And how does this relate to the Ancient Greeks' definition of ethics? I'm quite confused...
If the ethics of a society does dictate whether or not something is ethical doesn't that imply that the majority opinion is always objectively right?
The conventions of a society determine, fix, what is regarded as ethical in that society - to the extent that the society has consensual conventions. These have become rare in the culturally heterogeneous societies of the present day.
If there is an objective moral reality, independent of human beliefs, i.e. if moral realism is true, then there are (some) moral truths which are independent of whatever the conventions of any society. These 'truths' may coincide or agree with social conventions but they are no less truths (if you are a moral realist) whether they do or not.
Ancient Greek morality cannot be characterised in any single or simple way. Plato held that there is an absolutely objective morality which reflects a realm of values embodied in the Forms, transcendent realities knowable only by and to an intellectual elite. Aristotle's view was that there is an objectively correct way in which for a human being to develop and that this will involve (at least for free adult males) participation in citizenship. On the other hand, sophists such as Thrasymachus, mocked in Plato's Republic, are widely believed to have thought that ethics, morality generally, was a set of beliefs instilled in the 'strongest' to induce obedience to their rule. (Thrasymachus's exact position as depicted in Plato's 'Republic' is actually full of ambiguities and subject still to scholarly dispute.) Glaucon in Plato's 'Republic' is represented as putting forward (not holding) a 'social contract' theory of morality : morality is a set of rules of convenience which we'd all like to break but which are necessary for a safe and organised social life.
Even if the ethics of society does in some sense dictate what is ethical - morally right - either makes it actually right (conventionalism) or determines what is merely regarded as right - there is no logical link with majority opinion. Thraysmachus might be correct in holding that morality is decided by the interests of the strongest, who could be a minority, or it might be the case that moral opinions about right and wrong are transmitted by, and inherited from, tradition which the majority like everyone else accept as the guide to ethical behaviour.
The Greeks were greatly exercised, at least in the 4th and 5th centuries BCE, over whether morality was rooted in nature (phusus) or convention (nomos). There were powerful exponents of both views, with philosophers such as Plato and Aristotle coming down in their different ways on the side of phusis and the so-called sophists, including Protagoras, Gorgias, Hippias, Prodicus and Thrasymachus, opting for nomos. (But the actual nature of the sophists' views really needs careful handling; I am presenting at best a historically influential view of their ideas.)
Objectivity has nothing to do with the agrement of people. As you already know by experience leadership has a large influence in what is acceptable in a certain group. So no soceity does not have a part in morality and moral claims are supposed to be objective by definition.
I also want to point out ethical does not necessarily mean moral. Morality falls under Normative ethics. There are branches of ethics outside normative ethics.
Normative ethics by definition is supposed to differ from nonphilosophical ethics. That is the point of even using the term moral is to express a universal answer. If we are not giving universal answers why are you using the word moral? Would removing the word moral take anything away from your meaning? Some people do stuff just because they can. So descriptive ethics and applied ethics seems to have emotional overrones which would belong to psychology. This is why some people argue morals are subjective. By definiton alone morals are OUGHT statements not just for me or you or the few. If i claim abortion is immoral i am indicating that abortion is wrong for ALL people everywhere on this planet. You cannot say x is moral here and x is immoral over there. If you want to say nothing is objective then there is no reason to even use the word moral. To deny objectivity is automatically a rejection of morals (normative ethics). Also notice there is a diference between "you ought to do x" and "i personally think or feel this way about x . . ." Ought claims have no emotional content. This is not the case when a speaker is describing his personal feelings. Hence why this is type of description is part of psychology. He is using "i feel" or " i think" in the description of the reasoning!
There are many ethical systems. Beyond that one can decide on ones own ethical framework. Ethics are not empirical, that is to say they are not quantifiable, or externally measurable. As such they are never objectively anything. I believe you need to reconsider the question you are attempting to ask.
It is very difficult to defend the position that there is such a thing as objectivity in ethics and morality. Moral realists argue that statements about morality have truth values and can be true or false (see: moral realism) Arguably many things straddle the line between objective and subjective. We take for granted things such as causing harm is wrong, killing another innocent person is wrong, failing to save someone's life when there are no impediments to your safety in doing so. Some people believe there is an arbiter of universal morality such as a deity. Some believe that morality is an objective set of facts that we can access through reason (this is another form of moral universalism). What is moral is shaped by culture but it is also dependent on who the evaluator of a moral act is. As radical as it seems there is no objective way we can state that doing harm to others is wrong even though we feel that it is instinctively. Much of our moral actions are driven by impulse and emotions.
Nonetheless, once you take the step of accepting that doing harm to other innocent humans or animals is morally indefensible, then you can start to build ethical systems that are supposed to transcend cultural norms. This is difficult to apply to different human societies as many have different social norms as to what makes something moral or ethical.
Without a legal system and laws, it is very difficult to impose any form of moral standard across a society. A criminal would argue that stealing or murdering is acceptable if he stands to benefit from this. Without legal recourse, there would be nothing we could do as a society about this. Much of our innate moral sense would have been present in early human societies that lived before civilizations arose. Tribes had their own (and still do the ones that are left) codes of conduct and ethics as to what is acceptable and unacceptable behavior and what you will be banished for or killed for etc. Of course, our understanding of what is moral has evolved in step with what we know about human psychology, science, and what we know about the world. This is continually evolving. There was a time when slavery was condoned, women could not hold positions of power, racism was state-sanctioned, you'd be stoned to death for breaking the Sabbath, and so on.
The ancient Greeks also had their own ideas about what morality was. Taking Aristotle as an example, he was heavily focussed on virtue ethics when thinking about what makes somebody act morally good or bad. What made somebody act morally was determined by how well-developed their virtuous character traits were. He believed being virtuous would entail striking a balance between extreme points of view such as between extreme generosity and stinginess, and between extreme brashness and cowardice. An understanding of justice and political philosophy was also central to Aristotle's ethical philosophy (see: Nicomachean Ethics). The Greeks also saw human flourishing to be the most important aim, encompassing living morally and building your knowledge of the world around you of all things worthy of examination.
The study of ethics has come a long way since the ancient Greeks, however, very similar questions are still asked such as How should we live? and What makes a good life? The difference is that in modern ethics when we ask what ethics actually is rather than what is ethical we are in the realm of meta-ethics: Trying to define what words mean when we talk about whether something is moral or not. G. E. Moore is considered one of the first philosophers to think about ethics formally in this way. But this type of thought can be traced back to the ancient Greeks at least:
Callicles in Plato’s Gorgias (482c-486d) advances the thesis that Nature does not recognize moral distinctions, and that such distinctions are solely constructions of human convention; and Thrasymachus in Plato’s Republic (336b-354c) advocates a type of metaethical nihilism by defending the view that justice is nothing above and beyond whatever the strong say that it is. Socrates’ defense of the separation of divine commands from moral values in Plato’s Euthyphro (10c-12e) is also a forerunner of modern metaethical debates regarding the secular foundation of moral values. Aristotle’s grounding of virtue and happiness in the biological and political nature of humans (in Book One of his Nicomachean Ethics) has also been examined from the perspective of contemporary metaethics
See Metaethics articles on the IEP and SEP for more.