Let's start with some goals1 for a reputation system on this site. IMHO, a network-wide meta site should...
...allow all sufficiently-engaged2 members of any site to vote indicating their agreement or disagreement on proposed feature changes to the software.
...allow the site to be self-moderating to roughly the same degree as any other site, without favoring one site's topics to the exclusion of others.
...reward any member who takes the time to assist other members in using the software, working together effectively with their peers, or improving the software itself.
1These may not be your goals, but I think they're reasonable ones.
2Intentionally undefined; should be > MINIMUM_REPUTATION.
Now, let's see how various approaches stack up...
Current status: MSE has its own reputation, privilege levels, respects association bonus
Anyone who has earned the association bonus (earned 200 points on at least one site) can vote up and down here. No one else can vote unless they earn at least 15 rep (upvote) or 100 rep (downvote) by asking or answering questions on this site. In practice, this means...
- 2,253 users have earned up-vote privileges on MSE, without having earned the association bonus on any other site
- 772 users have earned both up-vote and down-vote privileges on MSE, without having earned the association bonus on any other site.
- 127,987 users can both up-vote and down-vote here due to earning the association bonus on Stack Overflow, without having earned it on any other site.
- 71,686 users can both up-vote and down-vote here due to earning the association bonus on a site that isn't Stack Overflow, without having earned it on Stack Overflow.
- 287,365 users can both up-vote and down-vote here due to earning the association bonus on multiple sites including Stack Overflow.
I'd argue this is pretty balanced; the majority of users able to vote here have some experience on more than one site.
Flagging follows from #1 - if you can vote, you can flag. Close and reopen voting privileges must be earned on site; to see where these voters allegiances may lie, I decided to look at which sites other than MSE they've earned reputation on:
User has profiles on Close/Reopen voters
-------------------- -------------------
SE Only 8
SO and SE 534
Notably, no one with close/reopen privileges here has only earned reputation on MSE and SO.
- This is the only option that really satisfies goal #4.
Aggregate rep method: all sites' reputations summed up
Given you start off with 1 reputation per site where you have an account, a naive implementation of this would allow anyone to vote if only they took the time to create 100 accounts first.
Let's pretend we're not naive, and count only the reputation you earn on each site. This also discounts the association bonus, which would allow you to quickly gain close/reopen privileges by the same method once you'd earned 200 rep on any site.
First thing to consider here is that a LOT more people will be able to upvote than will be able to downvote. This is true for most sites, but notably isn't currently true here on MSE. Out of a whopping 2,294,999 potential voters, 1,511,639 of them would only be able to upvote. Broken down further...
User has profiles on UpvoteOnly FullVoters
-------------------- ---------- ----------
SE Only 433888 93727
SO and SE 153199 321512
SO Only 924617 368287
Again, this only looks at sites where each user has earned some reputation, excluding both the initial +1 and any +100 for the association bonus.
As in the current system, the majority of folks with full voting privileges would have some experience on multiple sites. Unlike the current system, upvoters would be skewed heavily toward Stack Overflow.
Again, the flagging privilege is the same as the upvote privilege - so, skewed toward SO. Using the same approach as above, but now considering the close/reopen privilege, we get:
User has profiles on Close/Reopen voters
-------------------- -------------------
SE Only 4917
SO and SE 51115
SO Only 11854
As with the current system, this is a fairly cosmopolitan group. It is, of course, MUCH larger.
- As your reputation is strictly based on things you do elsewhere, there's no reward for assisting users who can only participate on this meta.
Maximum rep
As with the previous approach, this results in a lot more upvoters. Here's how that breaks down by site:
User has profiles on UpvoteOnly FullVoters
-------------------- ---------- ----------
SE Only 434123 89364
SO and SE 164737 290458
SO Only 924177 368812
...And, again, folks with upvote privileges are dominated by those who've only participated on SO.
Same story for flagging, here's the breakdown for close/reopen votes:
User has profiles on Close/Reopen voters
-------------------- -------------------
SE Only 4506
SO and SE 45872
SO Only 12237
Still pretty balanced.
Again, nothing in this rep system encourages participation here.
Potential advantages
The biggest potential advantage to either of these approaches is the massive increase in potential voters. If we're discussing a feature that stands to affect a lot of low-rep ( < 200/rep) users, right now most of 'em can't vote - they have to try to persuade, with their words, like some sort of writer. Under either of these systems, hundreds of thousands of additional users would be able to vote to show their support, while somewhat less than half of them would also be able to vote to show their disapproval.
Potential problems
The biggest potential problem with either of these approaches is simply the raw volume of voters on Stack Overflow.
The second-biggest potential problem would be the massive skew between upvotes and downvotes. When considering agreement or disagreement, this could be an issue.
The smaller potential problem... Is that it becomes even less enticing to actually participate here. Because there's no reputation, because voting is skewed toward SO, because the only people who have to participate here are rank newbies who can't post on any other meta... And employees.
