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Mere addition paradox

April 17, 2024

The mere addition paradox (also known as the repugnant conclusion) is a problem in ethics identified by Derek Parfit and discussed in his book Reasons and Persons (1984). The paradox identifies the mutual incompatibility of four intuitively compelling assertions about the relative value of populations. Parfit’s original formulation of the repugnant conclusion is that “For any perfectly equal population with very high positive welfare, there is a population with very low positive welfare which is better, other things being equal.”[1]

The paradox edit

Consider the four populations depicted in the following diagram: A, A+, B− and B. Each bar represents a distinct group of people. The bar's width represents group size while the bar's height represents group happiness. Unlike A and B, A+ and B− are complex populations, each comprising two distinct groups of people. It is also stipulated that the lives of the members of each group are good enough that they would rather be alive than not exist.

 

Parfit makes the following three suggestions regarding the value of the populations:

1. A+ seems no worse than A. This is because the people in A are no worse-off in A+, while the additional people who exist in A+ are better off in A+ compared to A, since it is stipulated that their lives are good enough that it is better for them to be alive than to not exist.
2. B− seems better than A+. This is because B− has greater total and average happiness than A+.
3. B seems equally as good as B−, as the only difference between B− and B is that the two groups in B− are merged to form one group in B.

Together, these three comparisons entail that B is better than A. However, Parfit also observes the following:

4. When we directly compare A (a population with high average happiness) and B (a population with lower average happiness, but more total happiness because of its larger population), it may seem that B can be worse than A.

Thus, there is a paradox. The following intuitively plausible claims are jointly incompatible: (1) that A+ is no worse than A, (2) that B− is better than A+, (3) that B− is as good as B, and (4) that B can be worse than A.

Responses edit

Some scholars, such as Larry Temkin and Stuart Rachels, argue that inconsistencies between the four claims (above) relies on the assumption that the "better than" relation is transitive. The inconsistency could then be resolved by rejecting the assumption. According to this view, although A+ is no worse than A, and B− is better than A+, it does not follow that B− is better than A.

Torbjörn Tännsjö argues that the intuition that B is worse than A is wrong. While the lives of those in B are worse than those in A, there are more of them, and thus the collective value of B is greater than A.[2] Michael Huemer also argues that the repugnant conclusion is not repugnant.[3]

However, Parfit argues that the above discussion fails to appreciate the true source of repugnance. He claims that initially, it may not be wrong to think that B is better than A. Assuming this is true, as Huemer argues, it follows that this revised intuition must hold in subsequent iterations of the original steps. For example, the next iteration would add even more people to B+, and then take the average of the total happiness, resulting in C−. If these steps are repeated over and over, the eventual result will be Z, a massive population with the minimum level of average happiness; this would be a population in which every member is leading a life barely worth living. Parfit claims that it is Z that is the repugnant conclusion.[4]

Alternative usage edit

An alternative use of the term mere addition paradox was presented in a paper by Hassoun in 2010.[5] It identifies paradoxical reasoning that occurs when certain statistical measures are used to calculate results over a population. For example, if a group of 100 people together control $100 worth of resources, the average wealth per capita is $1. If a single rich person then arrives with 1 million dollars, then the total group of 101 people controls $1,000,100, making average wealth per capita $9,901, implying a drastic shift away from poverty even though nothing has changed for the original 100 people. Hassoun defines a no mere addition axiom to be used for judging such statistical measures: "merely adding a rich person to a population should not decrease poverty" (although acknowledging that in actual practice adding rich people to a population may provide some benefit to the whole population).

This same argument can be generalized to many cases where proportional statistics are used: for example, a video game sold on a download service may be considered a failure if less than 20% of those who download the game demo then purchase the game. Thus, if 10,000 people download the demo of a game and 2,000 buy it, the game is a borderline success; however, it would be rendered a failure by an extra 500 people downloading the demo and not buying, even though this "mere addition" changes nothing with regard to income or consumer satisfaction from the previous situation.

See also edit

Notes edit

  1. ^ Derek Parfit, Reasons and Persons (Clarendon Press, 1984), p. 388.
  2. ^ Torbjörn, Tännsjö (November 2002). "Why We Ought to Accept the Repugnant Conclusion". Utilitas. 14 (3): 339–359. doi:10.1017/S0953820800003642. S2CID 233360601.
  3. ^ Huemer, M. (2008), "In defence of repugnance" Mind, 117, 899-933.
  4. ^ Parfit, Derek (1984). Reasons and Persons. New York: Oxford University Press. ISBN 978-0198249085.
  5. ^ Another Mere Addition Paradox? Some Reflections on Variable Population Poverty Measurement. UNU-WIDER. November 2010. ISBN 978-92-9230-358-7. Retrieved 31 March 2015.

