The r-button (⊂⊃) is a short name for a relationship button (or buttons) that address the need for UI (user interface) elements representing the ability of two parties to relate as equals in a marketplace.
Here is a sample grapical r-button design:
The two sides are meant to represent "magnets" facing each other and the equals (=) symbol.
The left (⊂) side is the first party's, and the right (⊃) side is the second party's. For individuals these represent the first and second grammatical persons. They also map well to commercial dealings, where the ⊂ + ⊃ roles are customer + vendor. (They can also represent person + person, citizen + government, member + organization). Since these buttons are also characters that can be typed, they have broader utility than they might if they were just graphic elements.
The purpose of the r-button is to open and represent relationships that are two-way rather than one-way — VRM meeting CRM, for example — and for scaffolding relationships based on freedom of contract rather than standard-form contracts of adhesion, which became defaulted as a mass-marketing norm in the Industrial Age, and leveraged further into pro forma dealings between companies and users in online markets. Adhesive contracts should be obsolete in a truly end-to-end and peer-to-peer marketplace, such as the Internet's protocols presume. R-buttons can help hasten that obsolescence while offering a new better way to represent relatings between equals.