1. Introduction

1If you consult Google on the theme "linguistic justice", the leading entries all refer to the writings of a Philippe Van Parijs (henceforth Philippe, or PVP: the ”Present Volume Progenitor”). Clearly, this Philippe is also the authority on the subject!

2One convenient introduction to our author’s thinking is provided by a relatively early joint paper – hereafter BVP – entitled 'Linguistic justice as cooperative justice' (de Briey & Van Parijs 2002), which starts with the statement: "Viewed as an issue in cooperative justice, linguistic justice bears on the way in which the costs of learning a common language should be apportioned between the various linguistic communities benefitting from the communication possibilities resulting from the existence of the common language... Thus, nothing is done to correct a possible pre-existing failure of distributive justice."1 The authors present a case (discussed under 3.2 below) for equating the ratios of costs to benefits across the different communities.

3Many aspects of the use of languages raise issues of cost-benefit analysis. I discuss here translations – a topic that lends itself more naturally to interpretation in terms of public goods, a concept familiar to economists and for which efficiency analysis is reasonably well developed.

4For concreteness, I consider the special case of official translations within the European Union – which, in Philippe's words (2011), has been "forced to develop the bulkiest interpreting and translating service in the history of mankind". The resulting challenges have recently been underscored in connection with patents. Under prevailing arrangements, a party wishing to protect an invention by patent over the EU territory must file an application in the official language(s) of each nation. The cost is easily prohibitive.2 The Commission recently proposed retaining 3 languages – English, French and German – as sufficient for enforceability in the 27 member nations. Determined opposition came from … Italy, followed by Spain. Limiting official translations to a small subset of the 23 official languages looks like a hopeless task…!

5The modest aim of the present note is twofol. First, I wish to explain how an economist relying on the theory of public goods would approach the task of selecting a small set of ”relay languages” for translations. Second, I will relate that economic reasoning to the norm of cooperative justice recommended by BVP.

6A broader question, raised by PVP’s work, is whether or not one should aim for a more efficient translation policy, instead of aiming for adoption of a single lingua franca3 (English, of course!). I return briefly to that question in conclusion.

2. Translating as production of public goods

72.1 For the economist, a "pure public good" is such that any one agent’s consumption of the good does not restrict the consumption by others.4 Simple examples include radio or television broadcasts, internet sites, and... translations! The contrast with ”private goods”, whose total supply must be divided among users, is self-evident.

8The theory of pure public goods, going back to Lindahl (1919) and Samuelson (1954), has been concerned with the definition of Pareto-efficient production levels for public goods.5 In the simpler cases, the Lindahl- Samuelson (LS) conditions record that the marginal cost of producing the public good should be equated to the sum over consuming agents of their marginal rates of substitution between the public good and "money".6

9These conditions apply to public goods for which supply is a continuous variable. But many public goods are produced in discrete quantities. For example, a mail-deposit box at a specific street corner is a public good. For a given area, let there be N potential locations for mail-deposit boxes. How many should be provided, and where should these be located? Consider a specific configuration C of n (N ³ n) boxes. A natural extension of the LS conditions imposes that the cost of each box in C should not exceed the cumulative "willingness-to-pay" (wtp) of the mail users for that specific box, whereas that property fails for any potential box not in C.7

10The LS conditions provide a useful clarification of the goal of efficient provision of public goods. But the wtp of potential users is not readily observed.8 A partial clarification has come with the definition of a process through which elicitation of the individual wtp’s can be organised, with some incentives for correct revelation. That process, sometimes called "the MDP process", was introduced in papers by Malinvaud (1971) and Dreze/de la Vallee-Poussin (1971). The second paper contains a convergence theorem (”every limit-point of the process satisfies the LS conditions”) and an analysis of incentives for correct revelation of wtp’s at limit-points. Rather than summarising these published contributions, I present their application to translations in the EU.9

112.2 The current EU policy stipulates that every official document should be available in every one of the 23 official languages of the Union. To that end, the EU currently translates all relevant documents into three "relay languages" (English, French, German), and from these into the 20 others. Extending the set of relay languages (for instance, to Italian!) is an open possibility.

12Alternatively, the EU could limit its official translations program to the first step – translating every relevant document into a set of relay languages – and stop there; that is, it would not translate systematically into all 23 languages. Subsequent translations of specific documents would remain open to demand. Under that alternative scheme, what would be an efficient set of relay languages? With 23 official languages, there are 223 = 8.038.608 possibilities… So, one needs an efficient selection process, like MDP! It is defined in Appendix 1 and illustrated as follows.

13Before the process starts, each country j is told by what amount Aj its annual financial contribution to the EU budget would be reduced if all translations were abandoned. At an initial step, each country j is asked how much it would willingly contribute towards using language i in N as a single relay10 – meaning that all relevant documents would henceforth be translated into language i, but no other one.11 Denote that amount dj i(0); it corresponds to the ”willingness to pay” (wtp) of country j for relay language i.

