Unpacking the Vandivier-Coase Theorem

In this article I want to further explain the <a href="http://www.afterecon.com/economics-and-finance/vandivier-coase-theorem/">Vandivier-Coase Theorem.

The theorem is as follows: "When transaction costs are sufficiently small relative to total surplus, an efficient and invariant outcome will prevail, and as transaction costs approach zero the result will become even more efficient."

There are 3 specific pieces of this definition that I would like to explain in better detail:

1. \"When transaction costs are sufficiently small relative to total surplus\"
   1. This is not clear wording. The point is that the benefits must be larger than the costs in order to incentivize action. In other words, transaction costs must be smaller than the gains from trade, or total surplus.
2. \"...an efficient and invariant outcome will prevail...\"
   1. There are two important pieces here. First, the notion of efficiency. I mean the exact opposite of what I have called VMF, which turns out to be precisely what Oliver Williamson calls remediableness in Transaction Cost Economics (TCE). To my knowledge we came up with our ideas independently, but both very much influenced by Coase. Let me reiterate, I am not necessarily talking about pareto-efficiency here. I am talking about a non-remediable outcome.
      1. To be a bit clearer, Williamson describes the concept of remediableness, in the linked article, in this way: \"The criterion is this: an extant mode of organization for which no superior feasible form of organization can be described and implemented with expected net gains is presumed to be efficient.\"
   2. Second is the notion of invariance. The idea here is that the same outcome will occur regardless of how property rights are allocated. It is actually the case that property rights allocation does sometimes, perhaps often, effect the distribution, but it seems that the overall level of utility will remain invariant despite differing allocations. Given time, the invariance idea may be altogether disproved.
3. \"...will be even more efficient.\"
   1. This will seem strange to anyone with a pareto-efficient mindset. If the previous outcome was efficient, then how can another outcome be more efficient? There are two answers.
   2. First, the efficiency I am referring to is non-remediableness, not pareto-efficiency. Second, the outcome with reduced transaction costs was previously not accessible, so it could not have been efficient. Now that it is accessible it can be considered, and the lowered transaction costs will predictably yield a better new choice.