regulation was imposed.34 (In a footnote, Epstein argues that the principle even can explain the rules governing judicial bias.35)

One common thread running through these academic discussions is use of the concept of reciprocal advantage to justify governmental restrictions on property owners—either through regulation or physically taking the property—by asserting that because average reciprocity of advantage has provided the burdened owners with sufficient compensation, those owners have no just grounds for complaint (and thus no claim for additional monetary compensation). The question that naturally arises then is exactly how ‘average reciprocity of advantage’ provides that compensation, and whether that sort of compensation can do the justificatory work that has been asked of it.

3. Sources of Average Reciprocity of Advantage

Addressing that question requires first identifying exactly what average reciprocity of advantage is, and how it arises. Justice Holmes’s seminal Mahon opinion offers no elaboration of the concept of ‘average reciprocity of advantage’ or of its role in justifying regulations.36 What it does offer is a reference to Plymouth Coal as a paradigm situation in which average reciprocity of advantage is present. Hence, identifying exactly how average reciprocity arises in that case will help us to identify more generally when such reciprocity will be available to provide compensation for the burdens of government action, and, I shall argue, will also reveal that this availability is likely to be infrequent. The key first step in this inquiry is to see that

34Epstein 1985, 195–215.

35Epstein 1985, 196 n. 2. Epstein’s argument in brief: ‘When the state resolves a dispute between A and B, it wrongfully takes property if it makes the incorrect judgment. Forcing A to pay B $100 for a debt not owed takes $100 from A. Not making A pay the $100 when it is owed takes it from B. The demand for unbiased judges therefore translates into a demand that the probability of error be symmetrically distributed, so that each side receives, in the form of erroneous judgments in its favor, ex ante compensation for those erroneous judgments entered against it’ (internal citations omitted). Thus, Epstein concludes, requirements that judges be unbiased ensure that litigants receive sufficient in-kind compensation for the rule that bars litigants from suing judges for allegedly erroneous judgments. Unfortunately, this argument suffers from a fatal flaw, springing from its tacit reliance on an assumption of repeated trips through the legal system. If a particular litigant appears in court only once, there is zero chance that any error will offset. If a litigant appears only a few times, the chances that errors will perfectly offset are poor. Only if a litigant appears so often that the Law of Large Numbers applies will Epstein’s result reliably occur. Outside of that extreme situation, all that one could say is that each litigant has an equal ex ante subjective probability of coming out ahead or coming out behind. However, that probability cannot plausibly be advanced as a form of compensation. If Jones suffers a loss as a result of an erroneous judgment, no one would say that she is made whole by the fact that there had been a chance that she might not have suffered the loss, or even by the fact that there had been a chance that she might enjoy an erroneous gain. Thus, whatever the justification is for judicial immunity for erroneous judgments, implicit in-kind compensation cannot be it.

36With respect to the purely constitutional question, the ‘reciprocity of advantage’ which a regulation offered appears to be relevant for calculating the net amount of burden that the regulated landowner suffers and therefore whether the regulation went ‘too far’. However, Holmes’s language was not entirely clear, and he does not indicate how ‘average reciprocity of advantage’ is distinct from simple ‘reciprocity of advantage’.

the reason why the regulation in Plymouth Coal produced an average reciprocity of advantage was because the regulation had the effect of solving a coordination problem.

Suppose that two owners of adjacent parcels are both engaged in mining coal. Both owners have a straightforward economic incentive to dig out as much coal as possible in order to maximize their profit. However, both owners also realize that the other owner may be the first to exhaust the mine on his property, at which point the abandoned mine may be flooded.37 If the amount of coal remaining between the two mines at that time is small, then it will not be able to withstand the pressure applied by the influx of water from a flood in a neighbouring mine, and if that coal barrier gives way, the dry mine will be flooded as well.

