Preference Ranking (COMSOC)

comsoc

Definition

Preference Ranking (COMSOC)

In COMSOC, a preference ranking is a linear ordering of the alternatives from most preferred to least preferred.

The set of all possible preference rankings over a set of alternatives $C$ is written as

$$\mathcal{L}(C).$$

Thus, if

$$\succ \in \mathcal{L}(C),$$

then $\succ$ is one possible ranking of all alternatives in $C$.

For a voter $v_i$, their individual ranking is usually written as

$${\succ }_i\in \mathcal{L}(C).$$

Examples

Ranking over three alternatives

If

$$C:=a,b,c,$$

then

$$a\succ b\succ c$$

is one preference ranking over $C$.

Another ranking over the same alternatives

The ranking

$$b\succ c\succ a$$

is also one element of $\mathcal{L}(C)$.

Voter ranking

If voter $v_i$ ranks $a$ above $b$ above $c$, then their ranking is

$${\succ }_i;=;a{\succ }_{i}b{\succ }_{i}c.$$

Number of possible rankings

If $|C|=m$, then there are

$$|\mathcal{L}(C)|=m!$$

possible preference rankings over $C$.