Borda Count (COMSOC)

comsoc

Definition

Borda Count

In COMSOC, Borda Count is a voting rule that scores each alternative by its position in every voter’s preference ranking.

Let

$$C:=\{c_1,\dots ,c_m\}$$

be the set of alternatives, and let

$$R:=({\succ }_1,\dots ,{\succ }_n)$$

be a preference profile. If an alternative is ranked in position $j$, it receives $m-j$ points from that voter. Borda Count returns the alternatives with maximal Borda score:

$${\lambda }_{\mathrm{Borda}}(R):=\arg \underset{x\in C}{\max }{\mathrm{Borda}}_R(x).$$

Each alternative in this set is a Borda winner.

Mechanism

Positional scoring

Each voter gives a descending score vector

$$(m-1,m-2,\dots ,1,0)$$

to their ranking. The first-ranked alternative receives $m-1$ points, the second-ranked alternative receives $m-2$ points, and the last-ranked alternative receives $0$ points.

Example

Four alternatives

Let

$$C:=\{A,B,C,D\}.$$

Since $m=4$, one voter with ranking

$$A\succ B\succ C\succ D$$

gives $3$ points to $A$, $2$ points to $B$, $1$ point to $C$, and $0$ points to $D$.