Abstract
In Chap. 2 I argued that an approach that aims to capture freedom’s agency value has to account for the value the availability of choice options has for a person’s deliberation about her values and goals before making decisions. Before addressing this question in greater detail in Chap. 5, I pose the question how this picture of a person reflecting upon a plurality of motives, as widely employed in the philosophy of action, relates to the assumption that a person’s (rational) choices can be represented by a transitive, all-things-considered preference over the alternatives, as is commonly assumed in rational choice theory and the freedom ranking literature. Under which conditions can a person indeed form a transitive, all-things-considered preference from a set of plural (possibly conflicting) values, or as I call it, from her plural identities? I make use of a social choice framework in order to explore this question and illustrate the task the person is facing as an intra-personal aggregation problem: a person has to derive his (transitive) all-things-considered preference from a profile of preference relations reflecting his plural identity. This chapter is a slightly modified version of Binder (Soc Choice Welf 42:959–976, 2014).
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Notes
- 1.
It is important to be aware of the ‘double use’ of the concept of preference in economic analysis. Preferences are used ‘as the basis of welfare judgements’ or as descriptions of one’s choices (Sen 1973, 253).
- 2.
For a discussion of pleasure or desire satisfaction accounts, see Griffin (1986).
- 3.
In addition to transitivity, a person’s preferences are commonly required to be complete. In this chapter the focus is on transitivity. For an investigation of utility theory without the assumption that a person’s preferences are complete, see Aumann (1962). For studies of the formal connection between multi-objective decision making and completeness of a person’s preferences, see Ok (2002) and Dubra et al. (2004).
- 4.
Strictly speaking this example illustrates a case of quasi-transitivity (rather than transitivity). In the framework I adopt in this chapter, which only allows for strict preferences, the two coincide.
- 5.
The crucial points of disagreement between Frankfurt and Watson concern, inter alia, the status of second-order desires: Frankfurt (1971) fails – according to Watson (1973, 218) – to explain what gives them the special status of being the person’s own desires. Furthermore, they disagree on whether agency is about formulating values over courses of actions (one might not have previously desired) or about an internal process in which the agent forms second-order desires over a set of given desires Watson (1973, 219). The stance on these points does not affect the argument presented here. What is relevant is that a person reflects on a set of values or desires in the process of choice.
- 6.
This conception of a person’s identity and the problem addressed with it differs from the way the term is commonly employed in philosophy. The problem of identity over time is prominent in metaphysics. Which conditions have to be satisfied in order to say that a person or object at one point in time is the same as at a later point in time? Is a person who loses her memory in a car accident identical to the person she was before? Is a person after a heart transplant identical to the person before? The main question is whether one can establish criteria of personal identity. One can distinguish between physical and psychological criteria. Roughly speaking, the first demands the physical continuity over time of a person’s brain and/or body, whereas the latter requires the continuity of a person’s memory over time. For a collection of seminal contributions within the philosophical identity debate, see Noonan (1993). For a discussion of different criteria of personal identity, see Parfit (1984, chap. 10) and Raymond and Barresi (2003). For a survey of logical approaches to the metaphysical problem of identity, see Hawthorne (2003).
- 7.
Strictly speaking, the case in which a person’s identity is ‘singular’ is a special case of the proposed framework.
- 8.
Strictly speaking, the generality of the framework adopted here does not presuppose any view of the source of a person’s various identity parts. These can be related to her social surroundings and the groups she identifies with, but they do not have to be. What is important, though, is that I refer only to those identity parts with which the person herself identifies; I neglect the way external ascriptions can affect (and constrain) a person’s identity. For a discussion of this point, see Sen (2006, 6–8, 31).
- 9.
Note that this does not mean that a person can choose any identity, but rather that there are some choices among alternative combinations of identities (Sen 2006, 38).
- 10.
