Borda’s Paradox with weighted scoring rules

Representations are obtained for the probabilities that a Strict Borda Paradox and a Strong Borda Paradox are observed for large electorates with three candidates under the standard assumptions of Impartial Culture and Impartial Anonymous Culture. These representations are obtained for general weighted scoring rules (WSRs), and the probabilities are found to be maximized for voting rules like plurality rule and negative plurality rule. It is found that these paradox probabilities are not reduced for every scoring rule with the introduction of some degree of dependence among voters’ preferences with IAC. It is concluded that actual observances of a Strict Borda Paradox should be extremely rare, and that while observances of a Strong Borda Paradox should also be rare, they might occasionally be witnessed.     

On the stability of a triplet of scoring rules

When choosing a voting rule to make subsequent decisions, the members of a committee may wish this rule to be self-selected when it is the object of a choice among a menu of different possible voting rules. Such concepts have recently been explored in Social Choice theory, and a menu of voting rule is said to be stable if it contains at least one self-selective voting rule at each profile of preferences on voting rules. We consider in this article the menu constituted by the three well-known scoring rules {Borda, Plurality, and Antiplurality}. Under the Impartial Culture assumption, which proposes an a priori model to estimate the likelihood of the profiles, we will derive a probability for the stability of this triplet of voting rules.     

The decline in average annual hours worked in the United States, 1947–1979

Using data from government agencies, a survey of 200 “Fortune 500” type companies, and data derived by the IRU, the average number of hours worked annually 1947–1979 was examined and found to have declined significantly. Because the workweek has remained stable and does not reflect the dramatic rise in paid time off since 1947, the workyear is now a more valid standard of measurement. To compensate for lost production hours, many firms have taken steps to raise the productivity of hours worked, including increased overtime and shift work, the introduction of automation and other technological advances, and flexible manufacturing systems.     

A model of deliberation based on Rawls��s political liberalism

In this article, we present a model of deliberation based on Rawls’s political liberalism. Our formalization gives a new perspective on his political theory. Moreover, we obtain quantitative results on political deliberation under Rawlsian rules. Finally, we elaborate two arguments in favor of Rawlsian deliberation: first, deliberation is epistemically valuable when, all other things being equal, it tends to favor the better view, because in this case, deliberators settle on the better view with high probability. Second, results suggest that when citizens deliberate within the limits of Rawlsian public reason, they can reach unanimity faster than when they deliberate outside these limits.