| 179,570 \|\| 5.16 \|\| 5 \|\| 6 \|\| 5.48 \|\| align="center" \| down \|\| 5~~
	~~\|- align="right"~~
	~~\| align="left" \|New York \|\| 331,589 \|\| 9.53 \|\| 9 \|\| 10 \|\| 9.49 \|\| align="center" \| up \|\| 10~~
	~~\|- align="right"~~
	~~\| align="left" \|North Carolina \|\| 353,523 \|\| 10.16 \|\| 10 \|\| 11 \|\| 10.49 \|\| align="center" \| down \|\| 10~~
	~~\|- align="right"~~
	~~\| align="left" \|Pennsylvania \|\| 432,879 \|\| 12.44 \|\| 12 \|\| 13 \|\| 12.49 \|\| align="center" \| down \|\| 12~~
	~~\|- align="right"~~
	~~\| align="left" \|Rhode Island \|\| 68,446 \|\| 1.97 \|\| 1 \|\| 2 \|\| 1.41 \|\| align="center" \| up \|\| 2~~
	~~\|- align="right"~~
	~~\| align="left" \|South Carolina \|\| 206,236 \|\| 5.93 \|\| 5 \|\| 6 \|\| 5.48 \|\| align="center" \| up \|\| 6~~
	~~\|- align="right"~~
	~~\| align="left" \|Vermont \|\| 85,533 \|\| 2.46 \|\| 2 \|\| 3 \|\| 2.45 \|\| align="center" \| up \|\| 3~~
	~~\|- align="right"~~
	~~\| align="left" \|Virginia \|\| 630,560 \|\| 18.12 \|\| 18 \|\| 19 \|\| 18.49 \|\| align="center" \| down \|\| 18~~
	\|}

	~~Compared with the actual apportionment, [[Pennsylvania]] and [[Virginia]] would have lost one seat each, while [[Delaware]] and [[Vermont]] would have gained one seat each.~~

	~~{{reflist}}~~

	~~{{DEFAULTSORT:Huntington-Hill Method}}~~
	~~[[Category:Voting systems]~~]