Perek 8

The differences between Beith Shamai and Beith Hillel in the meal.

kiddush and the order of the brachoth: 

B"S says that the blessing of the day comes first 

because: 

1. It is the sanctification of the day that causes the blessing over the wine 
1. cause takes precedence over effect
2. cause should precede effect
2. The day is, de facto, sanctified prior to the blessing on the wine
1. the order of blessings reflects the facts
2. the day would receive its blessing, even in the absences of wine ( or bread)
1. establishing the day's priority

 Beith Hillel says that blessing over the wine comes first 

because

•  The wine is a prerequisite to the kiddush

•   in the absence of wine, there would be no kiddush
•    necessity is recognized by precedence
• preventing the accidental (aborted) kiddush in the absence of wine
• wine is drunk more frequently than kiddush is said  
• frequency dictates precedence 

Fundamentally, B"H seems to accept the premise of B"S  ; and B"S accepts the ideas of B"H.
The question is which principle(s) are the priority