In metaphilosophy and ethics, metaethics is the study of the nature, scope, and meaning of moral judgment. It is one of the three branches of ethics generally studied by philosophers, the others being normative ethics and applied ethics.
Non-cognitivism is the meta-ethical view that ethical sentences do not express propositions and thus cannot be true or false. A noncognitivist denies the cognitivist claim that "moral judgments are capable of being objectively true, because they describe some feature of the world". If moral statements cannot be true, and if one cannot know something that is not true, noncognitivism implies that moral knowledge is impossible.
Arrow's impossibility theorem is a key result in social choice theory, showing that no ranking-based decision rule can satisfy the requirements of rational choice theory. Most notably, Arrow showed that no such rule can satisfy independence of irrelevant alternatives, the principle that a choice between two alternatives A and B should not depend on the quality of some third, unrelated option C.
The Gibbard–Satterthwaite theorem is a theorem in voting theory. It was first conjectured by the philosopher Michael Dummett and the mathematician Robin Farquharson in 1961 and then proved independently by the philosopher Allan Gibbard in 1973 and economist Mark Satterthwaite in 1975. It deals with deterministic ordinal electoral systems that choose a single winner, and shows that for every voting rule of this form, at least one of the following three things must hold:
- The rule is dictatorial, i.e. there exists a distinguished voter who can choose the winner; or
- The rule limits the possible outcomes to two alternatives only; or
- The rule is not straightforward, i.e. there is no single always-best strategy.
Sir Michael Anthony Eardley Dummett was an English academic described as "among the most significant British philosophers of the last century and a leading campaigner for racial tolerance and equality." He was, until 1992, Wykeham Professor of Logic at the University of Oxford. He wrote on the history of analytic philosophy, notably as an interpreter of Frege, and made original contributions particularly in the philosophies of mathematics, logic, language and metaphysics.
In philosophy, economics, and political science, the common good 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."
A random ballot or random dictatorship is a randomized electoral system where the election is decided on the basis of a single randomly-selected ballot. A closely-related variant is called random serialdictatorship, which repeats the procedure and draws another ballot if multiple candidates are tied on the first ballot.
In social choice theory, May's theorem, also called the general possibility theorem, says that majority vote is the unique ranked social choice function between two candidates that satisfies the following criteria:
In meta-ethics, expressivism is a theory about the meaning of moral language. According to expressivism, sentences that employ moral terms – for example, "It is wrong to torture an innocent human being" – are not descriptive or fact-stating; moral terms such as "wrong", "good", or "just" do not refer to real, in-the-world properties. The primary function of moral sentences, according to expressivism, is not to assert any matter of fact but rather to express an evaluative attitude toward an object of evaluation. Because the function of moral language is non-descriptive, moral sentences do not have any truth conditions. Hence, expressivists either do not allow that moral sentences to have truth value, or rely on a notion of truth that does not appeal to any descriptive truth conditions being met for moral sentences.
Social choice theory is a branch of welfare economics that analyzes methods of combining individual opinions, beliefs, or preferences to reach a collective decision or create measures of social well-being. It contrasts with political science in that it is a normative field that studies how societies should make decisions, whereas political science is descriptive. Social choice incorporates insights from economics, mathematics, philosophy, political science, and game theory to find the best ways to combine individual preferences into a coherent whole, called a social welfare function.
In game theory, and particularly mechanism design, participation constraints or individual rationality constraints are said to be satisfied if a mechanism leaves all participants at least as well-off as they would have been if they hadn't participated.
The Duggan–Schwartz theorem is a result about voting systems designed to choose a nonempty set of winners from the preferences of certain individuals, where each individual ranks all candidates in order of preference. It states that for three or more candidates, at least one of the following must hold:
- The system is not anonymous.
- The system is imposed.
- Every voter's top preference is in the set of winners.
- The system can be manipulated by either an optimistic voter, one who can cast a ballot that would elect some candidate to a higher rank than all of those candidates who would have been elected if that voter had voted honestly; or by a pessimistic voter, one who can cast a ballot that would exclude some candidate to a lower rank than all of those candidates who were elected due that voter voting strategically.
The revelation principle is a fundamental result in mechanism design, social choice theory, and game theory which shows it is always possible to design a strategy-resistant implementation of a social decision-making mechanism. It can be seen as a kind of mirror image to Gibbard's theorem. The revelation principle says that if a social choice function can be implemented with some non-honest mechanism—one where players have an incentive to lie—the same function can be implemented by an incentive-compatible (honesty-promoting) mechanism with the same equilibrium outcome (payoffs).
Richard Booker Brandt was an American philosopher working in the utilitarian tradition in moral philosophy.
Economic justice is a component of social justice and welfare economics. It is a set of moral and ethical principles for building economic institutions, where the ultimate goal is to create an opportunity for each person to establish a sufficient material foundation upon which to have a dignified, productive, and creative life.."
Reginald Robin Farquharson was an academic whose interest in mathematics and politics led him to work on game theory and social choice theory. He wrote an influential analysis of voting systems in his doctoral thesis, later published as Theory of Voting, and conjectured the Gibbard–Satterthwaite theorem together with the philosopher and logician Michael Dummett.
Rated, evaluative, graded, or cardinalvotingrules are a class of voting methods that allow voters to state how strongly they support a candidate, by giving each one a grade on a separate scale. Cardinal methods and ordinal methods are the two categories of modern voting systems.
Arunava Sen is a professor of economics at the Indian Statistical Institute. He works on Game Theory, Social Choice Theory, Mechanism Design, Voting and Auctions.
Maximal lotteries refers to a probabilistic voting rule. The method uses preferential ballots and returns a probability distribution of candidates that a majority of voters would weakly prefer to any other.
In the fields of mechanism design and social choice theory, Gibbard's theorem is a result proven by philosopher Allan Gibbard in 1973. It states that for any deterministic process of collective decision, at least one of the following three properties must hold:
- The process is dictatorial, i.e. there is a single voter whose vote chooses the outcome.
- The process limits the possible outcomes to two options only.
- The process is not straightforward; the optimal ballot for a voter "requires strategic voting", i.e. it depends on their beliefs about other voters' ballots.
