Abstract
Extensive social choice theory is used to study the problem of measuring group fitness in a two-level biological hierarchy. Both fixed and variable group size are considered. Axioms are identified that imply that the group measure satisfies a form of consequentialism in which group fitness only depends on the viabilities and fecundities of the individuals at the lower level in the hierarchy. This kind of consequentialism can take account of the group fitness advantages of germ-soma specialization, which is not possible with an alternative social choice framework proposed by Okasha, but which is an essential feature of the index of group fitness for a multicellular organism introduced by Michod, Viossat, Solari, Hurand, and Nedelcu to analyze the unicellular-multicellular evolutionary transition. The new framework is also used to analyze the fitness decoupling between levels that takes place during an evolutionary transition.
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Notes
For a good introduction to multilevel selection theory, see Okasha (2006).
In multilevel selection theory, “individuals” and “groups” are used relatively to denote a lower and higher level in the biological hierarchy, respectively. What is considered to be an individual in one context may be considered to be a group in another.
For an in-depth survey of the literature that employs social welfare functionals, see Bossert and Weymark (2004).
Formally, they argue that the function showing how maximum group viability is related to group fecundity is concave for unicellular organisms, but becomes increasingly convex as the transition to multicellularity progresses due to the increased cost of reproduction as group size increases.
This is an example of what Calcott (2011) calls a conflict-mediating explanation.
It is straightforward to modify our analysis to take account of a finite upper limit on the size of a group.
Michod et al. (2006) normalize the value of their index by dividing by n 2 when comparing it with average group fitness. This amounts to replacing v and b with their averages. For a fixed number of individuals, it is of no consequence whether group fitness is measured using the indices C and M or their normalized versions. Okasha (2009) uses the normalized indices.
Okasha (2006, p. 238) regards this view as being overly restrictive and offers examples in which the individuals remain Darwinian individuals at the end of an evolutionary transition.
In an appendix to their article, Michod et al. (2006) show that germ-soma specialization can still be optimal if the individual contributions to group viability are not additive. However, they do not explicitly construct an index of group fitness with nonadditive viabilities.
A binary relation R on a set S is an ordering if it is reflexive (for all \(s \in S, sRs\)), complete (for all distinct \(s,t \in S, sRt\) or tRs), and transitive (for all \(r, s, t \in S,\) [rRs and sRt] ⇒ rRt).
For a binary relation R on a set S, the asymmetric factor P and symmetric factor I are defined as follows: for all \(s, t \in S, sPt \Leftrightarrow [sRt \hbox{ and } \neg (tRs)]\) and \(sIt \Leftrightarrow [sRt \hbox { and } tRs]\).
We use the superscript f when the individual characteristics being considered are fitnesses and the superscript vb when they are viabilities and fecundities.
This axiom is named after the Italian economist-sociologist Vilfredo Pareto, who introduced a related criterion for ranking vectors of utilities.
The example involves four distinct alternatives but the argument also applies if there are only three alternatives in A.
See Ooghe and Lauwers (2005, Proposition 1) for a statement of the extensive social choice version of the welfarism theorem.
We are indebted to Samir Okasha for this example.
We are grateful to Burak Can for suggesting that it would be useful to describe the indices C and M in terms of two-stage aggregation.
Row-first and column-first aggregation procedures are commonly used in the measurement of multidimensional inequality (see Weymark 2006). The analogue of the matrix in Table 3 has a row for each individual and a column for each of the components of well-being (e.g., income, health status, educational attainment, etc.) being considered.
Sen’s social welfare functionals have been generalized to allow for variable population size by Blackorby and Donaldson (1984). See Blackorby, Bossert, and Donaldson (2005) for a detailed investigation of population issues in ethics, social choice, and welfare economics using this framework. No variable population version of an extensive social welfare functional has been used up to now.
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Acknowledgments
Financial support from the Fonds de recherche sur la société et la culture du Québec and the Social Sciences and Humanities Research Council of Canada is gratefully acknowledged. We have benefited from discussions with Samir Okasha and Yannick Viossat, from the commentary of Burak Can when he served as a discussant of this article, and from the comments of our referees. We are also grateful for the comments we have received when this research was presented at the Conference on Choice, Games and Economic Organizations held at the Center for Operations Research and Econometrics, the Workshop on From Social Choice Theory to Logical Aggregation Theory held at the Université Paris-Dauphine, the Choice Group Seminar at the London School of Economics, the Research Seminar at the Erasmus Institute for Philosophy and Economics, and the Urrutia Elejalde Foundation Summer School on Measurement in Economics in San Sebastían.
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Bossert, W., Qi, C.X. & Weymark, J.A. Extensive social choice and the measurement of group fitness in biological hierarchies. Biol Philos 28, 75–98 (2013). https://doi.org/10.1007/s10539-012-9348-9
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DOI: https://doi.org/10.1007/s10539-012-9348-9