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During the 1996 term, the United States Supreme Court made a candid confession about its voting practices. In Seminole Tribe of Florida v. Florida, the Court overruled Pennsylvania v. Union Gas Co. and recognized that when a justice defers to the majority against his or her own reasoning inconclusive precedent results. Union Gas was particularly unusual because Justice White switched his vote to assure a result in a three-remedy case where none of the three remedies had the support of a majority. In Seminole Tribe, the Court admitted Union Gas "has, since its issuance, been of questionable precedential value, largely because a majority of the Court expressly disagreed with the rationale of the plurality." Accordingly, the Court recognized the problems created when a justice votes against his or her own reasoning to ensure a result. While scholars frequently have analyzed the strategic voting practices of legislators, similar analysis of voting on judicial panels is relatively new. Frank Easterbrook was the first scholar to apply Arrow's Theorem systematically to the Supreme Court's voting practice, and several scholars followed his lead. After Justice White's vote in Union Gas, Professor John Rogers warned the Court against abdicating its role as a reasoned decision maker. He concluded, however, that the contradictory vote in Union Gas was aberrational. More recently, Professors David Post and Steven Salop published an article encouraging multimember courts to abandon their traditional practice of outcome voting and instead to adopt a system of issue voting.' Shortly thereafter, Professors Lewis Kornhauser and Lawrence Sager urged appellate courts to adopt neither outcome voting nor issue voting as a rule. Rather, they suggested appellate courts should take a metavote on whether outcome or issue voting should control each case." Professor Maxwell Stearns advanced the debate over appellate court voting in a trilogy of articles published over the past two years. These articles apply social choice theory to the ...

When making collektive desicions, principals (voters or districts) typically benefit by strategically delegating their bargaining and voting power to representatives different from themselves. There are conflicting views in the literature, however, of whether such a delegate should be conservative (status quo biased) or instead progressive relative to his principal. I show how the answer depends on the political system in general, and the majority requirement in particular. A larger majority requirement leads to conservative delegation, but sincere delegation is always achieved by the optimal voting rule.

When a group of people with identical preferences but different abilities in identifying the best alternative (e.g., a jury) takes a vote to decide between two alternatives, the question of strategic voting arises. That is, depending on the voting rule used to determine the collective decision, it may or may not be rational for group members to always vote for the alternative believe to be their private information indicates is better (i.e., vote informatively). In fact, we show in this paper that, if a qualified majority rule is used, then informative voting is rational only if the rule is optimal in the class of all qualified majority rules, in the sense the sense that, when everybody votes informatively, none of the other rules in this class would yield a higher expected utility. However, this necessary condition is not sufficient for informative voting to be rational. Specifically, even if the qualified majority rule used is optimal in the above sense, some of those who are least competent in correctly identifying the better alternative may increase the expected utility by sometimes voting for the alternative they believe to be inferior. A sufficient (but not necessary) condition for informative, non-strategic, voting to be rational is that the voting rule is optimal among the class of all qualified weighted majority rules, i.e., rules assigning (potentially) unequal weights to different individuals, this cannot happen: informative, non-strategic voting is rational.

The theory of "constitutional" choice of voting rules developed by J. Buchanan & G. Tullock (The Calculus of Consent: Logical Foundations of Constitutional Democracy, Ann Arbor: U of Michigan Press, 1962) is extended to an explicit decision-theoretic form. Voters in the constitutional position choose what they believe will be their optimal share or majority rule for making social decisions under conditions of uncertainty by maximizing their individual expected utility from the anticipated social decisions. The rule that maximizes expected social benefits depends on: (1) the expected distribution & intensity of preferences on future issues, & (2) the decision-making procedures & costs, which are shown to be interrelated. Failure to pass laws imposes external costs in the same way that passing them does, so that the optimal majority may be lower when desirable laws are viewed as changing over time. Decision-making costs depend on the way in which voters are persuaded to support or oppose bills, on the distribution of preferences on bills, & on vote-trading possibilities. If vote-trading is almost costless, a wide range of decision rules has nearly equal social benefits. Finally, the model is used to discuss optimal voting rules for several decision-making bodies. 4 Figures, 1 Appendix, 21 References. Modified HA.

