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Individuals, groups, fitness and utility: multi-level selection meets social choice theory

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Abstract

In models of multi-level selection, the property of Darwinian fitness is attributed to entities at more than one level of the biological hierarchy, e.g. individuals and groups. However, the relation between individual and group fitness is a controversial matter. Theorists disagree about whether group fitness should always, or ever, be defined as total (or average) individual fitness. This paper tries to shed light on the issue by drawing on work in social choice theory, and pursuing an analogy between fitness and utility. Social choice theorists have long been interested in the relation between individual and social utility, and have identified conditions under which social utility equals total (or average) individual utility. These ideas are used to shed light on the biological problem.

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Notes

  1. Social choice theory is a branch of decision theory which is concerned with devising aggregation mechanisms for forming ‘social preferences’, or ‘social choices’ from the preferences/choices of individuals in a society. See for example Sen (1986), Bossert and Weymark (2004) or Gaertner (2006) for good overviews.

  2. ‘Group utility’ would normally be called ‘social utility’ in the social choice theory literature.

  3. This is sometimes called ‘realized fitness’, and is the appropriate measure of fitness in a model in which stochastic factors are ignored.

  4. In fact, total rather than average individual fitness is the salient notion of group fitness in the Price equation, since the covariance is actually a weighted covariance, where the weights are the group sizes (Okasha 2006, p. 65 n. 26).

  5. Thus Michod and Nedelcu (2003) write: “group fitness is, initially, taken to be the average of the lower-level individual fitnesses; but as the evolutionary transition proceeds, group fitness becomes decoupled from the fitness of its lower-level components” (p. 66).

  6. Essentially, a linear trade-off means that if the cells specialise, this will reduce Cov (v i, b i) but reduce C by the same amount, with no overall effect on G. A concave trade-off means that specialization will reduce Cov (v i, b i) but reduce C by even more. (Remember that Cov (v i, b i) is less than zero, so reducing it increases G).

  7. The crucial question of what utility numbers really measure, and whether they are inter-personally comparable, are discussed in Sect. “Axioms on social welfare functionals”.

  8. Thus xP U y iff xR U y and it is not the case that yR U x; and xI U y iff xR U y and yR U x.

  9. ‘Ordinally measurable’ means that utility assignments are mere representations of preference orderings, and do not capture intensity of preference. So utility differences are not meaningful, i.e. it makes no sense to ask whether an individual’s preference for x over y exceeds his preference for y over z.

  10. Temperature in degrees celsius (or farenheit) is an example of a quantity that is measured on a cardinal scale.

  11. Obviously, average utilitarianism and total utilitarianism co-incide if the population size is fixed.

  12. ‘In effect’ because the actual definition of utilitarianism adopted here makes no explicit reference to social utility, but only to a social preference order.

  13. See for example d’Aspremont and Gevers (1977), Maskin (1978), Roberts (1980) and Sen (1977). Good surveys of these theorems are given by Roemer (1997) and Blackorby et al. (2002).

  14. Blackorby et al. (2002) offer a characterization of utilitarianism that does not rely on any informational assumptions, but instead uses an axiom called ‘incremental equity’ (I.E.). This axiom requires that the SWFL be impartial with respect to utility gains and losses, i.e. transfers of utility between individuals are a matter of social indifference. However, as they note, I.E. is conceptually extremely close to utilitarianism itself, which is a major disadvantage.

  15. See for example Maynard Smith and Price (1973). Skyrms (1996) and Gintis (2000) contain good discussions of the move from classical to evolutionary game theory.

  16. ‘Course of action’ can be interpreted very broadly here; for example, a particular developmental pathway in ontogeny could count as a course of action.

  17. The distinction between these two cases is similar to the distinction in evolutionary game theory between a monomorphic population playing a single mixed strategy, and a polymorphic population playing different fixed strategies; see Maynard Smith (1982).

  18. A ratio scale is one where the permissible transformations are of the form w′ = aw, a > 0, meaning that there is zero point; this implies that that levels, differences, and ratios are comparable. Length is an example of a quantity measured on a ratio scale.

  19. Though exceptions are certainly possible. For example, permuting the fitnesses among group members may alter the sex ratio in future generations, thus affecting group fitness in the long-run. Thanks to a referee for this observation.

