Simple Betting Dilution Mechanic

I think he wants the score to resemble the number of tokens more.

But applying the way you described is a good start.
Perhaps substracting until a desired minimum score is reached?

23 points?
3 tokens, but 4 against: 23-4=19, 15, 11
2 tokens, but 5 against: 23-5=18, 13, 8
2 times 1 token, but 6 against: 23-6=17, 11, 5(minimum reached)

So 11, 8 and 2 times 5.

Actually, now that I think about it. It makes no sense to subtract. (it wont work) The total score doesn't compare either. The difference in dividing is bigger than supposed to be. Unless you want to have that.
My example actually makes it way more complicated.

You calculation of 9, 6 and 2 times 3 is simple and perfect enough. Logical too.
If you are troubled with the remaining 2 score points in your 23 example. Simple have them assigned to the player with the highest number of tokens.

With higher scores, it could be that the remaining score is higher then the number of tokens for player 1. Then simply give the rest to player 2 and so on.

With a tied in tokens while a wrong number remains. Simply discard them. Or at least distribute 1 to each that have the same amount of tokens.

So with 27 score points. The points awarded are 12, 8, and 2 times 3. With a discard of 1.

This will encourage players to be just a little bit ahead of other players when placing tokens.

Player 3 OR 4 might get another token placed. In that case they will be fighting with player 2 about the score points. Both having 2 tokens, might still get them both 1 score point. If another score point remains, this one gets discarded. While ignoring the last player.

Perhaps there's a way to make it so that certain limits provide X number of points per token?

For example:

Have benchmarks on a simple chart for the levels.
If a faction earns 10 points or more points you gain 1 point per token of yours.
" " 15 points " " 2 per token.
" " 20 points " " 3 per token.
etc. until it's balanced as you see fit. Perhaps add a bonus for supplying a certain number, or for having the most on 1 faction.

In the case above, the faction earned 23 which would break the 20 point limit, so each token earns 3 per player.
Player 1 earns 9 (plus a possible bonus for supplying the most).
Player 2 earns 6.
Player 3 & 4 earn 3 each.

Funny how it ended up providing the exact same points as your method, but without the hassle of dividing, rounding, and doing multiple steps, eh?

I'd have to see how the other elements of gameplay would effect it, but essentially it gives incentive to really invest in certain colors and see them succeed since you don't get points on a direct relation, but rather you get points for passing certain benchmarks. It's an emotional moment (in a good way) seeing your faction just 1 point shy of a benchmark and potentially losing the game because of it!

Have you played Colossal Arena by Reiner Knizia?
http://boardgamegeek.com/boardgame/105/colossal-arena
This game fits the description of what you're trying to achieve, you should check it out.