Polynesia does not have the highest population. Population of Melanesia (PNG, Solomon Islands, Vanuatu, Fiji and New Caledonia) excluding Western New Guinea is a bit more than 10 million, If the Indonesian part is also counted as Melanesia the population goes to about 15 million. The population of Polynesia is only a bit over 7 million.
Polynesia holds the lowest amount of countries out of the three, actually. Micronesian: Palau, The Federated States of Micronesia, Marshall Islands, Nauru, and Kiribati. (5) Melanesia: Papua New Guinea, Vanuatu, Solomon Islands, Fiji (And Indonesia if you want) ((4 or 5)) Polynesia: Tuvalu, Tonga, Samoa (3) Three is less than both 4 and 5, so it would be Polynesia :)