Weakly additive




In fair division, a topic in economics, a preference relation is weakly additive
if the following condition is met:[1]


If A is preferred to B, and C is preferred to D (and the contents of A and C do not overlap) then A together with C is preferable to B together with D.

Every additive utility function is weakly-additive. However, additivity is applicable only to cardinal utility functions, while weak additivity is applicable to ordinal utility functions.


Weak additivity is often a realistic assumption when dividing up goods between claimants, and simplifies the mathematics of certain fair division problems considerably. Some procedures in fair division do not need the value of goods to be additive and only require weak additivity. In particular the adjusted winner procedure only requires weak additivity.



Cases where weak additivity fails


Case where the assumptions might fail would be either



  • The value of A and C together is the less than the sum of their values. For instance two versions of the same CD may not be as valuable to a person as the sum of the values of the individual CDs on their own. I.e, A and C are substitute goods.

  • The values of B and D together may be more than their individual values added. For instance two matching bookends may be much more valuable than twice the value of an individual bookend. I.e, B and D are complementary goods.


The use of money as compensation can often turn real cases like these into situations where the weak additivity condition is satisfied even if the values are not exactly additive.


The value of a type of goods, e.g. chairs, dependent on having some of those goods already is called the marginal utility.



See also


  • Responsive set extension#Responsiveness


References





  1. ^ Brams, Steven J.; Taylor, Alan D. (1996). Fair division: from cake-cutting to dispute resolution. Cambridge University Press. ISBN 0-521-55644-9..mw-parser-output cite.citation{font-style:inherit}.mw-parser-output .citation q{quotes:"""""""'""'"}.mw-parser-output .citation .cs1-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Lock-gray-alt-2.svg/9px-Lock-gray-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .citation .cs1-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Lock-red-alt-2.svg/9px-Lock-red-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration{color:#555}.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration span{border-bottom:1px dotted;cursor:help}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/12px-Wikisource-logo.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output code.cs1-code{color:inherit;background:inherit;border:inherit;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;font-size:100%}.mw-parser-output .cs1-visible-error{font-size:100%}.mw-parser-output .cs1-maint{display:none;color:#33aa33;margin-left:0.3em}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration,.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-right{padding-right:0.2em}











-

Popular posts from this blog

Y

Image
This article is about the letter of the alphabet. For other uses, see Y (disambiguation). See also: Wye (disambiguation) Y Y y (See below) Usage Writing system Latin script Type Alphabetic and Logographic Language of origin Latin language Phonetic usage [ y ] [ ɨ ] [ j ] [ iː ] [ ɪ ] [ ɘ ] [ ə ] [ ɯ ] [ ɛː ] [ j ] [ ɥ ] [ ɣ̟ ] / w aɪ / / aɪ / Unicode value U+0059, U+0079 Alphabetical position 25 History Development Υ υ 𐌖 Y y Time period 54 to present Descendants  • U  • V  • W  • Ỿ  • ¥  • Ꮙ  • Ꮍ  • Ꭹ Sisters F Ѵ У Ў Ұ Ү ו و ܘ וּ וֹ ࠅ 𐎆 𐡅 ወ વ ૂ ુ उ Variations (See below) Other Other letters commonly used with y(x), ly, ny This article contains IPA phonetic symbols. Without proper rendering support, you may see question marks, boxes, or other symbols instead of Unicode characters. For an introductory guide on IPA symbols, see Help:IPA. ISO basic Latin alphabet Aa Bb Cc D...
Read more

Mount Tamalpais

Image
Mount Tamalpais Mount Tamalpais, viewed from the south Highest point Elevation 2,571 ft (784 m)   NAVD 88 [1] Prominence 2,456 ft (749 m)  [1] Listing California county high points 55th Coordinates 37°55′45″N 122°34′40″W  /  37.929088°N 122.577829°W  / 37.929088; -122.577829 Coordinates: 37°55′45″N 122°34′40″W  /  37.929088°N 122.577829°W  / 37.929088; -122.577829   [1] Geography Mount Tamalpais Marin County, California, U.S. Show map of California Mount Tamalpais Mount Tamalpais (the US) Show map of the US Parent range California Coast Ranges Topo map USGS San Rafael Geology Mountain type Sedimentary Climbing First ascent 1830s by Jacob P. Leese (first recorded ascent) [2] Easiest route Railroad Grade fire trail Mount Tamalpais ( / t æ m əl ˈ p aɪ . ɪ s / ; TAM -əl- PY -iss ; Coast Miwok: /t̪ɑmɑlˈpɑis̺/ , known locally as Mount Tam ) is a peak in Marin County, California, United State...
Read more

Indian Forest Service

Image
Indian Forest Service Service Overview Preceding service Imperial Forest Service (1864 to 1935) Year of Constitution 1966 Country India Staff College Indira Gandhi National Forest Academy (IGNFA), Dehradun, Uttarakhand Cadre Controlling Authority Ministry of Environment, Forests and Climate Change Legal personality Governmental: Government service General nature Administration of Forest and Wildlife resources Cadre strength 3131 (2182 Direct Recruits and 949 Promotion Posts) Website ifs.nic.in Service Chief Director General of Forests Siddhanth Das, IFS (1982 Batch, Odisha Cadre) [1] Head of the All India Civil Services Cabinet Secretary Pradeep Kumar Sinha, IAS Indian Forest Service (भारतीय वन सेवा) [2] is one of the three All India Services of the Government of India. The other two All India Services being the Indian Administrative Service (IAS) and the Indian Police Service (IPS). [3] [4] [5] It was constituted in...
Read more