Karl recently said: "It is equally impossible to imagine any society or human collecvtive built upon the principle of determinism." I'll take that challenge if I may:
The Judicial System
I think this is the main thing you meant when you talked of a deterministic society - how the law would react to people's actions, rather than their 'choices'. My view is that in a deteministic society the outcome would actually be better for everyone, including criminals, and would make a better, more negative utilitarian world.
All crimes are committed due to either mental illness, a character fault or anger, jealousy etc. Every prison sentence therefore will not be to 'punish' criminals, but rather to reform them and make them fit into society again. If for the good of society they cannot be reformed, they will not be tortured in bad living conditions or killed against their will, simply kept away from the rest of society so as to minimise the total suffering of the world.
The Monetary System
Since everyone is necessarily not responsible for their own success, staunch capitalism is completely immoral. However since some people could not handle money very well, and because Communism has been shown by history to be a failure, the rich will be allowed to be rich, but they will be taxed heavily and the welfare system for the poor will be extensive - so everyone has a good quality of life.
Healthcare will be free
No one can help their familial background, so it is essential that a great social service is in existence, so abusive or otherwise unfit parents can be separated from their offspring, and so that the children can be given the time and care they need to grow into mentally balanced adults. No one should be told to 'suck it up' or 'pull yourself up by your bootstraps' if their life is bad. The government should instead help them maintain a quality of life equal to that of others.
There are numerous other ways that life could be improved if the government simply stopped believing in the myth of free will. Steven Pinker in his book The Blank Slate goes into them in more detail, I think. But the point is, a society like this could be possible and not collapse - in fact the UK and other places in Europe are actually becoming like this.