  With the Dodgson rule, cloning the electorate can change the winner, which
Young (1977) considers an "absurdity". Removing this absurdity results in a new
rule (Fishburn, 1977) for which we can compute the winner in polynomial time
(Rothe et al., 2003), unlike the traditional Dodgson rule. We call this rule DC
and introduce two new related rules (DR and D&). Dodgson did not explicitly
propose the "Dodgson rule" (Tideman, 1987); we argue that DC and DR are better
realizations of the principle behind the Dodgson rule than the traditional
Dodgson rule. These rules, especially D&, are also effective approximations to
the traditional Dodgson's rule. We show that, unlike the rules we have
considered previously, the DC, DR and D& scores differ from the Dodgson score
by no more than a fixed amount given a fixed number of alternatives, and thus
these new rules converge to Dodgson under any reasonable assumption on voter
behaviour, including the Impartial Anonymous Culture assumption.
