[EM] In defense of the Electoral College (was Re: Making a Bad Thing Worse)

[Kristofer Munsterhjelm]

>> A possible tiebreaker for same names would be to prepend (or append) 
>> the state of origin to each candidate name. In case two have the same 
>> name in the same state, the state decides who gets to be "number one" 
>> and "number two". These corner cases would be extremely unlikely, but 
>> it doesn't hurt to specify them.
> 
> My point was that this is a problem affecting ANY election method, thus 
> not needing special attention for Condorcet.

That's true, but for methods that only need an array (like Plurality, or 
a weighted positional method where the method was agreed upon in 
advance), this happens more or less informally. States don't pass around 
explicit arrays with candidates in specific orders when tallying 
Presidential votes, they just say "Bush got this many, Gore got that many".

The other side of the coin is that non-summable methods would be in real 
trouble. Any compact solution defaulting to a method that isn't summable 
would somehow have to set up an infrastructure (either in counting or in 
communication), wherein a central unit coordinates.

>> The results should be the same with a plain merge as with a single 
>> count, since a Condorcet matrix entry cm[a][b] just lists how many 
>> voters ranked A > B. Consider voters that couldn't vote on a given 
>> candidate as if they had no effective preference regarding that 
>> candidate. Then, by including the results of some other Condorcet 
>> matrix, if A and B wasn't on that other matrix, cm[a][b] won't change.
>>
> Not being sure what you mean by "simple merge", I will repeat my demand.
> 
> For example, assume A is a write-in which CANNOT be planned on but must 
> be adjusted for when counting the ballots.  The national NxN array must 
> include A reflecting proper counts for all votes in the US.  True that 
> such an A is  unlikely, but to be expected more if you assume it will 
> never happen.

A simple merge sorts the arrays by name (and tie-breaking info, like 
name of state of origin). Then it merges the data, summing cells if the 
candidate in question exists in both matrices, otherwise inserting the 
relevant rows and colums in the right place so that the result (merged) 
matrix is still sorted.

For instance, consider these matrices:

x A  B
A -- 30
B 35 --

and

x A  C
A -- 100
C 25 --

The result is

x A  B  C
A -- 30 100
B 35 -- 0
C 25 0  --

and the expanded matrix stays sorted. Individual write-ins can be 
handled by considering each voter's ballot as a Condorcet matrix, then 
merging that in as above. In extreme case (each voter names a different 
write-in), that would make the matrix expand by a lot, but if that's a 
concern, sparse representation formats can be used.