We provide exact relations giving the probability of individual and coalitional manipulation of three specific social choice functions (Borda rule, Copeland rule, Plurality rule) in three-alternative elections when the notion of self-selectivity is imposed. The results suggest that the Borda rule is more vulnerable to coalitional manipulation than the Copeland rule and the Plurality rule. However, Plurality rule seems to be more vulnerable to individual manipulability when the number of voters is greater than a certain threshold value. In addition, the probability of individual and coalitional manipulation tends to vanish significantly when the notion of selfs-electivity is imposed.
