Two minor items to get out of the way:
1. The Likud event yesterday was the usual uninspiring stuff. The result -- primaries will not be moved up (earlier) -- was very disappointing. I am partly to blame -- I only voted once.
2. What's the deal with yihyu leratzon in shma koleinu of selichos? Does anybody actually say it? If not, why is it there? Is this just a trick to expose baalei teshuvah?

Now for the main point.

There is a rule cited a number of times in the gemara that kol kavua ke-mechtza al mechtza dami. The canonical example is that if there are ten butcher stores in town and someone bought meat in one of them but does not know in which of the ten, we do not follow the usual principle of following the majority but rather it is treated as "mechtza al mechtza" (roughly translated as "50-50" but this is not quite right). By contrast, if a piece of meat is found on the street in that town, we follow the rule of kol de-parish mi-ruba parish. That is, we follow the majority.

Most commentators, including RGN, explain that for one reason or another (either logical or psychological), cases of kavua are such that the set from which the object originates (e.g. the ten stores) is rendered irrelevant so there is no majority to follow and we're left with a 50-50 problem (safek hashakul) by default. I'm quite certain that this is wrong.

The proper explanation, I believe, is that cases of kavua are such that the object in question is so inextricably part of the set (e.g. of the ten stores) that in assigning it some status, we must first assign the set of stores a status, namely "mixed", and the object in question then inherits that mixed status. In the case of parish, however, where the object has been isolated from the set, the status "mixed" is inappropriate (it's a single object) and we must therefore assign it a definite staus. So we assign it the majority status.

My explanation is the opposite of the usual one. Kavua means that the object is in the set, not out of the set. It inherits the set's "mixed" status only where bitul could not be applied to the set; where bitul is applicable the set is not regarded as mixed. According to this explanation, "mechtza al mechtza" does not mean 50-50 (safek hashakul) but rather is a definite status, like that of a mixture of two objects, one kosher and one not kosher (hence, "mechtza al mechtza").

There are numerous proofs that kavua is not treated as safek hashakul, but I'll spare you.