# Keiretsu, Proportional Representation, and Input-Output Theory

This is Chapter 9 in my book: Ellerman, David. 1995. Intellectual Trespassing as a Way of Life: Essays in Philosophy, Economics, and Mathematics. Lanham MD: Rowman & Littlefield.

This essay grew out of an attempt to model mathematically the possible cross-ownership arrangements that might arise between privatizing firms in the former Yugoslavia [see Ellerman 1991].  The cross-ownership arrangements resemble the groups of Japanese companies called keiretsu.  There is cross ownership between the companies in the group as well as some ownership outside the group that is traded on the stock market.  In spite of the partial outside ownership, the keiretsu often behave as “self-owning” groups.  If firm A owns shares in B, then the management in A usually signs over its proxy on shares in B to the management in firm B.  And the management in B does likewise with respect to the managers in A.  Thus within certain constraints, each firm can act like a “self-owning” firm, not totally unlike the self-managing firms of the former Yugoslavia.

In this essay we investigate the opposite alternative to this proxy assumption.  We make the more classical assumption that the managers act only as “transmission belts” for the wishes of the shareholders.  But with cross-ownership, the shareholders are in part other corporations whose managers also pass along the wishes of their shareholders.  Thus the determination of the votes on a question put to a corporation can generate an infinite regression of the type familiar from input-output theory.  As long as some external shareholders exist, the infinite regression is benign and decisions would ultimately be made by the external shareholders.  A similar “pass-through” or “transmission-belt” assumption is made for dividends.  Each company passes through to its own shares any dividends received on shares it owns.  Thus the dividends will also eventually trickle into the hands of the external shareholders.

Given the votes of the shareholders (external and other companies in the group), there are two ways that the board can vote on the owned shares.  The board could majoritize and vote all the owned shares as a block according to the majority outcome, or the board could simply pass along the percentages for and against on the owned shares.  For instance, if the shareholders vote 60 percent in favor and 40 percent against, the majoritizing board would vote all the owned shares in favor, while the pass-through board would vote 60 percent of the owned shares in favor and 40 percent against.

The pass-through board is the corporate version of proportional representation (PR), while the majoritizing board corresponds to the system of districts with single representatives representing a majority of the voters in the district.  It is well-known that the system of majoritizing districts can lead to violations of majority rule.  If the districts did not majoritize but only passed through the proportions for and against the proposal, then the result would be the same as in the direct referendum without districts.  Thus the pass-through system gives a correct representation of the electorate while “premature majoritization” at the district level can allow manipulation of the results.  The PR system with large districts and many party representatives for each district to roughly represent the voters’ party preferences is an attempt to reproduce the pass-through system in a system of party representatives.

Pyramidal holding-company schemes are the corporate versions of the premature majoritization.  We construct an example of an ownership federation with five companies.  Using premature majoritization, the external majority shareholder of one of the companies can control the other four companies through a pyramidal structure.  But with pass-through voting, that majority shareholder in one firm controls only that firm and the other four firms are controlled by their own direct external shareholders.

It is clear that a corporation of any size could be controlled by any small amount of capital with enough intermediate layers of holding companies.  Why use a voting rule that makes the fundamental questions of corporate governance and control sensitive to the mere legal repackaging of capital through intermediaries?  Pass-through voting for intermediaries would make control independent of legal repackaging.  These questions of premature majoritization versus proportional representation (or pass-through voting) have not received much attention in the literature on corporate law.  The chapter concludes with a discussion of the light these arguments shed on proportional representation in political theory.