As a member would you give priority to your individual objective or teams objective, considering that your and others' objectives together give success?

In general this is not a matter for you to decide: this is what your team leader is for.

this situation  happens most likely in the matrix organization, so you should take the organization interest as criteria to decided which objectives has more benefit to your organization.

 

 

I believe that there is always a given criteria & procedure of doing things in busines which people must follow. In this regard; what matters mostly is your communication skills & interpersonal relations. You must always study the team members as well as reviewing creterias & procedures, this gives you an upper hand in dealing with such situations. It is very important to be patient, reserved & polite while handling such issues. You can also pick out 2 or 3 most approachable & trusted team members to you, put them aside & explain or convience them accordingly. If these members buy your idea, you can then introduce it or they can propose it for you to whole team for further discusion & approval.