[EM] Philosophical question for IRV experts

[Paul Kislanko]

Thank you very much! That is exactly the answer I was looking for, and
confimed my experience with playing around with it. 
> 
> Ah, I get it. This isn't like IRV so much as Bucklin. That is 
> definitely
> an easier way to go. With IRV, in the above scenario, only 
> the "votes for
> second" of the 9 C voters would be added in. So using the table format
> that you're using, it wouldn't be possible to determine the IRV winner
> in this scenario, because we need to know who the 9 C voters 
> placed second.

Thanks very much. Perhaps instead of asking for input from "IRV" experts I
should've asked for help in general with iterative methods. For my purposes
(since I'm not electing anyone, just trying to order a list) I think it is
ok to say that if there is no majority in column n, the results for column
n+1 should be used to order however many candidates have majorities,
regardless of whether they were "in play" in column n.
> 
> With Bucklin, all votes for second are added in and actually 
> B would receive 
> 1st.  It's also possible to pick A as you have done, since A started
> with more votes.

I would pick B as you suggest - in my original table (not the email
example), there was a majority winner for positions 1, 2, and 3. In my
example, when adding in 2nd place votes, I also selected B as you suggest.

> 
> Douglas Woodall has suggested a method called QLTD (Quota-Limited 
> Trickle-Down) which elects the one of the two which needs the smallest
> percentage of its votes-for-second to reach half the votes. In this
> case A needs 1.5 of its 15 new votes (10%) while B needs 7.5 of its 22
> new votes (34.1%) so A would be elected.

This is probably too complicated for my trivial task. All I want to be able
to say is that "more than half of the voters ranked this team this high or
higher." 

> In the example you attached, I would definitely rank Miami 
> ahead of LSU,
> since Miami has an earlier majority.

I would too, having seen both teams play. However, here's the "philosophical
problem" bit. Suppose I'm trying to find the team rated 11th and I've had to
get to column 14 to get to where one team has a majority for 11th, but also
four other teams have a majority at a column 14. 

My experience suggests that 11,12,13, and 14 should all come from column 14,
but something tells me before I assign rank 15 to a team I should add in the
votes for #15, and that might move the team ranked 15th based upon column 14
worse than 15th.

This is close to...
> 
> In general, what I would do is have 25 columns corresponding 
> to each slot
> that the voters had. For each team, shade the square in the column at
> which they got a majority, so that more than one square may be shaded
> per column. Then use whatever rule you've chosen to break 
> ties among teams
> receiving a majority in the same column.
> 
> It won't look as nice, but I think it will make more sense 
> than what you
> attached. For example, under column 5, three teams receive majorities.
> But California and Utah are shaded under columns 6 and 7, after votes
> corresponding to those ranks have also been added in. That seems to me
> to be confusing and harder to explain.
> 
> I hope that is interesting or helpful.

Indeed. You've convinced me that earliest majority matters most, and the
solution to my philosophical question is that a team ranked 15th by a
majority of voters at column 14 should remain 15th even if there's a team
with a higher majority for 15th in column 15.

I do not know that is easier to explain, but it conforms to my single
criterion "a majority of voters ranked this team this high OR HIGHER" so I
can get away with it without having to explain if I'm lucky....