AN/FPS-17 - Revision history

en>BD2412: /* Aftermath */clean up - no longer dab needed, replaced: {{disambiguation needed| → AWB

2014-09-12T13:16:53Z

Aftermath: clean up - no longer dab needed, replaced: {{disambiguation needed| → [[ using AWB

← Older revision		Revision as of 15:16, 12 September 2014
Line 1:		Line 1:
	~~{{Other uses\|Power index (disambiguation){{!}}Power index}}~~		Hi there, I am Alyson Pomerleau and I believe it sounds fairly great when you say it. She works as a travel agent but soon she'll be on her own. Alaska is the only location I've been residing in but now [http://www.010-5260-5333.com/index.php?document_srl=1880&mid=board_ALMP66 online psychics] psychic ([http://165.132.39.93/xe/visitors/372912 165.132.39.93]) I'm considering other choices. The preferred pastime for him and his kids is style and he'll be beginning some thing else along with it.<br><br>Feel free to visit my weblog; [http://www.publicpledge.com/blogs/post/7034 psychic phone readings]
	~~The '''Shapley–Shubik power index''' was formulated by [[Lloyd Shapley]] and [[Martin Shubik]] in 1954<ref>Shapley~~, ~~L.S.~~ and M. ~~Shubik, A Method for Evaluating the Distribution of Power in~~ a ~~Committee System,~~ '~~'American Political Science Review'', 48, 787–792, 1954~~.~~</ref> to measure the powers of players in a voting game. The index often reveals surprising power distribution that~~ is ~~not obvious on~~ the ~~surface.~~

	~~The constituents of a voting system, such as legislative bodies, executives, shareholders, individual legislators, and so forth, can be viewed as players~~ in an [[n-~~player game\|''n''~~-~~player game]]~~. ~~Players with the same preferences form coalitions~~. ~~Any coalition that has enough votes to pass a bill or elect a candidate is called winning, and the others are called losing. Based on [[Shapley value]~~]~~, Shapley and Shubik concluded that the power of a coalition was not simply proportional to its size.~~

	~~The power of a coalition~~ (~~or a player) is measured by the fraction of the possible voting sequences in which that coalition casts the deciding vote, that is, the vote that first guarantees passage or failure~~.~~<ref>Hu, X~~.~~, An asymmetric Shaplay–Shubik power index, ''International Journal of Game Theory,'' 34, 229–240, 2006~~.</~~ref>~~

	~~The power index is normalized between 0 and 1~~. ~~A power of 0 means that a coalition has no effect at all on the outcome of the game; and a power of 1 means a coalition determines the outcome by its vote~~. ~~Also the sum of the powers of all the players is always equal to 1~~.

	~~== Examples ==~~
	~~Suppose decisions are made by majority rule in a body consisting of A, B, C, D, who have 3, 2, 1 and 1 votes, respectively~~. The ~~majority vote threshold is 4. There are [[Factorial\|4!]] = 24 possible orders~~ for ~~these members to vote:~~

	~~{\| class="wikitable"~~
	\|-
	~~\| A'''B'''CD~~
	~~\| A'''B'''DC~~
	~~\| A'''C'''BD~~
	~~\| A'''C'''DB~~
	~~\| A'''D'''BC~~
	~~\| A'''D'''CB~~
	\|-
	~~\| B'''A'''CD~~
	~~\| B'''A'''DC~~
	~~\| BC'''A'''D~~
	~~\| BC'''D'''A~~
	~~\| BD'''A'''C~~
	~~\| BD'''C'''A~~
	\|-
	~~\| C'''A'''BD~~
	~~\| C'''A'''DB~~
	~~\| CB'''A'''D~~
	~~\| CB'''D'''A~~
	~~\| CD'''A'''B~~
	~~\| CD'''B'''A~~
	\|-
	~~\| D'''A'''BC~~
	~~\| D'''A'''CB~~
	~~\| DB'''A'''C~~
	~~\| DB'''C'''A~~
	~~\| DC'''A'''B~~
	~~\| DC'''B'''A~~
	\|}
	~~For each voting sequence the pivot voter – that voter who first raises the cumulative sum to 4 or more – is bolded. Here, A~~ is ~~pivotal in 12 of the 24 sequences. Therefore, A has an index of power 1/2. The others have an index of power 1/6. Curiously, B has no more power than C~~ and ~~D. When you consider that A~~'~~s vote determines the outcome unless the others unite against A,~~ it ~~becomes clear that B, C, D play identical roles. This reflects in the power indices~~.

	~~Suppose that in another majority-rule voting body with <math>2n+1</math> members, in which a single strong member has~~ <~~math~~>k<~~/math~~> votes and the remaining <math>2n</math> members have one vote each. It then turns out that the power of the strong member is <math>\dfrac{k}{2n+2-k}</math>. As <math>k</math> increases, his power increases disproportionately until it approaches half the total vote and he gains virtually all the power. This phenomenon often happens to ~~large shareholders and business takeovers.~~

	~~==See also==~~
	* [[Shapley value]]
	* [[Arrow theorem]]
	* [[Banzhaf power index]]

	~~== References ==~~
	~~<references/>~~

	~~== External links ==~~
	*[http://www.~~warwick.ac~~.uk/~~~ecaae/ Computer Algorithms for Voting Power Analysis] Web-based algorithms for voting power analysis~~
	*[http://~~korsika.informatik.uni-kiel.de/~stb/power_indices/index.php Power Index Calculator] Computes various indices for (multiple) weighted voting games online. Includes some examples.~~

	~~{{DEFAULTSORT:Shapley-Shubik power index}}~~
	~~[[Category:Game theory]]~~
	~~[[Category:Cooperative games]]~~
	~~[[Category:Voting systems]~~]

en>Livers21: Corrected transmitter power.

