A 3000 could easily beat a 2000, but could a 4000 easily beat a 3000?

Even if that is the case, and it is linear, there will be a certain level where both players are playing absolutely perfect moves. Even if the difference between 3500 and 3000 is the same as between 1000 and 1500, after say, 1000000000000000000000000000000000000000^100000000000000000, the player can't get any better =maximum rating.

True, i was just making a point that even though players were at the maximum possible rating, the game might not end in a draw because we don't know if chess is a theoretically drawn game. I understand your point about the ratings, I was just saying that it is a misconception to think that 2 players making perfect moves results in a drawn game as opposed to one side winning.

For the love of God, no, it's no linear.

It's logarithmic. A basic wiki search would tell you this.

What this means is a 1000 point difference will hardly score better than a million point difference.

It does not mean a ten thousand rated player will be nearly equal when facing a 1 million rated player. That is by definition not possible.

I agree, we don't know if perfect play is a draw.

But it very likely is.

Correct, based on what we know about chess there is probably a maximum rating (current estimates put it somewhere between 3500-4500) at which all games will be a draw, or white always wins so by alternating colors two equal top players are still gaining and losing equivalent numbers of points. A much higher rated player will lose points if they draw against a lower rated player, the system really is linear in that regard, and if you're not winning 99.7% of your games against an opponent then you cannot be 1000 points higher. 

I don't know the algorithm, but I never thought chess ability was linear. I thought it was exponential.

Not necessarily, White has that tempo, OR white could be in Zugzwang from the very beginning of the game!

exponential, logarithmic, (basically) the same thing

It's probably higher than that. There are over 10^1000000000000 possible chess GAMES. Current engines can only calculate a mere billion positions per second, a perfect payer would be able to calculate GOOGOLS of positions every move.

That is true, and I apologize for not being specific enough. The point I'm making is that the win percentage is directly correlated (linear) to the difference in rating regardless of whether that difference is between a 4000 and 3000 or between a 2000 and 1000 level player. But yes, as the difference increases the percentage of wins moves as a log function. 

I think it would be a draw. 

I wonder how they calculated that function?

I agree. I think there is the highest of chance of chess being a draw with perfect play, a less high chance of white having a winning tempo, and a low chance of white being in zugzwang from the beginning of the game.

http://www.glicko.net/glicko/glicko.pdf

Read that if you want the full technical explanation of how the rating system works. The function is defined so that there can be unlimited players added into a game environment, and those who keep winning will continue to increase their score relative to everyone else. This function also allows the calculation of the table from page 3 of this thread, which shows that win percentages increase on a logarithmic scale based on rating differences, but remain constant regardless of where in the overall scale that difference is found. 

Got it. Also, does it make much of a difference if you rate a person after a cumulative tournament of 6-7 games then if you rate them after each individual game?

It makes some, look up 'live ratings' for the top 10 players in the world and you'll see their current estimated strength is often off by up to 10 points from their current rating. And if you follow tournament results as they're posted on this site you'll almost always see a 'performance' rating, which can swing pretty wildly if players are having really good or bad games. This is smoothed out by the way players ratings are adjusted relative to each other after the tournament. 

In other words, is rating people after each individual game commutative with rating them after every X number of games? I'm too lazy to do the math.

Similar, but not exactly the same. The way tournament ratings are calculated effectively change your rating relative to the post-tournament rating of your opponents, so say you beat an opponent rated 800, but they had a great tournament and gained 100 points, your rating after the tournament would be adjusted as though you beat them when they were rated 900. This also gets into provisional ratings and glicko numbers, which allow for larger gains and losses of rating points for players who haven't played a lot of rated games and therefore their ratings are regarded as less certain so they can swing more widely and will impact your rating less than someone who has played thousands of games and can be pretty confident where their rating falls. 

I get the difference. It's more of about average than accuracy in tournament ratings. How do they keep track of all this. They must have one hell of a computer program!

I should also note that while the glicko system I referenced earlier is the basis for the chess rating systems, and the basic facts about relative strengths are the same, the exact implementation can vary whether you're talking about FIDE, USCF, or chess.com. The exact ratings also are highly dependent on the number of people in the system, what the 'average' rating assigned to a beginner is, and who those people are. So someone may be 2100 USCF but only 2000 FIDE because they're being rated against different players, but they'll still beat a 1100 USCF player as easily as they'll beat a 1000 FIDE player.