  20. See Sect. “Axioms on social welfare functionals”.

References

  • Blackorby C, Donaldson D (1982) Ratio scale and translation full interpersonal comparability without domain restrictions: admissible social-evaluation functionals. Int Econ Rev 23(2):249–268

    Article  Google Scholar 

  • Blackorby C, Bossert W, Donaldson D (2002) Utilitarianism and the theory of justice. In: Arrow K, Sen A, Suzumura K (eds) Handbook of social choice and welfare. Elsevier, Amsterdam

    Google Scholar 

  • Bossert W, Weymark P (2004) Utility in social choice. In: Barbera S, Hammond P, Seidl C (eds) Handbook of utility theory, vol 2. Springer, Kluwer

    Google Scholar 

  • Buss L (1987) The evolution of individuality. Princeton University Press, Princeton

    Google Scholar 

  • d’Aspremont C, Gevers L (1977) Equity and the informational basis of collective choice. Rev Econ Stud 44:199–209

    Article  Google Scholar 

  • Damuth J, Heisler IL (1988) Alternative formulations of multi-level selection. Biol Philos 3:407–430

    Article  Google Scholar 

  • Dawkins R (1995) A river out of Eden. Harper-Collins, London

    Google Scholar 

  • Gaertner W (2006) A primer in social choice theory. Oxford University Press, Oxford

    Google Scholar 

  • Gintis H (2000) Game theory evolving. Princeton University Press, Princeton

    Google Scholar 

  • Grafen A (1999) Formal Darwinism, the individual-as-maximising-agent analogy, and Bet-Hedging. Proc R Soc Lond B 266:799–803

    Article  Google Scholar 

  • Grafen A (2007) The formal Darwinism project: a mid-term report. J Evol Biol 20(4):1243–1254

    Article  Google Scholar 

  • Hamilton WD (1975) Innate social aptitudes in man: an approach from evolutionary genetics. In: Fox R (ed) Biosocial anthropology. Wiley, New York, pp 133–155

    Google Scholar 

  • Hammond P (2005) Utility invariance in non-cooperative games. In: Schmidt U, Traub S (eds) Advances in public economics. Springer, Amsterdam, pp 31–50

    Google Scholar 

  • Maskin E (1978) A theorem on utilitarianism. Rev Econ Stud 45:93–96

    Article  Google Scholar 

  • Maynard Smith J (1982) Evolution and the theory of games. Cambridge University Press, Cambridge

    Google Scholar 

  • Maynard Smith J (2002) Commentary on Kerr and Godfrey-Smith. Biol Philos 17(4):523–527

    Article  Google Scholar 

  • Maynard Smith J, Price G (1973) The logic of animal conflict. Nature 146:15–18

    Article  Google Scholar 

  • Maynard Smith J, Szathmary E (1995) The major transitions in evolution. Oxford University Press, Oxford

    Google Scholar 

  • Michod R (1999) Darwinian dynamics. Princeton University Press, Princeton

    Google Scholar 

  • Michod R (2005) The group covariance effect and fitness trade-offs during evolutionary transitions in individuality. Proc Natl Acad Sci 103(24):9113–9117

    Article  Google Scholar 

  • Michod R, Nedelcu A (2003) On the reorganisation of fitness during evolutionary transitions in individuality. Integr Comp Biol 43:64–73

    Article  Google Scholar 

  • Michod R, Viossat Y, Solari C, Hurand M, Nedelcu A (2006) Life-history evolution and the origin of multicellularity. J Theor Biol 239:257–272

    Article  Google Scholar 

  • Okasha S (2005) ‘Multi-level selection and the major transitions in evolution. Philos Sci(Proceedings) 73:1013–1028

    Article  Google Scholar 

  • Okasha S (2006) Evolution and the levels of selection. Oxford University Press, Oxford

    Book  Google Scholar 

  • Okasha S (2007) Rational choice, risk aversion and evolution. J Philos 104(5):217–235

    Google Scholar 

  • Orr HA (2007) Absolute fitness, relative fitness and utility. Evolution 61(12):2997–3000

    Article  Google Scholar 

  • Price G (1972) Extension of covariance selection mathematics. Ann Hum Genet 35:485–490