The sole way in which a change in a person’s identity over time enters the analysis in this chapter is via one of the conditions imposed on the process in which he derives his all-things-considered preference from his plural identity. The monotonicity condition, which I introduce in Sect. 4.4, requires a certain continuity of the choices a person derives from her plural identity, in case the composition of her plural identity changes. For an analysis of a person’s plural identities, or multiple selves over time, see Heilmann (2008, sect. 4.3).
- 11.
One of the classics in the analysis of decision making under the unresolved conflict of multiple objectives is Levi (1986). For a survey of the literature on multiple objectives decision making and a discussion of several different approaches, see Davis (2003), or Ellis (2006) on various approaches to the individual in economics in general and (rational) choice theory in particular.
- 12.
- 13.
Hurley (1985) shows furthermore that conditions necessary to lead to single profile impossibilities violate supervenience in a similar way.
- 14.
Sen, however, as far as I know, never used this point as part of an argument that Arrow’s impossibility is less problematic in an intra-personal context.
- 15.
Strictly speaking, acyclicity is sufficient but not necessary for a binary relation R on X to induce a choice function if R is complete. I shall return to this issue in Sect. 4.6.
- 16.
For an overview over different interpretations of incomparability and incommensurability, see Chang (1997).
- 17.
Raz (1986, 347–348) raises a similar case when he argues that for many people it is inconsistent with their identity as parents to rank (compare) their child(ren) with sums of money.
- 18.
- 19.
Note that for all x, y ∈ X if xNy then yNx.
- 20.
Note that the usual definition of acyclicity, that is R on X is acyclic if, and only if, for all x 1, x 2, …, x j, j being a finite positive integer, x 1 Px 2, x 2 Px 3, …., x j−1 Px j implies x 1 Rx j, is equivalent to the definition adopted here if the preference relation is complete.
- 21.
In Table 4.1 any two alternatives x and y which are not ranked vis-à-vis each other are denoted by [xy].
- 22.
These differ, though, depending on the conditions imposed on the preference relations R on X.
- 23.
There are other substantive and methodological reasons to impose Universal Domain: one is that we are interested in conditions which the Identity Aggregation Procedure of any person is supposed to satisfy. Thus the procedure is supposed to work for different persons, who are characterized by different identity profiles. Another (methodological) reason relates to the question the framework aims to address, namely under which conditions a person can indeed derive a transitive/acyclic all-things-considered preference. In order to gain a clear understanding of the structure of the aggregation problem at hand (and possible problems in a person’s preference formation) it is fruitful to start with the most admissible case, in order to then step-wisely restrict it in the light of emerging impossibility results.
- 24.
Note that the first, narrow line of interpretation would allow a person to be, say, a Buddhist and a Christian ‘simultaneously’, since both are reflected by different dimensions (partial orderings) in the identity profile. The second, broader line of interpretation precludes this though, since Christian and Buddhist are reflected as different partial orderings in one (the same) dimension (religious belief, say) in the identity profile.
- 25.
- 26.
Note that Monotonicity does not say anything about cases in which identity parts are added that are opposed to the previous all-things-considered preference, or in the case where a person gives up a part that ‘supported’ the former all-things-considered preference.
- 27.
Kelsey (1986) discusses the counter-intuitive flavour of a weaker form of imposition in the case in which the various identity parts, or objectives as he calls them, are defined very narrowly.
- 28.
To see the formal equivalence between profiles of quasi-transitive orderings and profiles of strict partial orderings, let for all x, y ∈ X, for all i ∈ M, [xN i y if, and only if, xI i y] and [yN i x if, and only if, yI i x]. Note that the relation N on X, as well as the relation I on X are symmetric and reflexive, but not transitive. If one reformulates the introduced conditions accordingly, the proofs of Theorems 4.1*–4.3* hold for the reformulated framework of quasi-transitive orderings.
- 29.
The term ‘lexicographic procedure’ refers to the following aggregation procedure (based on Houy and Tadenuma (2009, 1771)), xPy if, and only if, (1) xP 1 y or (2) xN 1 y and xP 2 y, or …, or (m) xN 1 y, …, xN m−1 y and xP m y. The relation N on X is transitive if, and only if, for all x, y, z ∈ X, xNy and yNz implies xNz.
