Society dictates government in many instances. The Arab Spring is a most recent example of this occurring, especially with the change in government in Egypt recently. All of this came about because of the people voicing, as well as demonstrating, their opposition to Hosni Mubarak and his policies. Therefore society directly influenced Egyptian government.
Of course, as mentioned in the above posts, government does dictate the actions, or lack thereof, in a society. Governments have the capability and authority to enact laws and policies that have a direct influence on what people, businesses, groups, and organizations can do within a particular government's jurisdiction. This government power subsequently impacts what courses of action individuals, companies, and others take, whether for the betterment of society or not.
A company may decide to invest heavily in alternative energy because of government financial incentives. This directly affects the society in which the company operates. It could promote better air quality, more jobs, and more economic growth - - all beneficial to that specific society within that government jurisdiction.
Look at how America became a unique independent country in the late 1700's. After being colonized by European countries, we carved out towns and farms in the colonies and pushed westward. We were in a situation unlike the countries whose citizens immigrated to America. It required a lot of individual toughness and responsibility. This was reflected in how we set up our governent once we became an independent country. In this case, society dictated government.
Later, when we became a settled and wealthy country, we added a lot of social programs that caused some changes in our society (some good, some not so good). In this case, government dictated society.
Ideally, society does dictate government. In America, we elect people into office, therefore, we are choosing who makes up our government. These people either decide on policies, or allow us to vote on certain policies.
There are some things in government, however, that society does not have control over, and in this respect I would say that government dictates society. The government decides where money goes, what laws need to be upheld and/or amended, etc. I would say, then, that it goes both ways. This allows us to keep our government balanced but also allows the government to keep society in check.
This is really a chicken and egg kind of question. To some extent, at least, government dictates society. For example, Chinese were known as entrepreneurs around Southeast Asia for a long time. Then their government changed and they became communists who did not engage in entrepreneurial activities. Now their government has changed again and they are becoming more entrepreneurial. This suggests that government can dictate society to some degree.
The Hadza, a tribe in Africa, have a few people who make the rules for the tribe, and they have very few rules. To me, that means that they have society, which means people who make the rules. However, they have very few rules, and members of the tribe may follow the rules or not. To me, that means that the Hadza have no government.
That seems to suggests that society comes before government, so the society would determine the kind of government.
google Hadza, National Geographic for more information.