Majoritarian Management of the Commons

YONG J. YOON [*] This article analyzes usage of a common property resource, "the commons," under collectivization as compared with more familiar privatization institutional arrangements. Particular emphasis is on majority decision rules. When separate majority coalitions may authorize simultaneous usage of a common resource, total value is dissipated, but the interdependencies introduced by possible membership in differing coalitions to an extent reduce the incentives for exploitation. The formal analysis is analogous to that familiar in Cournot-Nash duopoly-oligopoly models but with differing efficiency implications. The argument has relevance for differential-benefit public spending from general tax sources, as well as other applications. (JEL D7, H00, 02) I. INTRODUCTION The operation and management of common property resources, "the commons," have been exhaustively examined in economics and political science, both in formal analyses and in practical application. [1] However, the full range of institutional alternatives has not been covered, even at a level of stylized interaction models. Our purpose in this article is to fill in at least some of the gaps here and, specifically, to examine the predicted results that emerge when usage decisions are collectivized under majoritarian voting rules. To our knowledge, this analysis has not been undertaken. We shall, in section II, first summarize the classic analysis along with the familiar institutional reform suggested as a solution to the "tragedy." This solution, "privatization," is analyzed under several institutional variants in section III. We then shift attention, in section IV, to arrangements under which usage of the commonly shared resource or facility is chosen by some predesignated collective decision rule. Specifically, we concentrate analysis on the predicted results in several majority rule environments. We analyze thoroughly the case in which different majority coalitions make usage decisions separately and simultaneously. The analysis incorporates recognition on the part of any member of a specific majority of the prospect for membership in alternative majority coalitions. We demonstrate that instead of full dissipation the level of usage that emerges in the limit is structurally analogous to the outcome in the Cournot-Nash duopoly model, even if the efficiency implications differ in the two settings. II. THE CLASSIC MODEL SUMMARIZED The familiar "tragedy of the commons" lends itself to stylized illustration. An immobile but renewable resource exists (a common pasture, aquifer, fishing ground) and has economic value if used effectively through the application of units of complementary mobile resources that are themselves valued in their alternative market opportunities. There are no assigned ownership rights to the immobile resource or facility. Free and open access may dissipate most or even all of the potential value. Consider Figure 1. The productivity of mobile complementary resource units, as applied elsewhere in the economy (e.g., steers grazed on the open range, beyond the commons) is set at w, a value assumed constant. The quantity of such inputs applied on the commonly used facility is measured along the abscissa. In Figure 1, the marginal and average productivity curves for the units of applied complementary resource are shown as MP and AP. Total value is maximized when [Q.sub.m] units are applied, at which point marginal product values are equalized as between this usage and other opportunities. The maximal value of the commonly used resource is the area under the MP curve above w. If entry to usage is open, and if the institutional structure is such as to allow for decentralized decisions on the part of many potential users, rational choices made separately will generate a full behavioral equilibrium at [Q.sup.*], where "average" product per unit of the complementary resource is equalized as between the commons and other uses. …