 A second example of a preference aggregation rule that violates independence of irrelevant alternatives is the Borda count (e.g., Saari 1990). Here, for any profile \(\langle R_1, R_2 , \ldots ,R_n\rangle\) and any \(x, y \in X\), \(xRy\) if and only if \(\sum_{i \in N} |\{z \in X : xR_i z\}| \ge \sum_{i \in N} |\{z \in X : yR_i z\}|.\) Informally, each voter assigns a score to each alternative, which depends on its rank in his or her preference ranking. The most-preferred alternative gets a score of \(k\) (where \(k = |X\)|), the second-most-preferred alternative a score of \(k - 1\), the third-most-preferred alternative a score of \(k - 2\), and so on. Alternatives are then socially ordered in terms of the sums of their scores across voters: the alternative with the largest sum-total is top, the alternative with the second-largest sum-total next, and so on.