[EM] Philosophical question for IRV experts

[Paul Kislanko]

Thanks very much. Let me clarify my question...

> > Which approach is right?
> 
> The only non-PR way I can think to do IRV to obtain a ranking of the
> candidates is to
> 1. find the IRV winner
> 2. delete him from all the ballots as though he hadn't been an option
> 3. repeat.
> 
> This seems like too much work to me, so I wouldn't suggest 
> using IRV for
> this.
> 
> The method you describe is interesting, though. In the single-winner
> case, it seems equivalent to Plurality.

It is almost like plurality plus run-offs, because a team doesn't get ranked
x until a majority vote it higher than all remaining teams.

For example, with 65 voters, suppose the first place votes are A = 31; B=25,
C=9. There's no majority, so votes for second are added in. A=31+15=46;
B=25+22=47; C=9+28=37. Now B leads A and both have majorities.

My question is, at this point is it better to award only 1st to A and then
proceed to the next round, or go ahead and award 2nd to B since B also has a
majority?

It's not much work the way I do this. Let each time have its own row in a
matrix that has element (team),j = votes for (team) for all ranks from 1 to
j inclusive. Then sort column 1, if there's a winner sort remaining rows on
column 2, etc.

The philosophical question comes up because if there's a tie at any step,
going to the next column can result in a "win" for the rank in question by a
team that was not involved in the tie, and this made me think it would
always be right to let an iteration determine only one "winner". A few uses,
though, made me think that is less desirable than I'd thought.