The universal-instability theorem

Abstract

When individual or corporate creatures with partly conflicting preferences cooperate or compromise, form an alliance or make a deal, they exchange support across issues: they support a package of positions, one on each issue involved in the exchange; although none of them favors every position in the package, they agree (in effect) to all the positions because they prefer the package as a whole to the alternative package that would prevail without the exchange. Vote-traders obviously exchange support across issues. So do coalition-government partners; for them the issues concern legislation, portfolio assignments, or both. So, implicitly, do the supporters of a political candidate or legislative leader who builds a winning platform from planks that have too little support to be enacted singly. The participants in an ordinary economic trade also exchange support across issues: if I trade you a banana for a coconut, I have supported your favorite position on the issue of who gets the banana in return for your support of my favorite position on the issue of who gets the coconut. The exchange of support across issues generalized exchange, for short characterizes all political, economic, and other interpersonal activity involving partial conflict of interest. Kadane (1972), Oppenheimer (1972), and Bernholz (1973), building on an insight of Downs (1957), have independently proved that whenever a majority of voters with separable preferences support a package of