Many people find problem solving through the use of a family meeting to be a worthwhile experience. Being open to all suggestions and listening to other people's opinions are keys to making a family meeting most effective.
To make this family meeting more diplomatic, you might want to actually give the speaker a "piece of the floor." To do this, cut a small square from an old carpet sample or rug. When it's time for the meeting, suggest taking turns speaking and listening. The speaker will be the person holding the carpet piece. The rest of you will listen without interrupting. Take turns passing the carpet so everyone has time to share their thoughts.
Of course, if you don't have a piece of carpet, you can use an object such as a rod, a stone, a paperweight, or a spoon and pass it around to indicate whose turn it is to speak.