How could polycephaly evolve as a byproduct of natural selection?

Why this question is different from existing questions...

The closest question to mine is Anatomically Correct Cerberus. It is clear from the answers to that question and indeed it's axiomatic to the scientific community at large that polycephaly is not a particularly useful trait in OUR world. Therein lies the distinction -- in my post, I explicitly concede that point. My question is different because I'm flipping the script. Polycephaly is a losing proposition here on Earth, so let's envision an alien world where polycephaly makes sense.

In the Anatomically Correct Cerberus post, Green said: "I can't think of a set of circumstances where it's a clear and long-standing advantage to have three heads instead of just one." He has a point, it's a challenge. I read through a lot of material, and I just have some modest ideas. Still, just because some of us cannot think of the circumstances doesn't mean that none of us can.

I mean it's easy to say "it's just impossible, case closed." However, the most fascinating part of the topic (to me at least) is unresolved. Namely, thinking of a world with the circumstances to allow for polycephaly to occur is unresolved. That's why I think it's worth taking a deeper look. I would like to keep the use of faerie dust to a minimum (hence the science-based tags), but if it's a bit of a tall order for people, I can allow certain latitudes where necessary to generate useful and creative discussion.

Polycephaly

Premise

Having multiple heads, or Polycephaly is a very visually stirring trait that we often find in mythological creatures. Chimera and Cerberus 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

• a herbivorous or carnivorous creature is acceptable
• all biomes are fair game (tropical, tundra, desert, etc)
• the 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 Cerberus (pictured above)