Previously, a new World Champion had won the title by defeating the former champion in a match. Alekhine's death created an interregnum (gap between reigns) that made the normal procedure impossible. The situation was very confused, with many respected players and commentators offering different solutions. FIDE found it very difficult to organise the early discussions on how to resolve the interregnum because problems with money and travel so soon after the end of World War II prevented many countries from sending representatives - most notably the Soviet Union. The shortage of clear information resulted in otherwise responsible magazines publishing rumors and speculation, which only made the situation more confused. See Interregnum of World Chess Champions for more details.
The eventual solution was very similar to FIDE's initial proposal and to a proposal put forward by the Soviet Union. The 1938 AVRO tournament was used as the basis for the 1948 Championship Tournament. The AVRO tournament had brought together the eight players who were, by general acclamation, the best players in the world at the time. Two of the participants at AVRO - Alekhine and former world champion José Raúl Capablanca - had died; but FIDE decided that the other six participants at AVRO would play a quadruple round robin tournament. These players were: Max Euwe (from the Netherlands); Mikhail Botvinnik, Paul Keres and Salo Flohr (from the Soviet Union); and Reuben Fine and Samuel Reshevsky (from the USA).
The proposal was modified slightly, in that the Soviet Union was allowed to replace Flohr with Vasily Smyslov, a young player who had emerged during the war years and was obviously stronger. Reuben Fine elected not to play, for reasons which are not totally clear (see Reuben Fine#1948 World Championship). There was a proposal that he should be replaced with Miguel Najdorf, but in the end the tournament was played with only five players, and as a five-cycle round robin.
Read more about this topic: World Chess Championship 1948
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