There are a few groups out there that individually publish their own global livability rankings. One is Monocle. Another is the Economist, through their EIU, or Economist Intelligence Unit. Each has their own variable metrics, which spit out differing, but similar answers. The same cities generally comprise the top ten. Some tend to be more anglo-centric, or at least accused of it, however their results turn out. For example, the EIU tends to favor Australian and Canadian cities a little more than Monocle. That might be worth throwing out their results altogether. However, they both like Zurich and Vancouver.
Like anything it's up to you to choose. Sort of like in highly livable places. There is much subjectivity built-in to the metrics and methodology. That frightens people. They like hard, scientific answers. Unfortunately, cities tend to escape simple definition and horticultural explanation. They exist as complex organisms at a higher plane than can be realistically studied and measured and then reinterpreted to tell the whole story. To understand livability rankings you have to understand what livability means. It may differ from your preferences or preconceived biases. That's not the point.
Livability, and the study of it, is more like an election. It isn't about garnering ALL the support, but rather the greatest majority. And in the case of livability rankings, it means finding the cities that accommodate the needs of the most without impinging overtly on others in a way that is deleterious to the whole. Essentially, where is the greatest percentage of the population empowered, because they tend to be very specific to avoid biases towards nanny statehood.