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The fallacy of composition arises when one infers that something is true of the whole from the fact that it is true of some part of the whole (or even of every proper part). For example: "This wheel is made of rubber, therefore the vehicle to which it is a part is also made of rubber." This is clearly fallacious, because vehicles are often made with a variety of parts, many of which may not be made of rubber.

This fallacy is often confused with the fallacy of hasty generalization, in which an unwarranted inference is made from a statement about a sample to a statement about the population from which it is drawn.

The fallacy of composition is the converse of the fallacy of division; it may be contrasted with the case of emergence, where the whole possesses properties not present in the parts.

Examples

No atoms are alive. Therefore, nothing made of atoms is alive.

If someone stands up out of their seat at a cricket match, they can see better. Therefore, if everyone stands up, they can all see better.

Some people have survived every type of cancer. (Implying that there are individuals who have had, and have survived, every type of cancer.)

If a runner runs faster, he can win the race. Therefore, if all the runners run faster, they can all win the race. (Athletic competitions are examples of zero-sum games, wherein the winner wins by preventing all other competitors from winning.)

In voting theory, the Condorcet paradox demonstrates a fallacy of composition: Even if all voters have rational preferences, the collective choice induced by majority rule is not transitive and hence not rational. The fallacy of composition occurs if from the rationality of the individuals one infers that society can be equally rational. The principle generalizes beyond the aggregation via majority rule to any reasonable aggregation rule, demonstrating that the aggregation of individual preferences into a social welfare function is fraught with severe difficulties (see Arrow's impossibility theorem and social choice theory).^{[citation needed]}

In economics

The paradox of thrift is a notable fallacy of composition described by Keynesian economics.
Division of labour is another economic example, in which overall productivity can greatly increase when individual workers specialize in doing different jobs. An individual worker may become more productive by specializing in making, say, hatpins, but by satisfying the wants of many other individuals for a given product, the specialist worker forces other workers to specialize in making different things. What is true for the part (earning more by investing in the skills or equipment to make a given product faster) is not true for the whole (because not everybody can profitably make the same product).
Economists use the term representative agent to refer to the typical decision-maker of a certain type (for example, the typical consumer, or the typical firm); when this representative agent is poorly chosen in a model, it can be seen as a fallacy of composition.
In a tragedy of the commons, an individual can profit by consuming a larger share of a common, shared resource such as fish from the sea; but if too many individuals seek to consume more, they can destroy the resource.^[1]
In the free rider problem, an individual can benefit by failing to pay when consuming a share of a public good; but if there are too many such "free riders", eventually there will be no "ride" for anyone.^[1]

In chemistry and materials science, a single type of atom may form allotropes with different physical properties from each other, and from their individual constituent atoms, such as diamond and graphite each consisting of carbon atoms. What is true of a single carbon atom is not true of a collection of carbon atoms bonded into a material. Furthermore, the properties of an atom differ from the properties of the individual subatomic particles that constitute it.

In social network theory, a group of humans arranged into a social network can have abilities not possessed by the individual humans making up the network.^[2] A simple example is the bucket brigade, in which humans arranged into a chain can move buckets of water or other similar items across a distance faster and with less effort than can a disorganized group of individuals carrying the loads across the same distance. What is true of the part (an individual needing to move his or her body across the whole distance to move a load) is not true of the whole (in which individuals can move loads across the distance merely by standing in place and handing off the load to the next individual).

Modo hoc fallacy

The modo hoc (or "just this") fallacy is the informal error of assessing meaning to an existent based on the constituent properties of its material makeup while omitting the matter's arrangement.^[3] For instance, metaphysical naturalism states that while matter and motion are all that compose humans, it cannot be assumed that the characteristics inherent in the elements and physical reactions that make us up ultimately and solely define our meaning; for, a cow which is alive and well and a cow which has been chopped up into meat are the same matter but it is obvious that the arrangement of that matter clarifies those different situational meanings.^[3]

References

^ ^a ^b Pigliucci, Massimo (2012). "Chapter 15: On Justice". Answers for Aristotle: How Science and Philosophy Can Lead Us to A More Meaningful Life. Basic Books. ISBN 0465021387.
^ Christakis, Nicholas A.; Fowler, James H. (2009). Connected: The Surprising Power of Our Social Networks and How They Shape Our Lives. Little, Brown and Co. ISBN 978-0316036146.
^ ^a ^b Carrier, Richard (2005). Sense and Goodness Without God: A Defense of Metaphysical Naturalism. Prometheus Books. p. 130. ISBN 1-4208-0293-3.

