Trapezoidal rule that Monte-Carlo integration is most likely a better choice, but for 2 and 3 dimensions, equispaced sampling is efficient. This is exploited in computational solid state physics where equispaced sampling over primitive cells in the reciprocal lattice is known as "Monkhorst-Pack integration". For various classes of functions that are not twice-differentiable, the trapezoidal rule has sharper bounds than Simpson's rule. The trapezoidal rule is one of a family of formulas for numerical integration called Newton–Cotes formulas, of which the midpoint rule is similar to the trapezoid rule. Simpson's rule is another member of the same family, and in general has
Majority rule circumstances, such as a two-thirds rule to close debate. Many referendums are decided by majority rule. According to May, majority rule is the only reasonable decision rule that is "fair", that is, that does not privilege voters by letting some votes count for more or privilege an alternative by requiring fewer votes for its passing. Stated more formally, majority rule is the only binary decision rule that has the following properties: Strictly speaking, it has been shown that majority rule meets these criteria only if the number of voters is odd or infinite. If the number of voters is even,