[EM] Write-ins break condorcet summability

[bql at bolson.org]

How do you compare a new entry all the ones that came before? Having a 
policy for incomplete ballots isn't good enough because it doesn't compare 
a new name to the other names on ballots before the first ballot to 
include a new write-in candidate. So, there must always be a first pass 
through all the ballots to collect all the names.

There is an out depending on the partial ballot policy. I'm trying to 
write a ratings based implementation with signed ratings. Since voters can 
express positive or negative I think it's fair to assign zero to unvoted 
choices. This breaks summability because on encountering a new name you 
can't go back and compare to ratings. If however an unrated choice is 
assumed to be lower than all the rest, it's possible to record a new name 
as having lost to every other choice on as many ballots as there have 
been.

But I think the 'no-vote is negative-infitiy' policy pretty poorly 
represents what voters want.

If anyone can poke a hole in this and suggest a one-pass summable 
condorcet with write-ins algorithm I'd love to hear it.

Practically in the system I'm writing making it collect write-in names 
before counting votes won't be a problem.

Also, I'll note that Approval is still summable with write-ins.

Brian Olson
http://bolson.org/