Polycephaly

Premise

Having multiple heads, or Polycephaly is a very visually stirring trait that we often find in mythological creatures. Chimera and Cerebus are two such examples.

Conventionally, the polycephalous trait tends not to be favored by natural selection. It is a trait that is often very rare and even when it is observed, the organism is thought to be handicapped by the trait. Consider the following comments regarding a two-headed snake:

"Just watching them feed, often fighting over which head will swallow the prey, shows that feeding takes a good deal of time, during which they would be highly vulnerable to predators. They also have a great deal of difficulty deciding which direction to go, and if they had to respond to an attack quickly they would just not be capable of it." -- National Geographic

As I researched the concept, I became more acutely aware of the evolutionary challenges that would inhibit the existence of a polycephalous creature. In terms of evolution, having one brain is an expensive component -- let alone several. The energy resources that would be required would pose a challenge for the organism to be able to thrive and reproduce. However, just because polycephalous creatures do not fare well in our world, does not mean that there couldn't be a fictional world in which polycephaly would be an advantageous trait and thus favored by natural selection.

Question

I would now like to open the floor to answers that can address the following question: What kind of world could have the conditions that would be conducive to the emergence (and perhaps dominance) of a polycephalous creature?

Further Clarification

• herbivorous or carnivorous creature is acceptable
• all biomes are fair game (tropical, tundra, desert, ect)
• ecosystem is a complex variable and for the sake of simplicity you may assume other ecosystem constituents as necessary, just make sure you have a small list of assumptions for clarity
• (optional) Ideally, I would like to keep the scope as is, but to avert undue subjectivity or being too broad, if you so desire, you may limit the scope of the question to our buddy Cerebus (pictured above)