14For each language i, one then computes the sum of wtp’s, and one compares that sum with the cost Ci of using language i as a single relay. Hopefully, there will exist some language(s) i for which the sum of wtp’s exceeds the cost. The difference then defines the net aggregate benefit of using relay language i instead of doing without any translations. Choose the language i* for which the benefit, say B* > 0, is maximal. If one collects from each country j its wtp dj i*, one can cover the cost Ci* and be left with a disposable benefit B*. The process calls for redistributing that disposable benefit among the n countries with shares aj adding up to 1. (How these shares are determined will be discussed under 3.2 below). It is important to note that, whenever aj > 0, country j is strictly better off under relay language i* than without translations.

15The simple logic of the proposed process is to use the relay set and country contributions defined by this initial step as starting point for a second step of the same kind, and so on sequentially. Thus, step 2 starts with a relay set consisting of i* alone and with country contributions dj i* := dj i*(0) - aj.Bi*. Each country j is then asked how much it would willingly contribute towards the cost Di(i*) of adding country i (i ¹ i*) to the relay set.12 If the sum of these wtp’s exceeds the cost of adding i to i* as a second member of the relay set, there is scope for a net aggregate benefit Bi(i*). Choose the language i** for which that benefit is highest and adjust each country’s contribution by its wtp dj i**(i*) minus aj.Bi**(i*). That defines the second step, and the starting point for the third step - with S³ consisting of i* and i**, and with initial country contributions equal to

16At each step t, the member countries are presented with a specific relay set St and with country contributions dtj reflecting earlier steps. They are asked to communicate their wtp’s for all languages i in N. For i in St, the sum of these wtp’s will be compared with the cost savings Di(St) associated with dropping i from St. For i not in St, the sum of wtp’s will be compared with the cost of adding i to St. One then retains the language for which the cost-benefit differential is most favourable, one adjusts the country contributions by shares a of that net benefit, and one moves to the next step. When no further profitable step is revealed, the process terminates.

172.3 The iterative process defined under 2.2 has two desirable properties:

18P1 Let α^j> 0 for each j. Then, each step is strictly desirable for each country, according to its reported wtp’s. Consequently, under consistent reporting13, the process cannot cycle (visit several times the same relay set). Hence, the process must terminate after a finite number of steps.

19P2 When the process terminates, it is in the interest of each country to report truthfully its wtp for adding or subtracting a language to the relay set. Hence, the terminal relay set is Pareto efficient: there does not exist a modification of the relay set with associated cost-sharing that is preferred or indifferent from the viewpoint of all countries with strict preference for some.14

20Together, these 2 properties make the process entirely suitable to select an efficient set of relay languages. There remains to ask whether it is ”fair”.

21Remark. Truthful revelation of wtp’s is not claimed along the process –only at termination. Consistent yet incorrect interim revelation may affect the end result. There is some literature on that issue,15 which remains tricky in applications.16

3. Cooperative justice and public goods

22Two themes will be addressed here: disregard for distributive justice in the pure theory of public goods (3.1); and cost-benefit ratios in the contributions towards financing public goods (3.2). These are indeed the aspects of linguistic justice privileged in BVP. Their counterparts for public goods are thus of interest.

3.1 Cooperative justice and the provision of public goods.

23The economic theory of public goods proceeds in the spirit of cooperative justice by omitting reference to "a possible pre-existing failure of distributive justice". The underlying logic is simple: it would be inefficient to use the provision of public goods as an instrument of distributive justice; better implement an efficient provision of public goods, while resorting to other measures (taxes and transfers) to promote distributive justice.

24In the framework of a given economy, that argument is tight when lumpsum transfers across individual agents are possible (when distributive justice can be implemented at no welfare cost). Otherwise, when the only instruments of direct redistribution are distortive taxes or subsidies, it would be commendable to resort to second-best theory: adjusting the provision of public goods (away from efficient levels) should be combined with other measures in an attempt at minimising the total welfare cost of the justicepromoting (redistributive) program.

25It is easy to give examples of public services that would not pass the LS test of cost-covering wtp’s: daily mail deliveries to remote residences, or frequent train-stops along a local line, are justified instead by a principle of "equality in the access to public service".17

26One simple approach to second-best, distribution-sensitive provision of public goods would recognise that the prevailing ("pre-existing") distribution of family incomes is more unequal than desired. Accordingly, the "social value" of an extra unit of income varies across households, whose private wtp’s should be replaced by social wtp’s – namely, the private wtp’s weighted by the social values of individual incomes. The LS conditions should thus be rewritten in terms of these weighted wtp’s.18

27The EU implicitly assigns ”welfare weights” to the per capita incomes of its member states, witness the national contributions to the EU budget. When expressed as "rates of contribution per unit of average individual income", the rates vary by a factor of 2 between a minimum (for new Eastern members) and the maximum (for Luxemburg). It would thus seem proper to recognise these implicit weights when defining "just" guidelines for the EU translation policy – if it were felt that international redistribution across member states is either costly or constrained.

