[CardinalSagehen]

Here's the bottom line:

Cases where a Utah win helps Stanford:
1) UW wins the head-to-head, but has one other conference loss (plus Utah); Stanford's only conference loss is to UW - Utah win sends Stanford to the Pac-12 championship.
2) Stanford wins the head-to-head, but has two other conference losses; UW's loss to Stanford is its only other conference loss (beyond Utah); no other Pac-12 North team has a record that sends it to the P12 championship - Utah win sends Stanford to the Pac-12 championship.
3) Neither Stanford nor UW are going to the Pac-12 championship, but otherwise have similar resumes.  A Utah win sends Stanford to a better bowl than UW.

Cases where a UW win helps Stanford:
1) Stanford is a one-loss Pac-12 champion and there are 5 P5 one-loss champions (or an SEC one-loss non-champion).  A win over a highly ranked UW might give Stanford a better resume compared to at least one of the other one-loss champions.
2) Stanford is a two-loss Pac-12 champion and there is at least one other two-loss P5 champion and (and no one loss P5 non-champions).  See above.
3) Stanford is not the Pac-12 champion, but is being considered for a NY6 bowl (and the Pac-12 champion will not be going to the playoff).  Playing a more highly rated UW would give Stanford a better resume compared to other non-champions being considered for a NY6 bowl.
4) Stanford is not going to the Pac-12 championship, but Stanford and Utah have otherwise similar resumes.  A Utah loss sends Stanford to a better bowl than Utah.

It's hard to do all the permutations and hypotheticals, so I default to "which team do I like more".  Go Utes!

BC

I agree with the conclusion that it’s very hard to know at this point, so just pick the team you like better.  

But in looking at your list, I’m left leaning toward my original premise - that much better things can happen for us if we first win the North.  The cases for a Utah win seem stronger and more concrete in that regard.  We just saw case #1 in 2015 with respect to Oregon v. Stanford for the North.  

In addition, nearly all of the cases for a UW win are predicated on the assumption that UW will actually prove to be a better team than Utah by the end of the season, which is probable but not yet known.  UW already has a stain on its record vs. the almighty SEC - it doesn’t work out so badly if they don’t turn out to be one of the conference’s top couple teams.  

All of this is just another roundabout way to say, who the heck knows, but Go Utes!

[CardinalSagehen]

Here's the bottom line:

Cases where a Utah win helps Stanford:
1) UW wins the head-to-head, but has one other conference loss (plus Utah); Stanford's only conference loss is to UW - Utah win sends Stanford to the Pac-12 championship.
2) Stanford wins the head-to-head, but has two other conference losses; UW's loss to Stanford is its only other conference loss (beyond Utah); no other Pac-12 North team has a record that sends it to the P12 championship - Utah win sends Stanford to the Pac-12 championship.
3) Neither Stanford nor UW are going to the Pac-12 championship, but otherwise have similar resumes.  A Utah win sends Stanford to a better bowl than UW.

Cases where a UW win helps Stanford:
1) Stanford is a one-loss Pac-12 champion and there are 5 P5 one-loss champions (or an SEC one-loss non-champion).  A win over a highly ranked UW might give Stanford a better resume compared to at least one of the other one-loss champions.
2) Stanford is a two-loss Pac-12 champion and there is at least one other two-loss P5 champion and (and no one loss P5 non-champions).  See above.
3) Stanford is not the Pac-12 champion, but is being considered for a NY6 bowl (and the Pac-12 champion will not be going to the playoff).  Playing a more highly rated UW would give Stanford a better resume compared to other non-champions being considered for a NY6 bowl.
4) Stanford is not going to the Pac-12 championship, but Stanford and Utah have otherwise similar resumes.  A Utah loss sends Stanford to a better bowl than Utah.

It's hard to do all the permutations and hypotheticals, so I default to "which team do I like more".  Go Utes!

BC

I agree with the conclusion that it’s very hard to know at this point, so just pick the team you like better.  

But in looking at your list, I’m left leaning toward my original premise - that much better things can happen for us if we first win the North.  The cases for a Utah win seem stronger and more concrete in that regard.  We just saw case #1 in 2015 with respect to Oregon v. Stanford for the North.  

In addition, nearly all of the cases for a UW win are predicated on the assumption that UW will actually prove to be a better team than Utah by the end of the season, which is probable but not yet known.  UW already has a stain on its record vs. the almighty SEC - it doesn’t work out so badly if they don’t turn out to be one of the conference’s top couple teams.  

All of this is just another roundabout way to say, who the heck knows, but Go Utes!