References edit

External links edit

  • The Repugnant Conclusion (Stanford Encyclopedia of Philosophy)
  • Contestabile, Bruno. On the Buddhist Truths and the Paradoxes in Population Ethics, Contemporary Buddhism, Vol. 11 Issue 1, pp. 103–113, Routledge 2010

April 17, 2024
mere, addition, paradox, this, article, tone, style, reflect, encyclopedic, tone, used, wikipedia, wikipedia, guide, writing, better, articles, suggestions, september, 2016, learn, when, remove, this, template, message, mere, addition, paradox, also, known, re. This article s tone or style may not reflect the encyclopedic tone used on Wikipedia See Wikipedia s guide to writing better articles for suggestions September 2016 Learn how and when to remove this template message The mere addition paradox also known as the repugnant conclusion is a problem in ethics identified by Derek Parfit and discussed in his book Reasons and Persons 1984 The paradox identifies the mutual incompatibility of four intuitively compelling assertions about the relative value of populations Parfit s original formulation of the repugnant conclusion is that For any perfectly equal population with very high positive welfare there is a population with very low positive welfare which is better other things being equal 1 Contents 1 The paradox 2 Responses 3 Alternative usage 4 See also 5 Notes 6 References 7 External linksThe paradox editConsider the four populations depicted in the following diagram A A B and B Each bar represents a distinct group of people The bar s width represents group size while the bar s height represents group happiness Unlike A and B A and B are complex populations each comprising two distinct groups of people It is also stipulated that the lives of the members of each group are good enough that they would rather be alive than not exist nbsp Parfit makes the following three suggestions regarding the value of the populations 1 A seems no worse than A This is because the people in A are no worse off in A while the additional people who exist in A are better off in A compared to A since it is stipulated that their lives are good enough that it is better for them to be alive than to not exist dd 2 B seems better than A This is because B has greater total and average happiness than A dd 3 B seems equally as good as B as the only difference between B and B is that the two groups in B are merged to form one group in B dd Together these three comparisons entail that B is better than A However Parfit also observes the following 4 When we directly compare A a population with high average happiness and B a population with lower average happiness but more total happiness because of its larger population it may seem that B can be worse than A dd Thus there is a paradox The following intuitively plausible claims are jointly incompatible 1 that A is no worse than A 2 that B is better than A 3 that B is as good as B and 4 that B can be worse than A Responses editSome scholars such as Larry Temkin and Stuart Rachels argue that inconsistencies between the four claims above relies on the assumption that the better than relation is transitive The inconsistency could then be resolved by rejecting the assumption According to this view although A is no worse than A and B is better than A it does not follow that B is better than A Torbjorn Tannsjo argues that the intuition that B is worse than A is wrong While the lives of those in B are worse than those in A there are more of them and thus the collective value of B is greater than A 2 Michael Huemer also argues that the repugnant conclusion is not repugnant 3 However Parfit argues that the above discussion fails to appreciate the true source of repugnance He claims that initially it may not be wrong to think that B is better than A Assuming this is true as Huemer argues it follows that this revised intuition must hold in subsequent iterations of the original steps For example the next iteration would add even more people to B and then take the average of the total happiness resulting in C If these steps are repeated over and over the eventual result will be Z a massive population with the minimum level of average happiness this would be a population in which every member is leading a life barely worth living Parfit claims that it is Z that is the repugnant conclusion 4 Alternative usage editAn alternative use of the term mere addition paradox was presented in a paper by Hassoun in 2010 5 It identifies paradoxical reasoning that occurs when certain statistical measures are used to calculate results over a population For example if a group of 100 people together control 100 worth of resources the average wealth per capita is 1 If a single rich person then arrives with 1 million dollars then the total group of 101 people controls 1 000 100 making average wealth per capita 9 901 implying a drastic shift away from poverty even though nothing has changed for the original 100 people Hassoun defines a no mere addition axiom to be used for judging such statistical measures merely adding a rich person to a population should not decrease poverty although acknowledging that in actual practice adding rich people to a population may provide some benefit to the whole population This same argument can be generalized to many cases where proportional statistics are used for example a video game sold on a download service may be considered a failure if less than 20 of those who download the game demo then purchase the game Thus if 10 000 people download the demo of a game and 2 000 buy it the game is a borderline success however it would be rendered a failure by an extra 500 people downloading the demo and not buying even though this mere addition changes nothing with regard to income or consumer satisfaction from the previous situation See also editA Theory of Justice Asymmetry population ethics Average and total utilitarianism Carrying capacity Ecological footprint Nonidentity problem Human overpopulation Person affecting view Sorites paradox Utility monster Industrial RevolutionNotes edit Derek Parfit Reasons and Persons Clarendon Press 1984 p 388 Torbjorn Tannsjo November 2002 Why We Ought to Accept the Repugnant Conclusion Utilitas 14 3 339 359 doi 10 1017 S0953820800003642 S2CID 233360601 Huemer M 2008 In defence of repugnance Mind 117 899 933 Parfit Derek 1984 Reasons and Persons New York Oxford University Press ISBN 978 0198249085 Another Mere Addition Paradox Some Reflections on Variable Population Poverty Measurement UNU WIDER November 2010 ISBN 978 92 9230 358 7 Retrieved 31 March 2015 References editParfit Derek Reasons and Persons ch 17 and 19 Oxford University Press 1986 Ryberg Jesper amp Tannsjo Torbjorn eds The Repugnant Conclusion Essays on Population Ethics Dordrecht Kluwer Academic Publishers 2004 Temkin Larry Intransitivity and the Mere Addition Paradox Philosophy and Public Affairs 16 2 Spring 1987 138 187 Tannsjo Torbjorn Hedonistic Utilitarianism Edinburgh University Press 1998 Hassoun Nicole Another Mere Addition Paradox UNU WIDER Working Paper 2010 1 External links editThe Repugnant Conclusion Stanford Encyclopedia of Philosophy Contestabile Bruno On the Buddhist Truths and the Paradoxes in Population Ethics Contemporary Buddhism Vol 11 Issue 1 pp 103 113 Routledge 2010 Retrieved from https en wikipedia org w index php title Mere addition paradox amp oldid 1218553057, wikipedia, wiki, book, books, library,

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