Dividing the indivisible: Apportionment and philosophical theories of fairness

Philosophical theories of fairness propose to divide a good that several individuals have a claim to in proportion to the strength of their respective claims. We suggest that currently, these theories face a dilemma when dealing with a good that is indivisible. On the one hand, theories of fairness that use weighted lotteries are either of limited applicability or fall prey to an objection by Brad Hooker. On the other hand, accounts that do without weighted lotteries fall prey to three fairness paradoxes. We demonstrate that division methods from apportionment theory, which has hitherto been ignored by philosophical theories of fairness, can be used to provide fair division for indivisible goods without weighted lotteries and without fairness paradoxes

Theories of Fairness and Aggregation

We investigate the issue of aggregativity in fair division problems from the perspective of cooperative game theory and Broomean theories of fairness. Paseau and Saunders (Utilitas 27:460–469, 2015) proved that no non-trivial theory of fairness can be aggregative and conclude that theories of fairness are therefore problematic, or at least incomplete. We observe that there are theories of fairness, particularly those that are based on cooperative game theory, that do not face the problem of non-aggregativity. We use this observation to argue that the universal claim that no non-trivial theory of fairness can guarantee aggregativity is false. Paseau and Saunders’s mistaken assertion can be understood as arising from a neglect of the (cooperative) games approach to fair division. Our treatment has two further pay-offs: for one, we give an accessible introduction to the (cooperative) games approach to fair division, whose significance has hitherto not been appreciated by philosophers working on fairness. For another, our discussion explores the issue of aggregativity in fair division problems in a comprehensive fashion

How to be fairer

We confront the philosophical literature on fair division problems with axiomatic and game-theoretic work in economics. Firstly, we show that the proportionality method advocated in Curtis (in Analysis 74:417–57, 2014) is not implied by a general principle of fairness, and that the proportional rule cannot be explicated axiomatically from that very principle. Secondly, we suggest that Broome’s (in Proc Aristot Soc 91:87–101, 1990) notion of claims is too restrictive and that game-theoretic approaches can rectify this shortcoming. More generally, we argue that axiomatic and game-theoretic work in economics is an indispensable ingredient of any theorizing about fair division problems and allocative justice

Duty and Distance

Ever since the publication of Peter Singer’s article ‘‘Famine, Affluence, and Morality’’ has the question of whether the (geographical) distance to people in need affects our moral duties towards them been a hotly debated issue. Does geographical distance affect our moral duties? If so, is it of direct moral importance? Or is it of indirect importance to other aspects that affect our moral duties, such as our power to help other people

Philosophy and Economics:Editorial and Interview with Peter Wakker

When I was about to move to Erasmus University Rotterdam several years ago, there were two topics of conversation that mentors and colleagues from all over the world would bring up. One of them was EIPE, the Erasmus Institute for Philosophy and Economics, which I was about to join, and its associated Research Master and PhD programme. The other topic was the work of decision theorist Peter Wakker and his research group. [...

How to be absolutely fair Part II:Philosophy meets economics

In the article ‘How to be absolutely fair, Part I: the Fairness formula’, we presented the first theory of comparative and absolute fairness. Here, we relate the implications of our Fairness formula to economic theories of fair division. Our analysis makes contributions to both philosophy and economics: to the philosophical literature, we add an axiomatic discussion of proportionality and fairness. To the economic literature, we add an appealing normative theory of absolute and comparative fairness that can be used to evaluate axioms and division rules. Also, we provide a novel definition and characterization of the absolute priority rule.</p

Liberal political equality does not imply proportional representation

In their article ‘Liberal political equality implies proportional representation’, which was published in Social Choice and Welfare 33(4):617–627 in 2009, Eliora van der Hout and Anthony J. McGann claim that any seat-allocation rule that satisfies certain ‘Liberal axioms’ produces results essentially equivalent to proportional representation. We show that their claim and its proof are wanting. Firstly, the Liberal axioms are only defined for seat-allocation rules that satisfy a further axiom, which we call Independence of Vote Realization (IVR). Secondly, the proportional rule is the only anonymous seat-allocation rule that satisfies IVR. Thirdly, the claim’s proof raises the suspicion that reformulating the Liberal axioms in order to save the claim won’t work. Fourthly, we vindicate this suspicion by providing a seat-allocation rule which satisfies reformulated Liberal axioms but which fails to produce results essentially equivalent to proportional representation. Thus, the attention that their claim received in the literature on normative democratic theory notwithstanding, van der Hout and McGann have not established that liberal political equality implies proportional representation.</p

How to be absolutely fair Part I:The Fairness formula

We present the first comprehensive theory of fairness that conceives of fairness as having two dimensions: a comparative and an absolute one. The comparative dimension of fairness has traditionally been the main interest of Broomean fairness theories. It has been analysed as satisfying competing individual claims in proportion to their respective strengths. And yet, many key contributors to Broomean fairness agree that ‘absolute’ fairness is important as well. We make this concern precise by introducing the Fairness formula and the absolute priority rule and analyse their implications for comparative fairness.</p