Sufficientarian Grading Rules and Rankings: Characterizations and Implementation

Sufficientarian grading rules are defined using a finite family of sufficientarian judgements on individual capability assignments as embodied in a sufficientarian binary grading function (BGF).

Both sufficientarian grading rules and the sufficientarian total preorders on capability-type assignments they induce are characterized.

Moreover, several further total preorders based upon sufficiency-gap information provided by a sufficientarian grading rule are explicitly defined and some of them are also characterized.

It is also shown that there exists a class of inclusive, unanimity-respecting and suitably strategy-proof protocols (including simple majority when the number of agents is odd) which can be deployed in order to select one specific sufficientarian grading rule.