How project management keeps the development process neutral in a politically charged environment without taking risks?

Its got to do more with negotiations. The people with political interest s must know that greater benefit comes from your project delivery, since they would only entice you and never directly demand monetary benefits, you also entice them and not dire ctly demand peace if mind. This will buy you some time. Meanwhile you inform senior mgmt as to your own requirements of political muscle or there patience to allow you to see thongs through.

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by assigning the roles to each and every team member according to their capability and by treating the all team members equally important. You should also let the all members gathered around you and let them openly talk about how they can think better or best to work together to make the proect successful.

keep the heart and key factors of the Process Management out of the heat, stir up the discussion about a topic far from the Process, yes blow smoke....

Office politics is a fact of life in any organization. And, like it or not, it's something that you need to understand and master to be sure of your own success.

"Office politics" are the strategies that people play to gain advantage, personally or for a cause they support. The term often has a negative connotation, in that it refers to strategies people use to seek advantage at the expense of others or the greater good. In this context, it often adversely affects the working environment and relationships within it. Good "office politics", on the other hand, help you fairly promote yourself and your cause, and is more often called networking and stakeholder management.

Perhaps due to the negative connotation, many people see office politics as something very much to be avoided. But the truth is, to ensure your own success and that of your projects, you must navigate the minefield of Office Politics. If you deny the 'bad politics' that may be going on around you, and avoid dealing with them, you may needlessly suffer whilst others take unfair advantage. And if you avoid practising 'good politics', you miss the opportunities to properly further your own interests, and those of your team and your cause.