Sam Harris in his opinion video suggests that science can answer questions of morality
On this I have to say Sam Harris is wrong. Science cannot answer philosophical questions. In fact I would even suggest that Sam Harris is confusing mathematics with science. At the foundation of mathematics is logic, and this logic is critical to certain kinds of morality. It's the use of mathematics that allows for the cost benefit analysis calculations, but the "greater good" or utility function is not determined by science. Science is described below in Wikipedia:
Science (from Latin scientia, meaning "knowledge"):58 is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe.[a]
The mistake Sam Harris is making is ignoring the actual definition and function of science for the benefit of his own agenda to spread the idea that cultural relativism is incorrect. On this I would disagree because i think there is no objective right and wrong because if we cannot agree on the utility function, then we cannot agree on maximization of utility.
Then he goes on to say whether or not we will consult with super computers to answer personal questions? The joke is on him here because I would predict we will ask the equivalent of super computers these personal questions in the very near future. In fact the future of morality in my opinion is the invention of moral calculators which can help people to handle the mathematics, the probabilities, the whole "expected utility" from different choices. Mathematics is not science but is formal language, while science utilizes mathematics but is not specifically mathematics. Some forms of morality can be reduced entirely to mathematics (consequentialism, utilitarianism), and most morality is describable by logic.
** Science (from Latin scientia, meaning "knowledge"):58 is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe.[a]**
Emphasis is on testable. Morality isn't testable and predictions cannot be made about the universe under a moral system. Morality is about life and social interaction, about values, about what the right or wrong thing to do is. Science can never tell us what to value because value is subjective. Science can never tell us about life as it can merely test models and make predictions. Science will not answer questions of why, nor will it provide purpose, nor will it explain why life has value, as it's not designed to replace philosophy and mathematics.
Sam Harris says we need a universal conception of human values? This is not possible. What is possible is merely an approximation based on current consensus (public sentiment) on what is right or wrong behavior given a situation. It's not possible to use science to replace that and while you can use mathematics to make sure it's all logical and reasonable it will not involve science.
Game theory, economics, social exchange theory, consequentialism, utilitarianism, probability theory, formal logic, are not science. All fall into the category of either philosophy or mathematics. Science helps us build our knowledge by testing models, where predictions can be made based on previous knowledge. Mathematics allows for the creation of models which cannot be directly tested but which are logical, valid, and useful, and consequence morality in my opinion falls into mathematics where value is subjective and right and wrong depend entirely on what we value.