From the perspective of the owner of the still-operational mine, the flooding is economically costly in several potential ways. First, it may make remaining coal deposits wholly inaccessible. Second, even if access to some of the remaining coal can be restored by means of pumping, draining those areas will be quite expensive. Third, the cost of rescuing miners trapped by the flooding and of compensating the families of miners who were killed will further decrease profits. (Even a mine owner who is bereft of any compassion for his miners cannot abandon trapped miners or the families of fallen miners without cost, since such behaviour would make it difficult or impossible to find people who would be willing to work in his mines. And without miners, a mine has no economic value.) As a result, a profit-maxi- mizing owner has strong self-interested reasons to avoid premature flooding of his mine.38

Now a coordination problem becomes evident. Suppose that the two adjacent miners are Jones and Smith, and that C is the number of feet of coal which must remain in order to provide an adequate barrier against flooding. Jones has three options. If she is cautious she can cease mining when the mine shaft reaches a point C feet from the property line. Unless Smith has trespassed on her property, Jones then can be sure that her mine will not flood even if Smith floods his mine. However, by leaving C feet of coal unextracted, Jones foregoes considerable

37Accidental flooding of coal mines was an ever-present danger. For a brief survey of the problem, written a few years after the ruling in Mahon, see Ash 1941. For a catalogue of major US coal mine disasters involving inundations, see Keenan 1963, 66–78.

38My reading of Plymouth Coal here diverges from Abraham Bell’s. Bell (2009) takes the ‘reciprocity’ in this case to be protection of the mineworkers. Bell’s reading seems incompatible both with the text of Holmes’s opinion—which explicitly distinguished between protecting workers’ safety and average reciprocity of advantage—and with the logic of the argument. It is not at all clear that diminishing the risk to the workers’ health would necessarily provide as much value to the mine owner as the unextracted coal did. Moreover, the Pennsylvania Supreme Court’s decision, which the US Supreme Court was reviewing, made it clear that providing an advantage to mine owners was an important aspect of the statute. Thus, in finding the statute to be justified, the Pennsylvania court quoted from its judgment in an earlier state case involving a similar regulation: ‘This rib of solid coal not to be mined into by either of the adjoining owners was to be contributed by each in equal parts for the mutual benefit of each, for the protection of the surface, to secure independent systems of ventilation, drainage and workings, and in aid of an industry so great and widely diffused that the State as a whole is interested therein. . . . This regulation works no hardship on one for the benefit of another, but is impartial, just and reasonable, imposing a common burden for the benefit of all such owners’. Commonwealth v Plymouth Coal Co. 1911, 149 (quoting Mapel v John 1896).

potential profit. So if Jones is daring or thinks she has accurate information that Smith is cautious, Jones might extend her mine all the way to the property line, in the hope that Smith will have chosen to leave C feet of coal unextracted on his property.

Either of these two options is potentially less than optimal both for society and for the individual owners. If Jones is daring but guessed wrong about what Smith would do, the barrier between the two mines will be thin, and Jones’s mine will flood when Smith’s does. In the likely event that the costs of a prematurely flooded mine are considerably greater than the market value of C feet of coal, Jones will have suffered a large loss (and total social wealth will have suffered to the same extent, since no one gained from Jones’s loss). On the other hand, if Jones acted cautiously but Smith was equally cautious, then both will have stopped excavating when C feet of coal remained on their property, leaving unextracted twice as much coal as necessary. Jones suffers a loss of profit from the needlessly unextracted coal, and again this is a deadweight social loss since no one gains from Jones’s loss.39

Either way, a third option is preferable: ideally, Jones and Smith would each mine up to C/2 feet from the property line. This would provide a total barrier of C feet to prevent flooding, while halving the amount of foregone profit that each would suffer as a result of leaving unextracted coal. The social product would be maximized, and both Smith and Jones would be better off compared to either scenarios noted above. This advantage would not necessarily be reciprocal in every circumstance; Jones would still personally be better off if she extracted coal all the way to the property line and Smith turned out to have acted cautiously. In those circumstances, she would maximize her profit from the coal near the border and would still enjoy safety from flooding. However, if Jones cannot be certain in advance which strategy Smith will follow and if she has multiple mines (as is likely for a mining company) and therefore will be engaging in this game many times, the expected payoff of following that strategy is likely to be less than the payoff from splitting the costs of safety, assuming that the costs of one or more prematurely flooded mines outweigh the profit obtainable from an extra C/2 feet of coal in the relevant mineshafts. Thus, on average both Jones’s mining company and Smith’s will enjoy a reciprocal advantage if they both reliably leave C/2 feet of coal on each side of the property line.

