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Adjudicating distributive disagreement


This paper examines different mechanisms for adjudicating disagreement about distributive justice. It begins with a case where individuals have deeply conflicting convictions about distributive justice and must make a social choice regarding the distribution of goods. Four mechanisms of social choice are considered: social contract formation, Borda count vote, simple plurality vote, and minimax bargaining. I develop an agent-based model which examines which mechanisms lead to the greatest degree of satisfying justice-based preferences over the course iterated social choices. Agents are ascribed two kinds of motivations: they wish to realize justice and to receive a greater package of goods. Each agent seeks to realize her ideal distribution, and the failure to do so leaves agents “disappointed,” resulting in their trading off the pursuit of gains in justice in favor of gains in self-interest. Mechanisms are assessed using the metric of how many agents remain interested in justice over the course of iterated adjudication. The mechanisms are also examined under some non-ideal conditions, such as the presence of power asymmetries or strategic behavior. Several significant results are addressed: social contract formation and simple plurality voting are robust under the conditions considered, bargaining is a highly ineffective means of adjudicating distributive disagreement, and lastly allowing for concessions in justice for gains in self-interest proves to be a crucial mechanism for ensuring the stability of resolutions.

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  1. 1.

    The results discussed here may naturally be applied to other accounts of social decision-making to account for how to proceed under the absence of consensus. Cf. Elster (2003) on the need to proceed without consensus in deliberative democracy.

  2. 2.

    On realization conditions see Gaus (2016, pp. 21–26).

  3. 3.

    “Goods” is used in a wide sense, describing those things which are desired by agents and which are the objects of distributive concern. The goods being distributed in the model may interpreted to be whatever the reader’s preferred account of distributive justice suggests they should be.

  4. 4.

    My thanks to an anonymous reviewer for drawing my attention to this point.

  5. 5.

    For present purposes I assume that the distribution of goods can be changed with relative ease. Of course, this is a simplification, which abstracts from factors tying the distribution of goods to their production. See Vallier (2010).

  6. 6.

    See Gaus (2016, pp. 43–56) for a formal model of justice perspectives.

  7. 7.

    In order to simplify future computation, I will suppose that for all agents when the x-axis is ordered sequentially, e.g. D1, D2…Dn, then the self-interest score is single-peaked, with the peak being in different locations for the agents.

  8. 8.

    On may be concerned here with whether individual preferences will be coherent. On the assumptions here, individual preferences must be synchronically consistent, but may be diachronically inconsistent (as has been observed in behavioral treatments, e.g. Tversky and Thaler 1990). The synchronic coherence of individual preferences is shown by indexing individual preferences to times. For any individual i, then, their preference relation must be indexed to some time t, Rt. Let R0 be i’s initial preferences, defined as discussed above. We assign subsequent preferences with the function F: Rt, e → Rt+1 where e is the set of exogenous conditions sufficient to cause individual preferences to shift, in our case that is a distribution’s falling outside i’s tolerance range. As defined in the model, the top option in Rt is the justice and self-interest optimizing option, and the placement of other options is determined by their distance from the top option on i’s justice perspective, generating an ordering. Hence at any given time i's preferences form a coherent ordering, though over time the ordering changes in response to exogenous factors allowing for the possibility of diachronic inconsistency, modelling the behavioral results which inspire this account. I thank an anonymous reviewer for drawing this concern to my attention.

  9. 9.

    Rawls, Justice as Fairness: A Restatement, p. 128.

  10. 10.

    My thanks to an anonymous reviewer for raising this point.

  11. 11.

    This project thus naturally extends social choice investigations into dynamic social contexts. For a philosophically oriented, and accessible, overview of the social choice project see Sen (2017).

  12. 12.

    This procedure is identical to approval voting, see Brams and Fishburn (1978).

  13. 13.

    Parameter sweeps of both population size and distribution range are shown in the Appendix. The relative performance of each adjudicative mechanism at the different variables is subject to almost no variation, making the choice of distributive range and population size is arbitrary. Hence, in order to keep values fixed, a population size of 5000 and distribution range of 6 are used.

  14. 14.