28A cogent reason for ignoring that issue is lack of quantitative relevance: the total EU budget for translations is of the order of 1% of 1% (one-per-tenthousand) of aggregate member incomes, thus hardly providing a relevant instrument for enhancing distributive justice between member nations. There is thus little incentive to revise the process of section 2 on that score: let it implement cooperative justice.

3.2 Cost-benefit ratios versus net benefits shares.

29What about the selection of the parameters aj governing the redistribution among member nations of the net benefits accruing at each step of the proposed process? Clearly, they affect the cost-benefit ratios prevailing at that step. BVP would thus advocate a’s that equate these ratios across member nations.19

30The case for equality presented in BVP (p.12) consists in showing that the proposed criterion is immune to drawbacks of three other criteria advocated in the literature. But it is not claimed that the proposed criterion is the unique way out of such drawbacks. Nor is any independent axiomatic basis offered in favour of the specific ratio. The underlying motivation is that "fairness requires some degree of burden sharing".

31Interestingly, the same suggestion appears in the economic literature on public goods (see Buchholz & Peters 2007). These authors introduce equal cost/benefit ratios as an axiom of fair cooperation. I understand their approach as logically equivalent to that of BVP.

32One significant technicality distinguishes "equal cost/benefit ratios" from fixed shares in net benefits (implied by given a’s under the MDP process): net benefits are additive, cost/benefits ratios are not. It follows that implementation of equal ratios requires specification of the level at which the criterion is applied.20 In my example, one could equate ratios for each language in the relay set, or alternatively for the relay set as a whole. More broadly, if one looked at the EU as a producer of public goods benefitting member nations, one could aim for EU-level equality of the ratios of costs (the national contributions to the EU budget) to benefits (national evaluation of which raises deep challenges!). Under this ambitious option, the overall net benefits associated with an efficient21 set of relay languages for translations could be returned to the EU budget – as happens when the fixed a’s under an MDP process correspond to national shares in the EU budget. Of course, this option is irrelevant to BVP, who were not concerned specifically with EU policy. And the EU might not wish to take national benefits into account…

33To conclude, equality of cost-benefit ratios is a consistent criterion for allocating the net costs of a translations program. However its merits remain to be assessed in comparison with alternatives. I modestly invite BVP to extend their comparisons – for my example - to fixed shares in net benefits consistent with the EU policy on sharing the Union’s overall costs (its budget).

4. Concluding remarks

344.1 The present note pursued two aims: apply the economic theory of public goods to an elementary issue in linguistic justice – namely, translations, which provide a simple example of "pure public good"; and relate that approach to the theory of cooperative justice. I feel justified in claiming some advances on both fronts.

35First, the theory of public goods offers a procedure apt to define an efficient provision of translations. And the dimension of cooperative justice receives a sharp characterisation in that simple case. In particular, the conditions under which it is "justified" to ignore pre-existing failures of distributive justice stand out clearly.

36Second, the case of translations invites comparison of the criterion of equality of cost-benefit ratios with new alternatives, like predetermined shares of net benefits.

374.2 Of course, translations are a special issue in linguistic justice. The issue of primary interest to Philippe is the adoption of a lingua franca and the just sharing of the associated learning costs. In search for policies promoting the adoption of a lingua franca, Philippe (2007) has mentioned (inter alia) "a ban on dubbing": replace dubbing by subtitles for English movies, TV programs a.s.o..In that spirit, he might object to reliance on a set of several relay languages for EU translations: just stick to English!

38Any country sharing Philippe’s view should then report a positive wtp for English and negative wtp’s for all other languages. If enough countries behaved that way, English would become the lingua franca for EU translations! Philippe does refer to a lingua franca as a "public good". The resulting net benefits for distinct linguistic communities consist of gross benefits, from which internal (learning) costs must be deducted. In the pure theory of public goods, internal costs of access to the public goods are implicit, as deductions from the wtp’s..

39In practice, adoption by a set of linguistic communities of one lingua franca is not a one-step process. Should, for instance, the EU ever adopt English as its single official language, a large number of distinct initiatives would be called for in order to implement that option. Written translations are one step; simultaneous interpretations at such meetings as the Parliament or Council are another; patents and a myriad of private activities are in line; teaching is crucial, a.s.o.. One could almost treat the lingua franca as a continuous public good, and attempt to mimic the MDP process in selecting the successive steps of implementation.

40That being said, I feel justified in concluding that theorists of linguistic justice stand to find useful inspiration in the economic theory of public goods... and conversely.