say three voters vote for three candidates (A,B,C) as follows: The second candidate is the Condorcet winner and the winner of the normal election with 12 to 10 and 0 points. In the case where all voters are voting strategically, range voting is equivalent to approval voting, and any Condorcet winner will win because of the Nash equilibrium as mentioned above. However, if voters change their voting strategy from honest to strategic only for the head-to-head elections, then range voting does not satisfy Condorcet. For the same example shown above, the head-to-head elections involving A would look like this: Since in both cases, A would be the winner, the Condorcet winner is A, but B still wins the full election. Some, like the authors of rangevoting.org, say that defining the Condorcet criterion in this way makes the criterion not always desirable. If the winners of the head-to-head contests were determined by range voting rules rather than pluralistic voting, range voting would satisfy Condorcet. STAR voting STAR voting is a variant of score voting with an additional runoff step, where the most preferred of the top-two rated candidates wins. STAR voting does not satisfy the Condorcet criterion. Nevertheless, provided the Condorcet winner is one of the top two rated candidates, it wins the election by virtue of the runoff step being based solely on the ranked preferences between the two. The following example is an election with 100 voters and 3 candidates {A, B, C}: 45 voters voting: A=5 B=1 C=0 (Preferences: A>B>C) 40 voters voting: A=0 B=1 C=5 (Preferences: C>B>A) 15 voters voting: A=1 B=5 C=0 (Preferences: B>A>C) Under STAR voting, the total ratings are A=240, B=160, C=200, thus A and C are chosen as finalists and the ballots are read again, taking only preferences between the two finalists into account. From the given ballots, we have that 60% of voters prefer A over C, thus A is the STAR voting winner. However, from the preference information alone, we see that B is preferred over A by 55% of voters, and over C by 60% of voters. This makes B the Condorcet winner, and thus STAR voting has failed to elect it. Proponents of STAR voting argue that this can be a superior result given the extra information available in rated ballots, as the ranking information alone is insufficient information to distinguish between a second-choice ranking being almost as good