"Small groups of persons can make the rest of us think what they please about a given subject". "Small groups of persons can make the rest of us think [whatever they want us to think] about a given subject". "Some people can make the rest of us think [whatever they want us to think] about a given subject". "Some people can make the rest of us think [whatever they want us to think] about [something]". "Some people can make [others] think [whatever they want us to think] about [something]". Do what you please = Do whatever you want to, whatever pleases you Do as you please = Do whatever you want to, whatever pleases you . Think what you please = Think whatever you want to think. . You WILL DO AS I PLEASE = You will do what I want you to do You WILL thinks what I please. = You will think what I want you to think. . They can make you think whatever they please. They can make you think what they please.

"Small groups of people can make the rest of us think what they please about a given subject." Yes, the sentence is correct but a bit awkward. The idea is that we can be influenced to agree with the opinions of others when more people are involved. For instance, when we see many people agreeing on facebook about a given subject, we can be influenced to agree with them.

Alessandro and Jeremy, thank you so much :)

I think "please" here means "want", but the sentence is a little weird to begin with. I'm not sure that "what they please" is the most fitting phrase here to begin with.

In this sentence the of "what they please" means "what they want". This isn't seen much today and is used in spoken English even more rarely. Examples are "You can eat whatever you please but you may feel ill afterwards." "I don't care, do as you please!" You can of course learn to recognize this usage while reading, just don't expect to use it while speaking or to hear it often. "Do what you like" or "think what you want" are the common phrases now. Hope this helps, J