Approximability of Dodgson's rule

Abstract

It is known that Dodgson’s rule is computationally very demanding. Tideman (Soc Choice Welf 4:185–206, 1987) suggested an approximation to it but did not investigate how often his approximation selects the Dodgson winner.We show that under the Impartial Culture assumption the probability that the Tideman winner is the Dodgson winner converges to 1 as the number of voters increase. However we show that this convergence is not exponentially fast. We suggest another approximation— we call it Dodgson Quick—for which this convergence is exponentially fast. Also we show that the Simpson and Dodgson rules are asymptotically different.