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For practical reasons there needs to be someone to break ties in decisions. However, this is different to thinking that your are somehow better than others. In business you should check your ego at the door, especially if you are in a position where you need to be the tie breaker.

The idea of "everyone is equal" is to remind yourself to respect your coworkers, actually consider their inputs, and remember that you too can be just as wrong as you might think others are. The idea not "we are equal thus if we disagree then nothing happens."