[EM] Re: Chain Climbing --> Chain Filling

[Jobst Heitzig]

Dear Ted!

You wrote:
> At first, I didn't understand what Frest meant by 'transitive, but I gather
> what he mans is, start a chain by adding the first candidate from the sorted
> list (Call that candidate A_i), to the new chain (call that B_j).  When adding
> a new candidate, start at the winning end, and test to see if the candidate
> defeats the first B_j.  If not, follow the list down to the next weaker
> candidate and test again.  Repeat until you find a defeated candidate.  Mark
> the location, but don't insert the A into the B list.
> 
> Then start testing from the losing end of the B list.  If the A candidate
> defeats the B candidate, continue following links to stronger B candidates.
> 
> If you end up at the same spot each time, the A candidate isn't in a cycle,
> and can be inserted.  Otherwise, you're effectively eliminating it from
> further consideration.  

Right.

> Thanks to both of your responses, I have an idea now that I think will work,
> and it should have (my) desired quality of encouraging generous approval
> cutoff and ranking of candidates below the cutoff.
> 
> Basically, the idea is simply Beatpath:  Break each cycle at the weakest link.
> But what should be the weakest link?  Why not call it the defeat made by the
> candidate with lowest approval?  We could call this Total Approval 
> Beatpath (TAB), but suggest a better name if you want.

I was thinking about this when writing the grand compromise proposal but
didn't propose it for some reason I don't remember, so I should give it
another thought. Did you prove any nice properties yet?

> This is similar to Jobst's grand compromise and James Green-Armytage's
> Approval-weighted Pairwise, but it isn't necessary to carry along a second
> pairwise array.

Right.

> Why might this be preferable to the other schemes mentioned?
> 
> - There is a strong disincentive to bullet vote or truncate (an exercise for
>   the reader, but consider the 35:A>B>>C, 25:B, 40:C, in which B voters ahve
>   truncated their true preference 25:B>A>>C).
> 
> - There is a strong incentive to be generous with approval cutoff -- you want
>   your nearest neighbors, if you will, to be considered earliest in the list.
> 
> - Much less strategic incentive to equal rank due to the approval cutoff.
>   Voters can express true preferences above the approval cutoff, AND below,
>   without fear of hurting their candidate.

Sounds promising, I'll think about that!

Yours, Jobst