[EM] Why I think IRV isn't a serious alternative 2

[Kristofer Munsterhjelm]

Aaron Armitage wrote:
> 
> Perhaps the voter is given an extra vote to augment his more strongly
> held preferences, so that if he gives it all to his first preference,
> that candidate gets two votes against all other candidates, but the
> second choice gets one vote against everyone ranked lower. On the other
> hand, if he gives half to his first choice and half to his second, then
> the second choice gets 1.5 against third and lower candidates, but the
> first gets 1.5 against the second and 2 against third and lower. If he
> gives it all to third, then the top three get 2 against everyone lower,
> but the preferences first > second > third all get 1, as does fourth >
> fifth. And so on. This would be more complicated and involve some
> interesting strategic choices. At first glance it would seem optimum to
> treat it as an approval cutoff. At least it would avoid the arbitrariness
> of assuming that the first vs. second preference is more important than
> second vs. third, and that by the same multiplier for every voter.

The endpoint of that line of thought, I think, is Cardinal Weighted 
Pairwise. The input is a rated (Range-style) ballot. Say, WLOG, that A 
is more highly rated than B. Then A beats B by (rating of A - rating of 
B). So, for instance, if on a 0-100 ballot:

A (100) > B (75) > C (20)

you get
A > B by 25
A > C by 80
B > C by 55.

Use your favorite method to find the winner, as CWP produces a Condorcet 
matrix that can be used by any method that employs the matrix alone 
(e.g, not Nanson, Baldwin, or similar).

If you want to vote nearly Approval-style, you would do something like

A (100) > B (99) > C (98) > D (2) > E (1) > F(0)

but that may not be optimal strategy; one could argue that in the same 
way that ranking Approval style is not optimal in ranked Condorcet 
methods, rating nearly Approval style isn't for CWP.