Social choice theory in the context of "Social welfare function"

In philosophy, economics, and political science, the common good (also commonwealth, common weal, general welfare, or public benefit) is either what is shared and beneficial for all or most members of a given community, or alternatively, what is achieved by citizenship, collective action, and active participation in the realm of politics and public service. The concept of the common good differs significantly among philosophical doctrines. Early conceptions of the common good were set out by Ancient Greek philosophers, including Aristotle and Plato. One understanding of the common good rooted in Aristotle's philosophy remains in common usage today, referring to what one contemporary scholar calls the "good proper to, and attainable only by, the community, yet individually shared by its members."

The concept of common good developed through the work of political theorists, moral philosophers, and public economists, including Thomas Aquinas, Niccolò Machiavelli, John Locke, Jean-Jacques Rousseau, James Madison, Adam Smith, Karl Marx, John Stuart Mill, John Maynard Keynes, John Rawls, and many other thinkers. In contemporary economic theory, a common good is any good which is rivalrous yet non-excludable, while the common good, by contrast, arises in the subfield of welfare economics and refers to the outcome of a social welfare function. Such a social welfare function, in turn, would be rooted in a moral theory of the good (such as utilitarianism). Social choice theory aims to understand processes by which the common good may or may not be realized in societies through the study of collective decision rules. Public choice theory applies microeconomic methodology to the study of political science in order to explain how private interests affect political activities and outcomes.

In welfare economics, a Pareto improvement formalizes the idea of an outcome being "better in every possible way". A change is called a Pareto improvement if it leaves at least one person in society better off without leaving anyone else worse off than they were before. A situation is called Pareto efficient or Pareto optimal if all possible Pareto improvements have already been made; in other words, there are no longer any ways left to make one person better off without making some other person worse-off.

In social choice theory, the same concept is sometimes called the unanimity principle, which says that if everyone in a society (non-strictly) prefers A to B, society as a whole also non-strictly prefers A to B. The Pareto front consists of all Pareto-efficient situations.

In social choice theory, the majority rule (MR) is a social choice rule which says that, when comparing two options (such as bills or candidates), the option preferred by more than half of the voters (a majority) should win.

In political philosophy, the majority rule is one of two major competing notions of democracy. The most common alternative is given by the utilitarian rule (or other welfarist rules), which identify the spirit of liberal democracy with the equal consideration of interests. Although the two rules can disagree in theory, political philosophers beginning with James Mill have argued the two can be reconciled in practice, with majority rule being a valid approximation to the utilitarian rule whenever voters share similarly-strong preferences. This position has found strong support in many social choice models, where the socially-optimal winner and the majority-preferred winner often overlap.

The two-round system (TRS or 2RS), sometimes called ballotage, top-two runoff, or two-round plurality, is a single-winner electoral system which aims to elect a member who has support of the majority of voters. The two-round system involves two rounds of choose-one voting, where the voter marks a single favorite candidate in each round. The two candidates with the most votes in the first round move on to a second election (a second round of voting). The two-round system is in the family of plurality voting systems that also includes single-round plurality (FPP). Like instant-runoff (ranked-choice) voting and first past the post, it elects one winner.

The two-round system first emerged in France and has since become the most common single-winner electoral system worldwide. Despite this, runoff-based rules like the two-round system and RCV have faced criticism from social choice theorists as a result of their susceptibility to center squeeze (a kind of spoiler effect favoring extremists) and the no-show paradox. This has led to the rise of electoral reform movements which seek to replace the two-round system with other systems like rated voting, particularly in France.

In the philosophy of economics, economics is often divided into positive (or descriptive) and normative (or prescriptive) economics. Positive economics focuses on the description, quantification and explanation of economic phenomena, while normative economics discusses prescriptions for what actions individuals or societies should or should not take.

The positive-normative distinction is related to the subjective-objective and fact-value distinctions in philosophy. However, the two are not the same. Branches of normative economics such as social choice, game theory, and decision theory typically emphasize the study of prescriptive facts, such as mathematical prescriptions for what constitutes rational or irrational behavior (with irrationality identified by testing beliefs for self-contradiction). Economics also often involves the use of objective normative analyses (such as cost–benefit analyses) that try to identify the best decision to take, given a set of assumptions about value (which may be taken from policymakers or the public).