[Pigliucci_2012-1] Pigliucci, Massimo (2012). "Chapter 15: On Justice". Answers for Aristotle: How Science and Philosophy Can Lead Us to A More Meaningful Life. Basic Books. ISBN 0465021387.

[Christakis_Fowler_2009-2] Christakis, Nicholas A.; Fowler, James H. (2009). Connected: The Surprising Power of Our Social Networks and How They Shape Our Lives. Little, Brown and Co. ISBN 978-0316036146.

[Carrier-3] Carrier, Richard (2005). Sense and Goodness Without God: A Defense of Metaphysical Naturalism. Prometheus Books. p. 130. ISBN 1-4208-0293-3.

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 The ''modo hoc'' (or "just this") fallacy is the informal error of assessing meaning to an existent based on the constituent properties of its [[matter|material makeup]] while omitting the matter's arrangement.<ref name="Carrier">{{cite book |last=Carrier |first=Richard |title=Sense and Goodness Without God: A Defense of Metaphysical Naturalism |publisher=Prometheus Books |year=2005 |page=130 |isbn=1-4208-0293-3}}</ref> For instance, [[metaphysical naturalism]] states that while matter and [[Motion (physics)|motion]] are all that compose [[human]]s, it cannot be assumed that the characteristics inherent in the elements and physical reactions that make us up ultimately and solely define our meaning; for, a cow which is alive and well and a cow which has been chopped up into meat are the same matter but it is obvious that the ''arrangement'' of that matter clarifies those different situational meanings.<ref name="Carrier" />
-== Apex fallacy ==
-The ''apex fallacy'' is a specific variation of the fallacy of composition, where the experiences and success of the top performers in a group are assumed to be representative of all members of that group.<ref>[https://hbr.org/2013/03/whats-worse-glass-ceilings-or-glass-cellars What’s Worse — Glass Ceilings or Glass Cellars?]</ref> <ref>[https://www.tandfonline.com/doi/abs/10.1080/21642850.2015.1049539 Public health surveillance and the media: a dyad of panoptic and synoptic social control]</ref>  This often overlaps with [[survivorship bias]] and [[selection bias]], because top performers tend to continue to be members of such a group, but those who fail tend to drop out over time.  An extension of this fallacy includes when the apex of one composition is compared to the average of another composition.  Members at the apex of a group are not necessarily representative of that group.
-For example, working space circumstances that are optimal for top performing employees in specific industry sectors are sometimes wrongly assumed to be optimal for lesser performing employees, different divisions, or even other industry sectors.<ref>[http://workplaceinsight.net/beware-great-apex-fallacy-workplace-design/ Beware the great apex fallacy of workplace design]</ref>
-As another example, in the United States, there are substantially more males than females in the roles of top tier business executives<ref>[http://fortune.com/2017/06/09/white-men-senior-executives-fortune-500-companies-diversity-data/ White Men Account for 72% of Corporate Leadership at 16 of the Fortune 500 Companies]</ref>, politicians, doctors, and attorneys.  Concluding that this alone is evidence of discrimination against women on its own is the apex fallacy.<ref>[http://www.enterstageright.com/archive/articles/1008/1008ihelensmithinterview.htm The apex fallacy: An interview with Dr. Helen Smith]</ref>  If that was logical and rational, then the fact that [[Incarceration in the United States | virtually all prisoners are male and not female]] would also be evidence of discrimination against men.
 ==See also==