THE THEORY OF 'CONSTITUTIONAL' CHOICE OF VOTING RULES DEVELOPED BY BUCHANAN AND TULLOCK IS AN EXTENDED TO AN EXPLICIT DECISION-THEORETIC FORM. VOTERS IN THE 'CONSTITUTIONAL' POSITION CHOOSE WHAT THEY BELIEVE WILL BE THEIR OPTIMAL SHARE OR MAJORITY RULE FOR MAKING SOCIAL DECISIONS, BY MAXIMIZING THEIR INDIVIDUAL EXPECTED UTILITY FROM THE ANTICIPATED SOCIAL DECISIONS, UNDER CONDITIONS OF UNCERTAINTY. THE RULE THAT MAXIMIZES EXPECTED SOCIAL BENEFITS DEPENDS UPON (1) THE EXPECTED DISTRIBUTION AND INTENSITY OF PREFERENCES ON FUTURE ISSUES, AND (2) THE DECISIONMAKING PROCEDURES AND COSTS. 'DECISIONMAKING' AND 'EXTERNAL' COSTS ARE SHOWN TO BE INTERRELATED. FOLLOWING THIS ANALYSIS, FAILURE TO PASS LAWS IMPOSES 'EXTERNAL' COSTS IN THE SAME WAY THAT PASSING THEM DOES, SO THAT THE OPTIMAL MAJORITY MAY BE LOWER WHEN DESIRABLE LAWS ARE VIEWED AS CHANGING OVER TIME. DECISIONMAKING COSTS DEPEND UPON THE WAY IN WHICH VOTERS ARE PERSUADED TO SUPPORT OR OPPPOSE BILLS, UPON THE DISTRIBUTION OF PREFERENCES ON BILLS, AND ON VOTE-TRADING POSSIBILITIES. IF VOTE-TRADING IS ALMOST COSTLESS, A WIDE RANGE OF DECISION RULES HAS NEARLY EQUAL SOCIAL BENEFITS. FINALLY, THE MODEL IS USED TO DISCUSS OPTIMAL VOTING RULES FOR SEVERAL DECISIONMAKING BODIES.

In this paper we address several issues related to collective dichotomous decision-making by means of quaternary voting rules, i.e., when voters may choose between four actions: voting yes, voting no, abstaining and not turning up-which are aggregated by a voting rule into a dichotomous decision: acceptance or rejection of a proposal. In particular we study the links between the actions and preferences of the actors.We showthat quaternary rules (unlike binary rules,where only two actions -yes or no- are possible) leave room for manipulability" (i.e., strategic behaviour). Thus a preference profile does not in general determine an action profile. We also deal with the notions of success and decisiveness and their ex ante assessment for quaternary voting rules, and discuss the role of information and coordination in this context.

We give an introduction to deductive verification methods that can be used to formally prove that voting rules and their implementations satisfy specified properties and conform to the desired democratic principles. In the first part of the paper we explain the basic principles: We describe how first-order logic with theories can be used to formalise the desired properties. We explain the difference between (1) proving that one set of properties implies another property, (2) proving that a voting rule implementation has a certain property, and (3) proving that a voting rule implementation is a refinement of an executable specification. And we explain the different technologies: (1) SMT-based testing, (2) bounded program verification, (3) relational program verification, and (4) symmetry breaking. In this first part of the paper, we also explain the difference between verifying functional and relational properties (such as symmetries). In the second part, we present case studies, including (1) the specification and verification of semantic properties for an STV rule used for electing the board of trustees for a major international conference and (2) the deduction-based computation of election margins for the Danish national parliamentary ...