Borda Winner (COMSOC)

comsoc

Definition

Borda Winner

In COMSOC, a Borda winner is an alternative selected by Borda Count because it has maximum Borda score in a preference profile.

Formally, for a set of alternatives $C$ and profile $R$, the set of Borda winners is

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

If this set contains more than one alternative, its elements are Borda co-winners.

Winner determination

Polynomial-time winner determination

To determine whether a given alternative $c^{\ast }\in C$ is a Borda winner, compute the Borda score of every alternative and compare $c^{\ast }$ with the maximum score.

Thus Borda winner determination is solvable in polynomial time.

Example

Winner from the course profile

In the lecture profile with alternatives $A,B,C,D$, the Borda scores are

$${\mathrm{Borda}}_R(A)=118,{\mathrm{Borda}}_R(B)=194,{\mathrm{Borda}}_R(C)=180,{\mathrm{Borda}}_R(D)=108.$$

Since $B$ has the largest score, $B$ is the unique Borda winner.