Various methods for decision-making / selection exist - however, these often don't address the criteria of 'bringing people together'. In my experience as a consultant, facilitator and manager, 'bringing people together' can be achieved through the open and collaborative process. A final decision could be made by a public or private voting, debate, or decision by some other means -- and still, the group may be equally 'bought in'.

The participants typically must feel that:
1) they've been heard -- able to share their input and/or feedback -- contribute what's on their mind (whether this actually fueled a decision or not is less important than being valued/respected enough be asked to share a view)

2) others who they value/respect or care about have been heard -- sometimes it's not the individual, but another person who's chance to speak up carries the weight towards brought together'

3) there's been some stated method or criteria for the decision -- vs. something hidden or ad-hoc. Most people like to know how a decision is being made and that this has been authentically followed vs. hijacked

4) that consequences have been aired -- it's tough for people to be brought together, or stay that way unless some future situations have been anticipated. This doesn't always need to be fully explored, details planned out or all items held in check.
However, since the whole purpose of most decision is about an unknown, most people need to feel that someone in the group is looking out for problems of groupthink, and protect against unwise outcomes.

The key to best outcome here is an approach that brings most people together to converge on an outcome and not one where team members get stuck on their positions and refuse to budge to other opinions.

An first step would be to decide what is your role in the situation: participant, chairman, responsible manager etc.

If you are a participant observing the group's standpoint and individual and determin what would be the best outcome for you and the section or department you are working and support that view on a cosntructive basis, so no negotiations on standpoints. Focus on similarities to build a basis from which everyone can move forward.

If you are chairman or manager you have to take more factors and stakeholders in account. It might be you have to execute a management decission yet the decission might be a tough one which could create a lot of resistance and different views. Listening to both the group's viewpoint and individual, in face to face meetings to get a grip on the emitions and reasons behind these emotions and standpoints. By communicating on different levels it is vital to bring most views in accordance with each other. While doing so you should not delude to much from the main goal which is executing a management decission. Personally I always set that decission at my barrier behind I can be flexible in waying in different views, argument and standpoints while moving forward as time is usually another factor to take into account as well. Ideally everyone should accept the decission yet in practice there will be situations in which not everyone will be satisfied.

In general my main focus in these situations is to give everyone the feeling they had the opportunity to speak their mind and share their view and for me to explain the situation and how things are to move forward and what other arguments and factors play part outside of people individual focus.

In my experience I would choose people from every level of the organization and even third party members (customers and vendors if needed). Depending on the situation. I would use a white board and write what are the goals. You know, the do’s and don’t. Make sure you get others opinions on this so that everyone is comfortable about the atmosphere. Not only do need to cover the emotional feelings but also the atmosphere in which everyone is gathered in. It can make a big impact on the comfort level if you can. Give examples of the problem and how it has impacted them and the company. Have a rule that if you are negative about something to have a positive solution behind it. Also make it clear that everyone will be heard without consequences. Higher ups need to keep an open mind as well. So now you have the do’ and don’t , the problem and some solutions. I like to play business games to get a team approach. One game I like is Pictionary or hangman in teams. There are a lot of games. There you will really see how people are perceiving the situation. Pictures remind people of the situation and gives them a creative mind to come up with more ideas. You will need to focus the group on the problem, solution or growth goals to solve. For example, how to increase production, sales, improve delivery time, etc. Keep an eye on the members that do not participate. Start getting them involved in the questions or game by asking them how they would do it. In my experience, people want attention and will give there input if you properly respect their space and let them get involved. These type of people have good ideas and need to be surfaced out of them. They start to feel empowered. I know that time is of an essence but taking time to invest in people can get employees to respect the companies vision and mission. Everything should be written in categories on the white board. Use post it notes to allow you to move suggestions, problems, solution, ownership, time frames, waste, etc. Vendors are a great ally. They talk to the competition, are versed with delivery, problems in the environment and can help with solutions they have heard about or can contribute to the company in hopes to gain or acquire your business. Sometimes, a customer can help you help them by giving incite to there business. Be careful with the customer as to not give away too much info. This may be at a selective day and time to have them in the meeting. When and if the meeting gets stressful take a pause to reflect what is being said and have others repeat the statement at that time. This will make sure others are listening and try to get others to understand what is being said. Many times others perceptions can get the best of them because they are not listening to what is being said but rather what they want. Clarifying issues can break down walls. It also makes the person who is presenting more comfortable to talk more and clarify the intention. Upon closing a meeting make sure you involve everyone in a project. Choose carefully. Get volunteers by letting them know that those that do not volunteer will get what ever projects are left. Ask politely to show you care and you respect them. Get or give time frames on projects. Make sure you follow up on projects and that the goals are being furthered or completed. Thank the team for a job well done and let them know when the next meeting will be held and what is expected of them.

Frame the current situation, which is the final goal? List pro and cons for any idea and then select the one that could be more beneficial based on these

The person that is held accountable for the outcome holds the ultimate decision. This person relies on fact-based assessments by the subject matter experts, including a candid review of the opposing opinions, as well as risk vs. benefit review and risk mitigation planning.

The approach should fit the group culture. Committee-based approach tends to be more risk-averse and less innovative, possibly resulting in a compromise that makes everyone feel better but results are average by definition. A strong leader, on the other hand, can inspire innovation or breed contempt or fear.

Humans are genetically programmed to rely on visionary leadership to plot the course forward. Leaders that take blame for failed ventures and praise the team for successes will be trusted and spur a healthy process, unconstrained by exaggerated fear of failure.

The job of a facilitator is to keep the process going, polish the message and adapt to the group culture.

Any design relies upon the generation of alternative ideas (i.e. ideation) and their effective evaluation to ensure that attention is directed in a worthwhile manner. Human cognition plays vital role in any ideation process. Critical to creative cognition and performance is both the generation of multiple alternative solutions in response to open-ended problems (divergent thinking) and a series of cognitive operations that converges on the correct or best possible answer (convergent thinking). Therefore, in any ideation/group discussion session presence of both divergent and convergent thinkers might be required. Choosing people from across the organization might help in any ideation process.  

Psychological pressures in the decision making process can be overcome, if we take out personality and anonymize the participants of the group. Traditional online-panels, often used by market research companies, had been taken to a next level by the company “Unanimous A.I.”, which developed an app, where a selected online community can answer, without discussion, different multiply-choice questions. The participants answer independently the questions and computer presents the real time results similar to a classic Ouija board, where in a séance a group of people try to contact the spirit of the death. The number of the participants’ answers move the “planchette” to the edges of the board, where in this version are no letters, but the different multiply choice answers. If a sufficient number of answers magnetic-like moved the planchette over the answer, the AI takes this as the group’s answer.

Artificial Intelligence and statistic formulas ensure that the participants are independent from each other, not only in relations, but also in character, knowledge and attitudes. With this, Unanimous A.I. achieved positive results via cognitive guessing by the single participants and predicted the results from horse racing or Oscar events. Based on this concept, Swarm Intelligence” or “Hive Mind” has one big difference to natural swarms, they not include all participants of total population, but only a small interested part, for every prediction parted into new groups.