Hmm, I'm not sure about just the elite members and up... here's another idea, slightly harder to implement but I think it would be more fair. It's basically Johnny's idea but everyone can vote, but we could have some sort of ranking system such as a newbie voting counts as 1 vote up to an admin counting as 10 votes or something. I say this because I'm not an elite member and I believe I have enough ability to vote fairly, as do a lot of other people who aren't there yet. Plus it would take a LOT of pressure off the elite+ members since there are a lot more full/senior/whatever members than elite, or whatever. Or another idea based on that: if you have a high rating from others, you get a good say in how respected others are. If you have a low rating you only count as a fraction of someone with higher ratings. I don't know PHP but I know it wouldn't be that hard to add.
Plus there is a bit more than respect involved... for example, I respect some people who don't post here often... I don't know, there are also things such as people who have 'abused the system' but whose replies are always helpful. It's the best idea we have but it's still not really foolproof.
Elaborating on the system above:
If all members started with a rating of 5 with elite+ starting higher, every vote could average out the votes people have already submitted (apart from the first one which just replaces the 5). This averaged-out result allows people to vote the equivalent of that many times. This means if people have a high respect rating people believe they are knowledgeable enough to have their votes count more than others' with low ratings.
For example, if someone out of 3 votes has a rating of 5, and someone with a rating of 5 votes them as '8', their new rating would be (3x5 + 5x8)/8 ((votes x rating + member's rating x new rating)/total). This would make the new rating 55/8 or 6.875. I think this is more fair because everyone gets to vote and there is less pressure, but also more respected members get a good say in what happens. Hope you understand. If not, ask me and I'll explain it again.
Just a few things to think about.