Balance or balancedness is a property of apportionment methods , which are methods of allocating identical items between among agens, such as dividing seats in a parliament among political parties or federal states . The property says that, if two agents have exactly the same entitlements, then the number of items they receive should differ by at most one. So if two parties win the same number of votes, or two states have the same populations, then the number of seats they receive should differ by at most one.
19-496: [REDACTED] Look up balance in Wiktionary, the free dictionary. Balance may refer to: Common meanings [ edit ] Balance (ability) in biomechanics Balance (accounting) Balance or weighing scale Balance, as in equality (mathematics) or equilibrium Arts and entertainment [ edit ] Film [ edit ] Balance (1983 film) ,
38-524: A 1 , … , a n {\displaystyle a_{1},\ldots ,a_{n}} . An allocation rule is called balanced if t i = t j {\displaystyle t_{i}=t_{j}} implies | a i − a j | ≤ 1 {\displaystyle |a_{i}-a_{j}|\leq 1} for all i,j . Equivalently, t i = t j {\displaystyle t_{i}=t_{j}} implies
57-441: A 1980s pop-rock group Albums [ edit ] Balance (Akrobatik album) , 2003 Balance (Kim-Lian album) , 2004 Balance (Leo Kottke album) , 1978 Balance (Joe Morris album) , 2014 Balance (Swollen Members album) , 1999 Balance ( Ty Tabor album), 2008 Balance ( Melly Goeslaw album), 2013 Balance (Van Halen album) , 1995 Balance (Armin van Buuren album) , 2019 The Balance ,
76-801: A 1982 French film Television [ edit ] Balance: Television for Living Well , a Canadian television talk show "The Balance" (Roswell) , an episode of the television series Roswell " The Balance ", an episode of the animated series Justice League Music [ edit ] Performers [ edit ] Balance (band) , a 1980s pop-rock group Albums [ edit ] Balance (Akrobatik album) , 2003 Balance (Kim-Lian album) , 2004 Balance (Leo Kottke album) , 1978 Balance (Joe Morris album) , 2014 Balance (Swollen Members album) , 1999 Balance ( Ty Tabor album), 2008 Balance ( Melly Goeslaw album), 2013 Balance (Van Halen album) , 1995 Balance (Armin van Buuren album) , 2019 The Balance ,
95-469: A 2019 album by Catfish and the Bottlemen Songs [ edit ] "Balance", a song by Axium from The Story Thus Far "Balance", a song by Band-Maid from Unleash "Balance", a song by Ed Sheeran from - (Deluxe vinyl edition) "The Balance", a Moody Blues song on the 1970 album A Question of Balance Other [ edit ] Balance (game design) , the concept and
114-404: A 2019 album by Catfish and the Bottlemen Songs [ edit ] "Balance", a song by Axium from The Story Thus Far "Balance", a song by Band-Maid from Unleash "Balance", a song by Ed Sheeran from - (Deluxe vinyl edition) "The Balance", a Moody Blues song on the 1970 album A Question of Balance Other [ edit ] Balance (game design) , the concept and
133-445: A Bulgarian film Balance (1989 film) , a short animated film La Balance , a 1982 French film Television [ edit ] Balance: Television for Living Well , a Canadian television talk show "The Balance" (Roswell) , an episode of the television series Roswell " The Balance ", an episode of the animated series Justice League Music [ edit ] Performers [ edit ] Balance (band) ,
152-555: A criterion for fair allocation of seats among parties or states Census balance , a census-designated geography in the United States Other uses [ edit ] Balance (advertisement) , a 1989 award-winning television advertisement for the Lexus LS 400 Balance (metaphysics) , a desirable point between two or more opposite forces Balance (stereo) , the amount of signal from each channel reproduced in
171-428: A criterion for fair allocation of seats among parties or states Census balance , a census-designated geography in the United States Other uses [ edit ] Balance (advertisement) , a 1989 award-winning television advertisement for the Lexus LS 400 Balance (metaphysics) , a desirable point between two or more opposite forces Balance (stereo) , the amount of signal from each channel reproduced in
190-420: A stereo audio recording The Balance, a personal finance website owned by Dotdash See also [ edit ] Balancing (disambiguation) Balanced, a wine tasting descriptor Topics referred to by the same term [REDACTED] This disambiguation page lists articles associated with the title Balance . If an internal link led you here, you may wish to change the link to point directly to
209-420: A stereo audio recording The Balance, a personal finance website owned by Dotdash See also [ edit ] Balancing (disambiguation) Balanced, a wine tasting descriptor Topics referred to by the same term [REDACTED] This disambiguation page lists articles associated with the title Balance . If an internal link led you here, you may wish to change the link to point directly to
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#1732765372206228-529: Is a resource to allocate, denoted by h {\displaystyle h} . For example, it can be an integer representing the number of seats in a h ouse of representatives. The resource should be allocated between some n {\displaystyle n} agents , such as states or parties . The agents have different entitlements , denoted by a vector t 1 , … , t n {\displaystyle t_{1},\ldots ,t_{n}} . For example, t i can be
247-588: The fraction of votes won by party i . An allocation is a vector a 1 , … , a n {\displaystyle a_{1},\ldots ,a_{n}} with ∑ i = 1 n a i = h {\displaystyle \sum _{i=1}^{n}a_{i}=h} . An allocation rule is a rule that, for any h {\displaystyle h} and entitlement vector t 1 , … , t n {\displaystyle t_{1},\ldots ,t_{n}} , returns an allocation vector
266-430: The free dictionary. Balance may refer to: Common meanings [ edit ] Balance (ability) in biomechanics Balance (accounting) Balance or weighing scale Balance, as in equality (mathematics) or equilibrium Arts and entertainment [ edit ] Film [ edit ] Balance (1983 film) , a Bulgarian film Balance (1989 film) , a short animated film La Balance ,
285-422: The indivisibility of the items. Balancedness requires that the difference between identical-entitlement agents should be the smallest difference allowed by the indivisibility, which is 1. For example, if there are 2 equal-entitlement agents and 9 items, then the allocations (4,5) and (5,4) are both allowed, but the allocations (3,6) or (6,3) are not - a difference of 3 is not justified even by indivisibility. There
304-418: The intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Balance&oldid=1233980754 " Category : Disambiguation pages Hidden categories: Short description is different from Wikidata All article disambiguation pages All disambiguation pages balance [REDACTED] Look up balance in Wiktionary,
323-463: The intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Balance&oldid=1233980754 " Category : Disambiguation pages Hidden categories: Short description is different from Wikidata All article disambiguation pages All disambiguation pages Balance (apportionment) Ideally, agents with identical entitlements should receive an identical number of items, but this may be impossible due to
342-459: The practice of tuning relationships between a game's component systems Balance (installation) , a 2013 glazed ceramic installation by Tim Ryan Balance (puzzle) , a mathematical puzzle "Balance", a poem by Patti Smith from the book kodak Government and law [ edit ] BALANCE Act (Benefit Authors without Limiting Advancement or Net Consumer Expectations Act), a proposed US federal legislation Balance (apportionment) ,
361-459: The practice of tuning relationships between a game's component systems Balance (installation) , a 2013 glazed ceramic installation by Tim Ryan Balance (puzzle) , a mathematical puzzle "Balance", a poem by Patti Smith from the book kodak Government and law [ edit ] BALANCE Act (Benefit Authors without Limiting Advancement or Net Consumer Expectations Act), a proposed US federal legislation Balance (apportionment) ,
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