This provides a solution for the case where you've got 60 points, the only other guy yet to be eliminated has 30, and one of the eliminated players has 40. Now you've got an incentive to play on (and thus try to keep the last surviving opponent in third), rather than hand him 20 points by immediately claiming victory.
Of course, in the case where you have 60, one of the eliminated players has 55, and the other surviving player has 30, the surviving player will actually like this change as the immediate 20 points wouldn't be enough for second but now he has a chance to pick up 26 points - and if you mess up badly, he's got an outside shot at first.
Where it doesn't help is if, in those situations, you've got much less material than the other surviving player and thus stand no chance of being the last man standing. Then you're still in the position of claiming a win to take first, but having the option, at no cost to yourself other than taking a couple minutes of your time, to let the opponent take one of your pieces before you claim the win to let him steal second.
Suggestion: The winner's rating is boosted by +25%, if he is the last man standing
Interesting idea... but I feel this feeds into the misconception of "rating-as-currency" (e.g. earned through "hard work" or "good sportsmanship") rather than "rating-as-skill-indicator" (e.g. an estimator of which of two ranked players is more likely to win). In a good rating system, if a 1600 player is pitted against three 1400 players, that should mean the 1600 player is the most likely to win; not that the 1600 player is less likely to win, but if they do, they're more likely to battle to be the "last-man-standing".
The reason a high-rating is sought after (in *any* sport/competition, not just four-player-chess) is the bragging rights; the ability to back up the claim of "yes, I really am good at this game". If the rating system allows any factor unrelated to skill level (that is, a given player's ability to win) to influence rating a player is assigned, it will reduce the accuracy and meaningfulness of the ratings. This, in turn, would dilute the intrinsic value of having a high rating. Which, ironically, would diminish the original motivation to boost one's rating by aiming to be the "last man standing".
@MGleason fair points. The first case you mentioned (less than 20 points between 2nd and 3rd) is happening to me quite often. I have yet to experience a case of the second type (more than 20 points between 2nd and 3rd). The third case is a problem that my suggestion indeed leaves unsolved!
Currently if you are about to die early (to be the first or second dead player), it's in your best interests to hurt anyone else except the leader. You are not going to outscore him, so you'd better try to keep the material and the score of the other players as low as you can. For example if you are checked by the leader and your queen is threatened by someone else, block the check with your queen to let him capture her. Or resign, so that your king will be captured by the leader. My suggestion complicates this decision, since you are now facing the danger of extra damage to your rating, if the leader happens to be the last man standing.
@kevinkirkpat I share your concerns about ratings. I think it's a devilish invention really. :-) If the rating was primarily an indicator of skill, you shouldn't be able to gain 60 points by winning one game. You didn't became so much better after 20 minutes of play! But it seems that most players love the idea of manipulating their rating, and would be dissatisfied by a minimal -but far more realistic- change of around 2-3 rating points. So my suggestion partly plays with the realities of human psychology. I am pretty sure that ALL players will happily take the chance to boost their ratings, and no one will think «no, it's not fair to gain rating this way, let's claim victory now». For the time being, beyond the fun of playing, we do not have anything else to fight for except for our precious little rating number. And for a place in the Top-10 list, if we are skilled, committed, persistent and lucky!
I don't know, it seems like an unnatural solution
I would propose 2 solutions to this problem:
1: auto claim win. No playing on when a playeris over 20 points ahead of his opponent ( heads up only)
2: No resignation whatsoever: You play on untill you are mated. You can't claim a win at all. That's the solution I would like to see, personally.
Claim win is unfair for the two players that have been already eliminated, since it gives +20 to the finalist without deserving it (IMHO). It is equally unfair either triggered manually or automatically.
"No resignation" is unrealistic. The leader can just win by timeout, which is worse.
But the other finalist might deserve it. He hasn't played as aggressively earlier, but maybe now he's in a position to destroy the last remaining opponent. It might not be enough for first, but is good for a solid second. If you remove the option to claim win, in that case, it won't change the result, and it might even result in him getting even more points.
