A comparison between the prudent order and the ranking obtained with Borda's, Copeland's, Slater's and Kemeny's rules

Arrow and Raynaud suggested that the result of a ranking rule should be a prudent order. We prove that we can construct profiles of linear orders for which the unique prudent order is the exact opposite of the ranking obtained with Borda's rule or Copeland's rules. Furthermore, we show that we can construct profiles of linear orders such that the unique prudent order winner can be found at any position in the corresponding unique order found by Slater's or Kemeny's rules. Finally, we show that there exist profiles where the unique Slater or Kemeny order is the exact opposite of one prudent order.