This is, of course, precisely the outcome which the regulation in Plymouth Coal produces.40 The regulation then is a permissible restriction on mine owners’ property rights because it in fact enhances the practical scope of those rights.

39This cost could be substantial. In Plymouth Coal, the counsel for the coal company stated that the amount of coal which the lower court had required be left unmined in that case ‘amounted to 734,147 tons, which could be mined at a net profit of about $300,000’. Plymouth Coal Co. v Pennsylvania 1914. Using the US Consumer Price Index to adjust for inflation, that sum would be equivalent to approximately $6.9 million in 2012 dollars.

40Because the effect of the regulation is mutually advantageous, in an ideal world private bargaining might have produced the same outcome without government intervention. However, the importance of many potential impediments to private bargaining has been thoroughly established since at least as far back as Coase 1960. When such impediments are significant, government regulation may accomplish what private bargaining cannot.

They are now free to mine to within C/2 feet of the property line rather than having to choose between stopping C feet from the property line or running a significant risk of a catastrophic loss. Thus, considered in its application over many mines, the regulation limits the amount of coal that might permissibly be extracted in any individual instance but increases the total amount of coal that the mines’ owner can extract in the aggregate. The ‘average reciprocity of advantage’ which the regulation provides removes any rational grounds for the burdened owners to complain about it.41

Once we turn our attention to the facts in Mahon, however, the picture looks quite different. The regulation prohibiting mining activities which cause subsidence protects owners of surface rights from harm (either economic or physical) but provides no benefit to mining companies that own the subsurface rights. The amount of coal that those companies are physically capable of extracting is not lessened by surface subsidence, nor does such subsidence impose any extra costs on the miners. Hence the regulation provides no advantage at all to the mining companies, for whom its imposition is a net loss. Their objections to the regulation cannot be dismissed as irrational.

Two important features of average reciprocity of advantage should now be evident. First, it arises in situations in which there is a commensurability between the burden and the benefit, and the benefit is at least as large as the burden. In Plymouth Coal, the burden and benefit were both measured in extractable amounts of coal, and the regulation had the effect of increasing the amount of coal that mine owners could practically expect to acquire over time. Since the burden and benefit were in the same currency, and they both are tangible and measurable, we can be confident that the regulation in fact does leave everyone better off, except perhaps in extraordinary circumstances. Hence, the parties ‘burdened’ by the regulation would be objectively irrational to object to it.42 Second, this net positive result was possible because the regulation in question solved a coordination problem.

41This is slightly overstated. If the burdened owner will not be a repeat player—perhaps because she owns only one mine, intends to close it in the near future, and leave the mining business forever— then the owner will not necessarily enjoy the long-term benefits of coordination. (If mining is the most valuable use for that property, she will still be able to benefit financially from the regulation by selling the property, since the regulation’s beneficial effect on the profitability of mining will be included in the property’s market price. However, if mining is not the property’s highest-value use, or if she happens to have a high personal value in using the property for some other purpose, then the regulation will not benefit her.) However, there is little that lawmakers can do about such a case when setting general rules. If this owner’s idiosyncratic preferences were to determine the general permissibility of regulations that serve a generally valuable coordinating function, then the law would let this owner impose her idiosyncratic preferences in a way that decreased the value of every other mining company’s property. As the basic law of nuisance demonstrates, property law in general does not recognize any such right (or, perhaps better stated, recognizes a duty not to impose too much on others). Thus uses which are idiosyncratic in a given area and unreasonably interfere with others’ use and enjoyment of their property can be abated as nuisances, while owners who suffer inconvenience as a result of their hypersensitivity to uses which are reasonable and ordinary in a given area have no remedy under nuisance. See e.g. American Law Institute 1979, } 821F; Walter v Selfe 1851 64 ER 849, 852 (Ch.); 4 De G & Sm 315, 322.

42Of course, a mine owner did care to challenge the regulation in Plymouth Coal, despite the advantage. The motivation for that challenge, however, was not any objection to the requirement that