Consent

Concise Definition
A given voter consents to an alternative if she is willing to form a consensus around that alternative.

More Details
If a voter does not consent to an alternative, then she is not willing to form a consensus around an alternative. A voter can consent to more than one alternative. However, there are some rationality restrictions as to which alternatives an individual voter can consent to when she publicly expresses them in conjunction with preference orders.

Rationality Restrictions
Suppose there exists some given voter i who is confronted with the alternatives Ax, Ay, and Az. There are four rationality restrictions.

First, if voter i Ax>Ay and consents to Ay, then voter i must consent to Ax.

Second, if voter i Ax>Ay and does not consent to Ax, then voter i must not consent to Ay.

Third, if voter i Ax=Ay and consents to Ax, then voter i must consent to Ay.

Fourth, if voter i Ax=Ay and does not consent to Ax, then voter i must not consent to Ay.

These rules allow us to express voter consent in conjunction with a preference order. Such expressions are called preference-approvals, or total preference orders when it contains all alternatives. Total preference orders look exactly like complete preference orders, except they have a line that separates consented alternatives from non-consented alternatives.