Dividing the indivisible

Abstract

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.

How to be absolutely fair Part I: The Fairness formula

“…While there are some contributions that distinguish between claim strengths and amounts (e.g. Wintein and Heilmann 2018;Hausman 2023), many contributors have neglected the distinction between claims strengths and amounts altogether, such as Curtis (2014). He develops a Broomean theory of fairness that identifies claims with their amounts.…”

“…Our theory, owing to the claims distinctions we will 4 One restriction of the present analysis is that we will only study and apply the Fairness formula with respect to problems with 'divisible good', such as in Owing Money. We have dealt with the allocation of 'indivisible goods' (such as horses, or seats in a parliament) from a Broomean perspective in earlier work (Wintein and Heilmann 2018). The Fairness formula can in principle be applied to such indivisible cases, and we will take up this issue in future work.…”

How to be absolutely fair Part II: Philosophy meets economics

“…Other examples of fairness structures include apportionment problems (cf. Balinski and Young 2001;Wintein and Heilmann 2018) and cooperative games (cf. Aumann and Maschler 1985;Wintein and Heilmann 2020).…”