    Article  Google Scholar 

  • Queller D (1992) Quantitative genetics, inclusive fitness and group selection. Am Nat 139:540–558

    Article  Google Scholar 

  • Queller D (1997) Cooperators since life began. Q Rev Biol 72:184–188

    Article  Google Scholar 

  • Queller D (2000) Relatedness and the fraternal major transitions. Philos Trans R Soc B 355:1647–1655

    Article  Google Scholar 

  • Rice S (2004) Evolutionary theory. Sinauer, Sunderland MA

    Google Scholar 

  • Roberts K (1980) Interpersonal comparability and social choice theory. Rev Econ Stud 47:421–439

    Article  Google Scholar 

  • Roemer J (1997) Theories of distributive justice. Oxford University Press, Oxford

    Google Scholar 

  • Sen A (1970) Collective choice and social welfare. Holden-Day, San Francisco

    Google Scholar 

  • Sen A (1977) On weights and measures: informational constraints in social welfare analysis. Econometrica 45(7):1539–1572

    Article  Google Scholar 

  • Sen A (1986) Social choice theory. In: Arrow KJ, Instiligator M (eds) Handbook of mathematical economics. Elsevier, North-Holland, pp 1073–1181

    Google Scholar 

  • Skyrms B (1996) Evolution of the social contract. Cambridge University Press, Cambridge

    Google Scholar 

  • Sober E, Wilson DS (1998) Unto others. Harvard University Press, Harvard

    Google Scholar 

  • Stearns S (2000) Daniel Bernoulli 1738: evolution and economics under risk. J Biosci 25:221–228

    Article  Google Scholar 

  • Sterelny K and Calcott B (2009) The major transitions re-visited, Cambridge MA: MIT Press (forthcoming)

  • Vrba E (1989) Levels of selection and sorting with special reference to the species level. Oxf Surv Evol Biol 6:111–168

    Google Scholar 

  • Weibull J (1995) Evolutionary game theory. MIT Press, Cambridge MA

    Google Scholar 

Download references

Acknowledgments

Thanks to Ken Binmore, Rick Michod, Yannick Viosatt, Sean Rice, Peter Godfrey-Smith, Steve Downes, Mark Campbell and Armin Schulz for comments and discussion, and to audiences at Bristol, Duke and Vancouver where versions of this paper were presented. This work was supported by the Arts and Humanities Research Council of the UK, Grant No. AH/F017502/1, which I gratefully acknowledge.

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    Samir Okasha

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Appendix: Invariance requirements on the social welfare functional

Appendix: Invariance requirements on the social welfare functional

Ordinal non-comparability (ONC)

For all profiles 〈U 1…U n 〉 and 〈V 1…V n 〉 ∈ Φ, if there exist increasing functions φ1…φ n such that V i = φi(U i) for all i, then for all x, y ∈ A, xR U y iff xR V y

Cardinal full comparability (CFC)

For all profiles 〈U 1…U n 〉 and 〈V 1…V n 〉 ∈ Φ, if there exist real numbers a and b, a > 0, such that V i = aU i + b for all i, then for all x, y ∈ A, xR U y iff xR V y

Cardinal unit comparability (CUC)

For all profiles 〈U 1…U n 〉 and 〈V 1…V n 〉 ∈ Φ, if there exist real numbers a and b 1…b n , a > 0, such that V i = aU i + b i for all i, then for all x, y ∈ A, xR U y iff xR V y

Ratio-scale non-comparability (RNC)

For all profiles 〈U 1…U n 〉 and 〈V 1…V n 〉 ∈ Φ, if there exist positive real numbers a 1…a n , such that V i = a i U i for all i, then for all x, y ∈ A, xR U y iff xR V y

Ratio-scale full comparability (RFC)

For all profiles 〈U 1…U n 〉 and 〈V 1…V n 〉 ∈ Φ, if there exists a real number a > 0, such that V i = aU i for all i, then for all x, y ∈ A, xR U y iff xR V y

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Okasha, S. Individuals, groups, fitness and utility: multi-level selection meets social choice theory. Biol Philos 24, 561–584 (2009). https://doi.org/10.1007/s10539-009-9154-1

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