[EM] Simpson-Kramer

[Russ Paielli]

MIKE OSSIPOFF nkklrp-at-hotmail.com |EMlist| wrote:
> 
> Dear Markus--
> 
> Levin & Nalebuff said:
> 
>> For our purposes, we assume that voters rank all the
>> candidates on their ballots, and do not score candidates
>> as ties

I haven't followed this discussion, but let me give my view based on my 
understanding of the English language. I'll assume that the method being 
discussed above by Levin and Nalebuff is the Simpson-Kramer method.

If the Simpson-Kramer method does *not* allow truncation, then Levin and 
Nalebuff had no need to make the statement above. That statement implies 
that either (a) Simpson-Kramer allows truncation or, less likely, (b) 
they are not sure. Why would they explicitly state an assumption that is 
known to be true? If you were writing about baseball, would you say 
explicitly that, "For our purposes, we assume that three strikes is an out"?

> 
> I reply:
> 
> Here are two possibilities: for what "For our purposes..."
> 
> 1. "For our purposes..." means that Levin & Nalebuff are telling what 
> Simpson-Kramer (and other methods)  would be if all the rankings were 
> complete. But if rankins aren't all complete, Simpson-Kramer could mean 
> something else, some unknown, unstated meaning.

No, the definition of the Simpson-Kramer method does not depend at all 
on Levin and Nalebuff's simplifying assumption about how voters choose 
use it within the rules. It is possible that all voters will choose not 
to truncate even if they are allowed to do so, which is what they are 
assuming.

> 2. "For our purposes..." means "For the purposes of defining the methods 
> defined in this paper", in which case Simpson-Kramer is not defined for 
> sets of rankings that include some incomplete rankings.
> Then Simposn-Kramer is undefined when there's truncation.

Wrong again. It simply means that Levin and Nalebuff chose, for whatever 
reason, not to address the effects of truncation. That may or may not be 
reasonable, but it has nothing to do with the definition of the 
Simpson-Kramer method itself, nor their understanding of that definition.