2013-10-26T17:02:20Z

Corrected transmitter power.

← Older revision		Revision as of 19:02, 26 October 2013
Line 1:		Line 1:
	~~Andera~~ is ~~what you~~ can ~~contact her but she~~ by no means ~~truly liked~~ that ~~title. Invoicing~~ is ~~what I do~~. ~~To play lacross~~ is the ~~thing I love most~~ of ~~all~~. ~~Alaska is where he~~'s ~~always been living~~.<br><br>~~Also visit my page; online psychics (~~[http://~~jplusfn~~.~~gaplus~~.kr/xe/~~qna/78647~~ http://~~jplusfn~~.~~gaplus~~.kr/xe/~~qna~~/~~78647~~])		{{Other uses\|Power index (disambiguation){{!}}Power index}}
			The '''Shapley–Shubik power index''' was formulated by [[Lloyd Shapley]] and [[Martin Shubik]] in 1954<ref>Shapley, L.S. and M. Shubik, A Method for Evaluating the Distribution of Power in a Committee System, ''American Political Science Review'', 48, 787–792, 1954.</ref> to measure the powers of players in a voting game. The index often reveals surprising power distribution that is not obvious on the surface.

			The constituents of a voting system, such as legislative bodies, executives, shareholders, individual legislators, and so forth, can be viewed as players in an [[n-player game\|''n''-player game]]. Players with the same preferences form coalitions. Any coalition that has enough votes to pass a bill or elect a candidate is called winning, and the others are called losing. Based on [[Shapley value]], Shapley and Shubik concluded that the power of a coalition was not simply proportional to its size.

			The power of a coalition (or a player) is measured by the fraction of the possible voting sequences in which that coalition casts the deciding vote, that is, the vote that first guarantees passage or failure.<ref>Hu, X., An asymmetric Shaplay–Shubik power index, ''International Journal of Game Theory,'' 34, 229–240, 2006.</ref>

			The power index is normalized between 0 and 1. A power of 0 means that a coalition has no effect at all on the outcome of the game; and a power of 1 means a coalition determines the outcome by its vote. Also the sum of the powers of all the players is always equal to 1.

			== Examples ==
			Suppose decisions are made by majority rule in a body consisting of A, B, C, D, who have 3, 2, 1 and 1 votes, respectively. The majority vote threshold is 4. There are [[Factorial\|4!]] = 24 possible orders for these members to vote:

			{\| class="wikitable"
			\|-
			\| A'''B'''CD
			\| A'''B'''DC
			\| A'''C'''BD
			\| A'''C'''DB
			\| A'''D'''BC
			\| A'''D'''CB
			\|-
			\| B'''A'''CD
			\| B'''A'''DC
			\| BC'''A'''D
			\| BC'''D'''A
			\| BD'''A'''C
			\| BD'''C'''A
			\|-
			\| C'''A'''BD
			\| C'''A'''DB
			\| CB'''A'''D
			\| CB'''D'''A
			\| CD'''A'''B
			\| CD'''B'''A
			\|-
			\| D'''A'''BC
			\| D'''A'''CB
			\| DB'''A'''C
			\| DB'''C'''A
			\| DC'''A'''B
			\| DC'''B'''A
			\|}
			For each voting sequence the pivot voter – that voter who first raises the cumulative sum to 4 or more – is bolded. Here, A is pivotal in 12 of the 24 sequences. Therefore, A has an index of power 1/2. The others have an index of power 1/6. Curiously, B has no more power than C and D. When you consider that A's vote determines the outcome unless the others unite against A, it becomes clear that B, C, D play identical roles. This reflects in the power indices.

			Suppose that in another majority-rule voting body with <math>2n+1</math> members, in which a single strong member has <math>k</math> votes and the remaining <math>2n</math> members have one vote each. It then turns out that the power of the strong member is <math>\dfrac{k}{2n+2-k}</math>. As <math>k</math> increases, his power increases disproportionately until it approaches half the total vote and he gains virtually all the power. This phenomenon often happens to large shareholders and business takeovers.

			==See also==
			* [[Shapley value]]
			* [[Arrow theorem]]
			* [[Banzhaf power index]]

			== References ==
			<references/>

			== External links ==
			*[http://www.warwick.ac.uk/~ecaae/ Computer Algorithms for Voting Power Analysis] Web-based algorithms for voting power analysis
			*[http://korsika.informatik.uni-kiel.de/~stb/power_indices/index.php Power Index Calculator] Computes various indices for (multiple) weighted voting games online. Includes some examples.

			{{DEFAULTSORT:Shapley-Shubik power index}}
			[[Category:Game theory]]
			[[Category:Cooperative games]]
			[[Category:Voting systems]]

en>Neshmick at 16:21, 2 August 2012

2012-08-02T16:21:44Z

New page

Andera is what you can contact her but she by no means truly liked that title. Invoicing is what I do. To play lacross is the thing I love most of all. Alaska is where he's always been living.<br><br>Also visit my page; online psychics ([http://jplusfn.gaplus.kr/xe/qna/78647 http://jplusfn.gaplus.kr/xe/qna/78647])