Strange Loops and Tangled Hierarchies | Tax Law Review
Updated: 5 days ago
This article was originally published in Tax Law Review (49 Tax L. Rev. 53) in 1993. The full pdf is linked below.
One of my first assignments as a tax lawyer involved the takeover battle between Kennecott and Curtiss-Wright. This was one of the first occasions for the use of the “Pac-Man” defense, where the target launches a counterattack by buying shares of its purported acquirer. The result, of course, is that both companies send up owning shares of each other.
As I started looking at the tax consequences of such a situation, it became apparent that the tax law was ill-equipped to deal with corporate cross-ownership. Even sorting out the economics of these arrangements was no trivial matter. And this was a relatively simple case involving just two corporations.
At that time Japan was looked to a model of the future of capitalism. A feature of the Japanese economy is the ownership of significant stakes by corporations in other corporations, forming a complex web of alliances. I started wondering, how do they figure out who ultimately owns what? This paper is an attempt to analyze, in a systematic way, the consequences of corporate cross-ownership, no matter how many corporations are involved, and no matter how complex the linkages are among them. Doing so required developing a notation that could represent a messy corporate chart in a way that was susceptible to analysis. This can be done my means of a simple table that shows the percentage stock ownership of each corporation in each other corporation. Such a table can be viewed mathematically as a matrix, which opens up the entire field of matrix algebra as a source of tools to answer the questions posed by these arrangements.
I settled on the term “strange loop” for the situation where two corporations own stock in each other. In the years since this article was published, that term never caught on, the term “hook stock” being used instead. As the paper points out, the terms “strange loop” and “tangled hierarchy” were borrowed from Douglas Hofstadter, who uses them to describe a variety of forms of indirect self-reference in logic and language. I alerted Professor Hofstadter to my appropriation of his terms in the field of corporate tax law, and to my relief he was perfectly happy with that.
This paper does not shy away from the use of equations and mathematical formulas. I appreciate that this will put off many readers; indeed, one such reader, a noted tax practitioner, took the trouble to write to me in order to express how offended he was by my use of math. Of course no offense was intended, and I hope that math-phobic readers will appreciate that the very task I set for myself—to create a formal theory of strange loops—made the use of mathematical language unavoidable.
Much of the paper consists of playful imaginings of how the tax law might apply to bizarre cross-ownership arrangements that are highly unlikely to arise in real life. But the Parts that discuss the creation and unwinding of strange loops deal with actual arrangements, such as those involving McDermott and May Department Stores, that have been the subject of IRS guidance and case law.
The analysis of the creation and unwinding of strange loops remains incomplete. The paper only deals with two-corporation cases, and in an ad hoc manner. What is needed is a more general way of representing transactions that change the number and strength of links of cross-ownership, that can provide insights into the proper computation of gain and loss, and the measurement of any deemed distributions, that result from adjustments to cross-ownership arrangements. But that will need to be the subject of a future paper.
You can read the full article here:
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