A fair bit over 1/2, I would guess. The only activities that I know of that gives you an odd number of reputation points are voting down (not being voted down) and getting an answer accepted. So among established users who have done both for a while, the proportion should be close to 1/2. The newbies will all have odd reputation.

No, being voted down gives you -2, while voting someone else down gives you -1.

If your reputation never passes over 100, you cannot have even reputation, which is why Harald's answer is obviously correct.

Okay, I'll admit that it's possible, but how many users came here and have posted only a few answers and had an odd number of them accepted?

Another way is to post an answer as a new user (you have 1 rep), somebody votes you down (still 1 rep), but then takes back their downvote (brings up to 3 rep). Then your answer wins a 100 point bounty (bringing you up to 103), you cast a downvote (down to 102), and get a post repeatedly flagged as spam, so it is automatically deleted an you're penalized 100 rep.

Wait, taking back a downvote increases the reputation of a 1-rep user? That doesn't seem like the intended behavior.

@fpqc: "If your reputation never passes over 100, you cannot have even reputation". This is surely false. The reason I made the original comment was that I was browsing through the users pages. From page 44:

http://mathoverflow.net/users?page=44

up to the last page (110 as I write) everyone has 1 rep. And then there's a jump to 3, and then to 5, etc etc. But someone has 10: check out

http://mathoverflow.net/users?page=41

sandwiched between all the 9s and 11s, and this guy has completely minimal activity. So what you write is surely wrong.

A bit more "seriously" (but not too seriously, hence the quotes): do MO reputations follow a power law, like John D. Cook says SO reputations do? (Yes, this is the same John D. Cook that is on MO.)

but how did he get ANY reputation? He has asked no questions, provided no answers. Is there any other way to get reputation?

That's a pretty good puzzle. This user posted an answer to an elementary homework-ish question that didn't belong on MO. The answer was accepted and got three downvotes before it was deleted by a moderator (which is the only way an accepted answer can get deleted). Technically the user "should have" reputation 1 since the post that earned the reputation no longer exists, and that's what it would come out to if a moderator triggered a reputation recalc on this user's account, but I'm not going to because it would be a shame to lose our only rep 10 user.

A bit more "seriously" (but not too seriously, hence the quotes): do MO reputations follow a power law

You can grab the database dump and run this command in a terminal to get a sorted list of reputations: awk -F '"' '{print $4}' users.xml | sort -n

@Jonas: looking at that user's reputation history graph, it appears he spent almost all his reputation on bounties. Not so long ago, he had something like 1700 reputation.

Yes, I think maybe he's trying to make a point that reputation does not matter to him or something? I really feel like we should discourage this sort of thing. I realize that Brian Conrad is doing it for a reason, but if people are really going to answer in comments to make a point, it just makes life a lot harder. Perhaps somebody could do something like turn off reputation/voting for people who are against it in principle, but what is currently being done is really irritating.

No, it's not. Please check Leonid's history. He has purposely drained his reputation and made all of his old posts community wiki. Since then, he has left all of his answers as comments. It is absolutely on topic.

I also wonder what made Leonid to get rid of all his reputation points (I was quite surprised by suddenly getting a 500 point bounty from him for an old answer, which, ironically, actually was just an echo of his answer to my question on AoPS). Maybe getting exactly 2 points seemed very cute to him. On the other hand, I find it rather amusing to see the BanAnaMan quote getting 35 upvotes and a full proof of a not completely trivial statement on the same page getting just 1 upvote. What is just amusing me could irritate him to the extent of dumping all his points, but it is just a wild guess. We should ask him directly if we want to know the answer.

Answering in comments is an interesting idea though. To squeeze a proof into 600 symbols without making it incomprehensible is quite a challenge. I should try it some day :-).

After you lose your reputation in such ways, do your powers go away? Such as, ability to retag, etc..

Hailong: +1

In fact, I propose that up-voted comments give more reputation than regular answers.... Or, rather, I prps tht up-vtd cmmts gv + rep than reg ans.