[EM] The critical importance of Precinct Summability.

[Kristofer Munsterhjelm]

On 2024-08-08 20:23, Chris Benham wrote:

> Why do you "agree"?
> 
> I've long regarded people running around with their hair on fire yelling 
> about "precinct summability" to be simply a propaganda furphy against 
> Hare RCV, the good single-winner method that currently has the most 
> traction as a reform proposal.
> 
> Why is determining which candidate has the fewest top-preference votes 
> inherently more problematic than determining which candidate has the 
> most top-preference votes?

It shouldn't be, and I agree that a method that elects, at random, 
someone who isn't the Plurality loser would be summable.

However, IRV doesn't just require one to determine the Plurality loser. 
If you want to get the IRV winner non-interactively, you need the first 
preference counts for every sub-election, and that requires exponential 
space.

Summability implies, at least for low orders, that errors are in some 
sense manageable. You can subtract an erroneous count and add another; 
and if you have access to every count but one corrupted instance, you 
can make a reasonable judgement about the outcome of the election if 
it's not too close.

But if you don't have summability, then that becomes much harder. 
Suppose that an erroneous contribution to the count leads X to be 
eliminated instead of Y. Then you can't easily know what impact that has 
on the election winner because the elimination of X can lead the 
elimination process on a very different path of eliminations than if Y 
were eliminated.

Even if you later find the true count for the district that were in 
error, that doesn't necessarily help you; all you know is that Y should 
have been eliminated instead of X. But the counts for the sub-election 
{A, B, Y} need not have much relation to the counts for {A, B, X}.

So having all the data lets you correct for errors and check 
counterfactuals/what-ifs without having to rerun the whole process. And 
low-order polynomial summability makes it easy to keep and investigate 
all the data that the method uses to determine the outcome.

-km