    That the complete population could become completely egoistic in the case of low tolerance values is, of course, a completely counterfactual result. It is hardly the case that in any real social group every single person will become an egoist. This result, I believe, is best understood as a case where adjudication would have broken down in actual conditions. Agents, seeing that no result is forthcoming, will withdraw from adjudication, treating results as unauthoritative. The costs associated with complete egoism, however, will likely still obtain. Agents withdraw from the social process of resolving conflict, at best foregoing the benefits of having a resolution for a shared problem, and at worst take it upon themselves to enforce their preferred outcome.

  15. 15.

    Note that even if tolerance improves upon the pragmatic outcome criterion there may still be reason to withhold from making individuals maximally tolerant. Trivially, if every agent is made maximally tolerant the pragmatic outcome criterion will be maximally satisfied. Nevertheless, under such conditions it no longer seems plausible to interpret the agents as concerned about justice, since they will accept the outcome of adjudication regardless of how it performs with respect to justice on their perspective. The social context we are concerned with here is one in which agents care deeply and disagree about justice, such that increasing tolerance too highly will constitute a departure from the social situation of interest. Moreover, surely we have some reasons to encourage individuals to develop a conception of justice which they then attempt to advance. There is, however, a relevant question as to what social reformers should do when given the opportunity to influence individual preferences. From the above, it follows that they should optimize between individual commitments to justice and tolerance. Too strong a commitment to justice makes social cooperation impossible, and too little trivializes justice. The significance of justice, whatever the correct conception, and satisfaction of the pragmatic outcome criterion are thus countervailing forces on the selection of adjudicative mechanisms and shaping of individual preferences in actual social contexts.

  16. 16.

    Plurality was the exception here, taking two rounds to reach equilibrium on 9 rounds of 20.

  17. 17.

    Recall that it was assumed that all agents’ self-interest preference is single-peaked when the distributions are ordered sequentially. See Sect. 3.1.

  18. 18.

    See Figs. 12 and 13 for parameter sweeps of power height and decay respectively. For the height test decay was held fixed at 100, and for the decay test height was held fixed at 500. As the Figures show, the only mechanism with significant variation is median selection, the relative performance of the remainder of the mechanisms is insensitive to the parameter values.

  19. 19.

    Note that with a radius of 2 approximately half the population will have access to some amount of power. The criterion is fairly inclusive in order to ensure that some gradient of rank can obtain in the aristocratic model, since a lower radius would not allow one to model high degrees of variation among those in power.

  20. 20.

    The results I have in mind are: the relative failure of bargaining mechanisms (Sect. 4.2), the instrumental justification of the condition of fairness (Sect. 5.3), and the robustness of both contract and simple plurality mechanisms (Sect. 7).

  21. 21.

    Three mechanisms were put forward to explain this shift: resolution of cognitive dissonance, response in accordance with a norm of reciprocity, or response to the observation of a norm of justice being eroded. Realistically, things will hardly be so uniform. Actual individuals will likely experience a shift for many diverse reasons, and will have preferences over a number of domains which they may shift toward. To take just one example, a politically disillusioned individual may find themselves more attracted to their religious commitments. The mechanism of shifting preferences, and the preferences among which they agents shift are thus likely to be far more complicated than the discussion here has assumed. Allowing for a greater range of trade-offs, however, does not challenge the result of the model showing that when no trade-off between justice and other interests is permitted adjudication cannot reach a stable outcome. Allowing a greater range of responses does not change the result which obtains when no response is permitted.

  22. 22.

    A population becoming completely egoistic is best treated as indicative of the breakdown of adjudication in real contexts (see note 9). In such a case, Rawls’ comments on the anti-social behavior of those disaffected from the public conception of justice still apply (Sect. 3.2)—the majority of individuals will still see that their conception of justice is unwelcome among the public, adopting anti-social attitudes of isolation or aggression.


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This paper is indebted to Jerry Gaus for numerous helpful conversations and comments on earlier drafts. My thanks also to participants at the panel on “The Effects of Disagreement About Justice” at the 2018 PPE Society Annual Meeting, and to two anonymous reviewers at this journal.

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Correspondence to Alexander Motchoulski.

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See Figs. 10, 11, 12, and 13.

Fig. 10

Resulting number of egoists under varying population size

Fig. 11

Resulting number of egoists under varying distribution range

Fig. 12

Resulting number of egoists under varying power height

Fig. 13

Resulting number of egoists under varying power decay value

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Motchoulski, A. Adjudicating distributive disagreement. Synthese 198, 5977–6008 (2021).

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  • Distributive justice
  • Agent-based model
  • Adjudication
  • Diversity