There is no unique statement of the Coase theorem

From The Coase Theorem: A Process of Becoming by Timothy Taylor.  He answers a question I have long had.  One of the authors of Marginal Revolution, Tyler Cowen, often invokes Coase's theorem, often instructing readers to "solve for the Coasean equilibrium."

And every time, I have to go look up the theorem and end up in a rabbit's warren of contradictory definitions.

Taylor offers a description of the problem Coase was trying to solve.

In one famous example, Coase discussed the hypothetical situation of a railroad running beside a farmer’s field. Sparks from the train would sometimes start fires in the crops. How should this external cost—a kind of pollution “externality”—be addressed?

For non-economists, an obvious answer is for the government to pass a law. For example, the government might require that the railroad company install spark arrestors on the smokestacks of its locomotives, use a different blend of fuel or a new engine, leave a buffer zone beside the field, or relocate the rails altogether. Alternatively, the government might declare that the farmer should build a fence to protect the field, install a sprinkler system, change crops, leave a buffer zone, or perhaps even relocate the farm.

Rather than viewing anti-pollution efforts in terms of how governments should choose which rule to impose, Coase took an altogether different approach. He pointed out that the problem could be rephrased in terms of property rights—in other words, who has what rights? For example, the government could say that the railroad company had a right to emit sparks, in which case the farmer would have to figure out the most cost-effective way of protecting the fields. Alternatively, the government could say that the farmer had a property right not to have sparks land among his crops, in which case the railroad would have to figure out an answer—which might include installing spark arrestors or other technology to prevent fires from occurring, or even just paying the farmer to put up with the annoyance.

In Coase’s approach, the question of how to respond to problems of pollution such as unwelcome railroad sparks did not need to be delegated to a government vote or board of experts. Nor did the problem of pollution, in Coase’s view, need to be solved by regulators imposing a Pigouvian tax to account for the “externality” imposed. After all, governments or any outside groups will inevitably possess much less detailed and hands-on information about the range of possible options—and how those options might be tweaked or combined—than railroads and farmers. Moreover, any choice of specific government regulations will be affected by politics and lobbying. Instead, Coase argued that once property rights were clearly defined, then one party or the other would have an incentive to seek out the most cost-effective way of reducing this form of “pollution.”

Taylor gets to part of my frustration with the theorem by quoting Steven Medema.

The Coase theorem is, by any number of measures, one of the most curious results in the history of economic ideas. Its development has been shrouded in misremembrances, political controversies, and all manner of personal and communal confusions and serves as an exemplar of the messy process by which new ideas become scientific knowledge. There is no unique statement of the Coase theorem; there are literally dozens of different statements of it, many of which are inconsistent with others and appear to mark significant departures from what Coase had argued in 1960. 

A nascent idea still not come to a fruition of clarity I guess.