- 30.
Contributions in the literature (Gibbard 1969; Weymark 1984) have shown that – over a domain of complete and transitive orderings – requiring the social ordering to be complete and quasi-transitive leads to oligarchies. An oligarchy is a set of individuals whose (i) unanimous strict preference over any two alternative x over y, implies x to be socially preferred to y; and (ii) the members of the oligarchy have veto-power, i.e. if some member of the oligarchy strictly prefers x over y, this implies that it is not the case that y is socially preferred to x. Furthermore, results in the judgment aggregation literature (Gärdenfors 2006; Dietrich and List 2008) indicate the emergence of ‘strong oligarchies’ if one allows for a domain of possibly incomplete judgement sets (Dietrich and List 2008, 27). In a social choice framework, strong oligarchies can be defined as a set of individuals who do not only dictate their unanimously held strict preferences on the social preference, but also dictate incompleteness between any two alternatives x and y which are not ranked by all members of the strong oligarchy. It can be shown that a strengthening of the Arrovian conditions to those employed in this article will imply the strong oligarchy to be a singleton which is equivalent to strong imposition as defined in this article.
- 31.
This example is a slightly modified version of an example invoked by Pettit (2001, 284).
- 32.
This example is based (very crudely) on the Borda procedure. For a more precise, formal exposition, see Gaertner (2006, 92–98).
- 33.
Fishburn (1970) considers inter-personal aggregation problems over a domain of quasi-transitive preference profiles. The difference between Theorem 4.2 and his example (Fishburn 1970, 482) is that he illustrates the occurrence of cycles for m = 3 and #X = 3, whereas Theorem 4.2 of this article holds for m ≥ 2 and #X > 3. I am very grateful to an anonymous referee for making me aware of this point made by Fishburn.
- 34.
Costello (2004, 2005) among others, has identified ‘identity dissonance’ as one possible reason for the persistent failure of affirmative action programmes in the classroom. This is mainly due to the fact that students, for whom the new professional identities at the relevant school are very new, or even stand in conflict with their other identity parts, need to spend much more time and energy on the resolution of internal conflicts, the monitoring of others and the understanding of the (implicit) rules that govern their new surroundings. Others (Thumma 1991) have explored the strategies people employ to resolve the value conflicts underlying their contradictory identities.
- 35.
To be more precise, Fishburn (1970) is concerned with inter-personal aggregation problems and considers a sub-domain of profiles of quasi-transitive orderings. He shows that for his sub-domain simple majority rule yields a quasi-transitive social ordering. If indifference (I on X) between alternatives is replaced by incompleteness (N on X) in his definition, then it can be shown that Value Overlap is contained in his sub-domain (Definition A in Fishburn (1970, 484)), which in turn guarantees a transitive all-things-considered preference.
- 36.
The condition Value Overlap in this article was inspired by Sen (1969) whose domain condition Value Restriction is sufficient for Majority Rule to generate quasi-transitive social preference orderings over a domain of profiles of weak orders. Pattanaik (1970) provides a generalization by establishing sufficient conditions for the class of binary, decisive, neutral, and non-negatively responsive social decision procedures to yield quasi-transitive social preferences over a domain of profiles of quasi-transitive individual preferences. It can be shown that the domain generated by Value Overlap is contained in Pattanaik’s domain condition VR* (Pattanaik 1970, 270).
- 37.
- 38.
Recall that a second interpretation of incompleteness adopted in this chapter was incompleteness as an irrelevance for a person’s identity part. This second interpretation, however, could plausibly be ‘taken over’ by indifference.
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Binder, C. (2019). Plural Identities and Preference Formation. In: Agency, Freedom and Choice. Theory and Decision Library A:, vol 53. Springer, Dordrecht. https://doi.org/10.1007/978-94-024-1615-2_4
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