If we are going to stick with the title of World Champion, I believe the best way to go about it is an annual double round robin tournament featuring the 10 highest rated players. Each player plays every other player twice, once with black, once with white, and the player with the most points (win = 1 point, draw = .5 points, loss = 0 points) wins.
The problem with having candidates matches--or really any qualifying tournaments--is that it heavily favors the current champion. Even a player as strong as Carlsen probably has a < 50% chance of winning a tournament(s)/series of matches against other top ranked players. This means that the top rated player may have a cumulative probability of <10% of gaining the title, while the current champion, even if ranked eighth like Anand currently is, could have a 40-50% chance of retaining the title.
This is why the title of World Champion should be based off a round robin tournament of all the top players. Chess already has a robust, accurate, and thoroughly tested and revised rating system. We ought to make more use of it.
[1] https://en.wikipedia.org/wiki/Elo_rating [2] http://www.gautamnarula.com/rating/ [3] https://play.google.com/store/apps/details?id=com.Centaurii....
Edit: Another problem with matches, as opposed to tournaments, is that transitivity doesn't exist in chess (as I've learned in my years of competitive play). If A regularly beats B, and B regularly beats C, it does not mean that A will regularly beat C. This is where matches are flawed--one player could have a particular weakness against the other and lose a match to him, while still being the strongest player in the world, as measured by his results against all the other top players (which is what the elo rating does).
On the other hand world championship matches have tradition. Most chess fans remember at least some of those. Maybe Fisher's match, maybe Kasparov-Karpov battles, maybe the one when Kasparov destroyed Anand or maybe the one when he banged his head (unsuccesfully) vs Kramnik's Berlin Wall. Matches are popular, they excite the audience, people talk about them long before and long after. The winner guarantees his place in history as a member of very narrow group of players (only 15 of them, for what is over 100 years of world championship history). People yelling "anachronism" don't understand what value this tradition have for chess players and chess fans around the world. Every sport has its own. Tennis has grand slams, football has the world cup, athletics has Olimpics. Chess has world championship matches and please all the armchair revolutionizers leave them alone.
Their personal 'career records' against other players in the field are also very hotly-contested. Nobody in the top 20 would give up a win or a draw against anyone else in the top 20 without a very serious fight.
Also, 1-vs-1 gets beyond the ongoing debate about whether draws should count for 0.5 or less, which is nice. More specifically, the question of whether and how to reward being consistent (many draws, few wins and fewer losses) but rarely brilliant versus uneven but generally great isn't as pressing in a match, since it'd (likely) end up not mattering.
Your comment about rewarding consistent but rarely brilliant versus uneven but great bring up another interesting nuance about matches versus tournaments. Fischer complained that once a player gets ahead in a match, there is no motivation to play fighting chess because every half point bring him closer to winning a match, and players are therefore incentivized to play for a draw. In a tournament, that usually isn't the case since the leader will typically have a few players nipping at his heels.
This tendency could be discouraged by making wins more weighted realtively than draws: win = 2 points (or, may be 1.5 pts), draw = .5 pts, loss = 0 pts.
Rankings are seen to be pretty accurate when you look at who gets through each Grand Slam round.
1) The number of points awarded for tournament performance seems pretty arbitrary. For instance, winning a grand slam results in 2000 points, while coming in second is worth 1200 points and coming in third/fourth is worth 720 points [1]. Is coming in second really only 60% as good as coming in first? It's hard to believe there's some deep, evidence-based rationale behind picking these precise values.
2) The tournament hierarchy is also arbitrary. A win at a Grand Slam is worth 2000 points, while winning gold in the Olympics is worth 750 points [1]. Why? Shouldn't the points awarded be based purely on the strength of your competition?
There are other issues, such as rewarding someone who plays a ton of tournaments with mediocre performances, versus someone who plays less often but with better results (though this is somewhat offset with the difference in points awarded based on performance). I've had friends complain about similar systems in video games-- apparently in Halo the top rung of players is full of mediocre players who play a lot, racking up points in the process and moving up the ranks.
Since tennis doesn't have a concept of "World Champion," I think the sport would be better served to switch to the Elo system like chess. It provides an accurate comparison of relative player strengths, it does a decent job dealing with the plays a lot vs. better results problem, and it functions exactly the same regardless of the tournament you play in-- you only get more points if you perform better or play stronger opponents. Another interesting tidbit is that it gives you a statistical probability of any player beating any other, which isn't possible under the ATP system.
[1] https://en.wikipedia.org/wiki/ATP_ranking
Edit: One other problem with ATP points--since most tennis tournaments are knockout (as opposed to swiss pairings used in chess tournaments [2]) the only thing you know for sure is that the winner as the best player in the tournament, assuming tennis results are transitive (a big assumption). But if you're unlucky enough to be in the knockout branch that features the best player, you could be knocked out earlier than your would otherwise merit, which means you could get far less points than you deserve.
The whole point of the article is that the current world champion isn't the strongest player in the world. In fact, there are several players that are stronger than he.
Winning Wimbledon in tennis is prestigious because of all the players who won it before and because all the great matches played there. It's because of tradition and living memories. It's the same in chess. The author proposes just scratching it off. His idea is similar to getting rid of Wimbledon and creating some new tournament in Dubai instead.
He holds the title which because of its tradition and all the battles fought for it has big value for chess fans around the world.
You're begging the question here. The author is saying that the title should not have so much value.
New system might be fairer, better, w/e but just because it's new you just lost many fans, interest and sponsors.
The author is too hung up on the rating being an absolute measure of ability, but Elo has its own set of problems (e.g. rating inflation). Anand has very little incentive to play open tournaments and compete for rating points when he can instead spend all his effort defending his title for a big payout.
There is often a difference between World Champion and World Number One.
However the Olympic marathon is special because it is completely different. In most other marathons, runners care more about their time than about winning, because it determines whether/how much they get paid to run other marathons. In the Olympics, on the other hand, nobody cares about times.
Similarly, the classical one on one match for the world championship in chess is different from tournament play. In the former, you have to beat the strongest player in the world; in the latter, you have to beat the weaker players or top players with an off day and prevent getting beaten on your off day or by stronger players.
It's the same in soccer. There, there are both national competitions where consistently beating weaker teams is the way to win and national knock out tournaments where one has to beat the best team to win.
And yes, knock out tournaments are more likely to have the weaker team win, but that can make them more attractive, as determining the strongest player may take a long time (for an example, see http://en.wikipedia.org/wiki/World_Chess_Championship_1984)
IMO, the 'only' problem with the chess world championship is that the organization is a shambles. Fix that, and nobody will complain that the knock out tournament is different from regular tournaments.