Read on Twitter
Ranked ballots usually refers to ordinal preference (1st, 2nd, etc) rather than cardinal values (say, /10). Arrow's Theorem ( https://plato.stanford.edu/entries/arrows-theorem/) only applies to ordinal rankings, because of the problems with interpersonal comparisons of cardinal utility.
1/
#economics
1/
#economics
However, Gibbard's Theorem ( https://en.wikipedia.org/wiki/Gibbard%27s_theorem) extends Arrow's result to cardinal systems, showing that if we want to avoid dictatorship or a duopoly, strategic voting is unavoidable (technically, the game is not 'straightforward').
2/
#economics #gametheory
2/
#economics #gametheory
There are variations on the above: approval voting (0 or 1) or relative preferences (we have N points to assign to the candidates), but we encounter the same problems. In addition, once we assign our preferences, there are different mechanisms for choosing the winner.
3/
#voting
3/
#voting
Usually, the candidate with the least 1st place votes is eliminated and their 2nd place votes are redistributed; this favours candidates in the centre (or with vague promises) and disadvantages smaller parties. We can maximize the mean, the median, or minimize lowest rankings.
4/
4/
Example: Consider the following cardinal utilities assigned to candidates a, b, c by voters A-E. Candidate a has the highest sum total (and so the highest mean), but candidate c has the highest median value.
5/
5/
Using approval voting, where a score of >=5 indicates 'approval', then c wins and a comes in last. We can see that voters A and E, gave a 10/10, and so the cardinal system favours them. Voters A and C have no impact under the approval method - they may have voted differently.
6/
6/
Finally, using a ranked ballot, c is eliminated after the first round since they received the least 1st place votes, and b wins after the second round.
Of course, the voting behaviour may have differed under different systems, which is an additional complexity to consider.
7/
Of course, the voting behaviour may have differed under different systems, which is an additional complexity to consider.
7/
