Libertarian conflicts in social choice: John L. Wriglesworth, Cambridge University Press, 1985

Intransitivities in multidimensional voting models and some implications for agenda control

Logrolling, vote trading, and the paradox of voting: A game-theoretical overview

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

The universal-instability theorem

Arrow's Impossibility Theorem shows that there exist no transitive social preferences in nonoligarchic societies for all possible profiles of individual preference orderings. Similarly, a generalization of Sen's Theorem of the Impossibility of a Paretian Liberal implies under the same conditions that non-Pareto-optimal outcomes may be present in the resulting cyclical preference relations. This essay changes the customary perspective. It demonstrates that, for any profile of individual preferences, we can always find a nonoligarchic assignment of rights to different subsets of society, to decide between pairs of outcomes, together with adequate decision rules, which escapes these problems. This assignment of rights can be a purely liberal one even for each profile, but not one in which everybody participates in all decisions and which uses simple or qualified-majority voting (Total Direct Democracy). The adequate purely liberal constitution, on the other hand, may imply an oligarchy if too few outcomes are present.

Libertarian conflicts in social choice: John L. Wriglesworth, Cambridge University Press, 1985

References

Intransitivities in multidimensional voting models and some implications for agenda control

Logrolling, vote trading, and the paradox of voting: A game-theoretical overview

The universal-instability theorem

A general constitutional possibility theorem

A general social dilemma: Profitable exchange and intransitive group preferences