Moral Foundations Theory (MFT) was developed by Jonathan Haidt and his colleagues. (See references at the end of this post). A good overview of the theory can be found in the book, The Righteous Mind (2012).
There are five core moral foundations in Moral Foundations Theory.
2 Fairness/cheating (*equality-Fairness)
4 Authority-Respect; aka Authority/subversion
5 Purity-Sanctity aka Sanctity/degradation
An additional foundation of liberty has been added to the theory so there are now six foundations.
2 Fairness/cheating: people have developed a sense of reciprocal altruism, which leads to concerns for justice, rights, and autonomy. Equality was dropped in favor of a sense of proportionality.
3 Loyalty-Betrayal: people form groups and tribes and a sense of loyalty to the group, which supports patriotism and a willingness to sacrifice for the group.
4 Authority/subversion: people organize themselves into hierarchies and consider leadership a virtue. Followers are expected to defer to legitimate leaders and show respect for group traditions.
5 Sanctity/degradation: derived from research into the psychology of disgust and contamination, people find certain things and by extension, some people, to be disgusting. There is a separation for that which is unclean. In religion, that which is sacred is set apart from that which is profane. Cleanliness of self and clothing are virtues. The body is a temple in some religious teachings.
Researchers usually find support for a two factor model.
*I added the "aka" because you will find somewhat different words in some articles.
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Here are some applications of moral foundations theory:
For applications to Christian views of moral issues see A House Divided: Sexuality, Morality and Christian Cultures.
For a recent study of Moral Foundations Theory, Identity, and Politics, see Sutton, Kelly, and Huber (2019).
Link to learn more about the Moral Foundations Questionnaire