@Skeftomilos I think #1 is a workable solution but I take issue (*In a good way 
) with this: " His extra rating points will be deducted from his opponents ratings (in other words their rating losses will be increased)."
I don't think it is fair to the losers to drop lower in ratings because the top person gets to control the outcome for them. Why should some people have to lose less in some games and others lose more points? If you had said the first place gets more points and left it at that no deduct from the losers side then I believe that solves the issue.. That said, I'm not sure how balance the point system works and if that's even possible or if it messes up the entire balancing of the system?
Yea, it sounds a bit strange, but I think it's fair. If a player's performance is so great that manages to dominate his opponents at both levels, points and army, it is only fair to be rewarded with bonus rating. This rating must come from somewhere, and I can't think of any other rating source than the rating of his opponents!
Keep in mind that the damage will be fairly distributed between them, so hopefully it won't be so terrible.
The +20 to the second remaining player is not as undeserved as some people are making it out to be. After all the person outlasted two-thirds of his opponents.
@losingforever the third survivor outlasted one-third of his opponents, and got 0 points for his achievement. Isn't it unfair?
Also, if outlasting two-thirds of your opponents worth 20 points, then you should get this bonus no matter what. Currently you get this bonus only if you checkmate the winner, or if he resign (claim-win in other words). But if he proceed to checkmate you, you get 0 points. Isn't it inconsistent?
Lastly, giving bonuses for outlasting opponents is against the spirit of the point system. This system was introduced precisely to discourage passive/ultra-defensive play, which is the dominant strategy when playing under the simple last-man-standing-wins rule.
Your, while original idea, has a flaw: more rating inflation (Current system is already inflationary. Just add points given and add points taken away in a random game.) You add points but you don't take away points from rating pool. A simple idea would fix that: Add 3 pts to last standing, 1 pt to second, subtract 1 from 3rd and 3 from 4th. Or any other progression....
@AndreD2 a rating boost of 2 extra points may be too small for a winning player to continue fighting. The temptation to "Claim victory" and start immediately another game may be too strong. Currently the winner is rewarded by at least 50 rating points (when playing against opponents of comparable strength) and 2 extra points is just 4% of that.
You didn't address my main concern, rating inflation. As I said, progression can be adjusted, as long as rating pool stays close to zero gain.
Rating inflation is not an issue because, as I said, winner's extra rating points will be deducted from his opponents ratings (in other words their rating losses will be increased).
FFA is really just a flawed game. Between cheating and blind opponents who dont understand anything about a game and ruin it through their idiocy, and not knowing if a player will see the moves they should play if you decide to attack a player, there isn't any room for playing the best moves. You give mate, or a free queen to a player, and he doesnt even see it and your game is ruined... Really, team play is way more interesting. In team, weak moves are punished as they should be in a chess game, cheating is literally impossible, and the way ratings are calculated doesnt matter because the best team win and the worse team loses anyway.
This suggestion aims to keep the game competitive at its last stage, when only 2 players are still in the game, and one of them outscores the other one by more than 20 points. Currently the leader has no incentive to prolong the fight, since he has secured the victory. The temptation to press the "Claim victory" button is very strong, and is not unheard for his opponent actually asking him to do so in the chat! This not only makes for an anticlimactic finish, but it's also unfair for the players who didn't make it to the final-round, but managed to gather a fair amount of points before being eliminated. The current system essentially offers an undeserved +20 bonus to the finalist of the game, for no particular reason. So I suggest to give an incentive to the leader to continue fighting. If he manages to checkmate his last opponent, or force him to resign, his rating gains will be boosted by +25%. His extra rating points will be deducted from his opponents ratings (in other words their rating losses will be increased). This means that the stakes are now higher for his last competitor. If he manages to checkmate the leader (or force him to claim victory) will probably finish in the honorable second place. Otherwise he may finish 3rd, suffering extra rating losses on top of that!
What do you think? Opinions are welcome!