Kirsan Ilyumzhinov, who became FIDE President in 1995, wanted to arrange the match between Karpov and Kasparov:

“The split in chess community was so big that its very existence was threatened,” Ilyumzhinov said. “I managed to meet with two "Ks" in Elista.
I brought vodka, they cooked genuine Kalmyk lamb. They drank like there’s no tomorrow. I put a million dollars on the table and asked them to play. And then we shook hands. It seemed that I did the unbelievable by reconciling two irreconcilable men. But as soon as we split, they took up their own and began to put forward impossible conditions. That was when my patience ran out. I raised the idea to hold the world championship according to the knockout system. The top 100 grandmasters should play elimination matches according to the Olympic system. They should play to win (this is how the World Cup is played among 128 grandmasters). I supported this offer with a prize fund of five million dollars.
Karpov agreed after lengthy negotiations. In the first knockout World Cup, he, as the reigning champion, was admitted to the final "out of turn" (and defended his title). Later, I decided that the champion cannot have any privileges and must participate in the knockout tournament on an equal basis with everyone. Karpov refused to play by such rules, and the FIDE world champion title went to Alexander Khalifman in 1999. Then, it passed onto Viswanathan Anand in 2000.