Dichotomous preferences

In economics, dichotomous preferences (DP) are preference relations that divide the set of alternatives to two subsets: "Good" versus "Bad".

From ordinal utility perspective, DP means that for every two alternatives ${\displaystyle X,Y}$:^: 292

${\displaystyle X\preceq Y\iff X\in Bad{\text{ or }}Y\in Good}$

${\displaystyle X\prec Y\iff X\in Bad{\text{ and }}Y\in Good}$

From cardinal utility perspective, DP means that for each agent, there are two utility levels: low and high, and for every alternative ${\displaystyle X}$:

${\displaystyle u(X)=u_{low}\iff X\in Bad}$

${\displaystyle u(X)=u_{high}\iff X\in Good}$

A common way to let people express dichotomous preferences is using approval ballots, in which each voter can either "approve" or "reject" each alternative.