Managing any initiative is a complex affair - juggling timelines, milestones, and dependencies; managing risks and mitigating factors. The management of design processes gets geometrically more complex when you add the wildcard of personal preference to decision points. Many non-designers are incapable of articulating their reasons for preference-based choices in a way that makes sense to designers. However, there are tactics you can use to minimize the risk of heated debates about the relative merits of Wedgewood vs. Cornflower.
In order to prioritize one party's personal preference versus another's, the first thing you need to do is establish traceability. Once you've tied organizational decisions to an enterprise's overall strategy to cut costs, the decision whether or not to source help desk functionality to India becomes more clear. The same can actually be said of design decisions. The overall enterprise strategy should inform sub-strategies like Marketing (how we sell our product/service) and Branding (how we choose to build a relationship with our prospects/customers). Once you have the basics of the Marketing and Branding strategies down, it should be a matter of reflecting choices of preference against those strategic directives. For example, let's say Edison likes the design that features green, while Ellie likes the design that features blue. There's often political sensitivities in promoting Ellie's or Edison's preferences over the other. The trick is to find a link between a choice and overarching strategic decisions that have already been made. There is plenty of literature that lays out the characteristics of color choices (for instance, green represents renewal while blue represents trustworthy-ness). If the branding directive says "we're a new kind of company," then green is probably your choice. If it says, "we've been trusted for 50 years," then probably go with blue.
The second thing you need to do is communicate. As I mentioned earlier, business stakeholders rarely "speak designer," and vice versa. In one direction, it is important to get the higher-level strategy articulated as clearly as possible. There are a number of tools and exercises to accomplish this. Personas, for instance, do a good job of encapsulating marketing and branding strategies in the form of a person most likely to respond favorably to them. They also give designers a target against which they can validate their design decisions. Another useful exercise is to work with the business stakeholders to create a design parti, a single statement that captures the essence of your goals for the design effort. The best way to generate a parti is by engaging the stakeholders in a session to create a laundry list of design goals. If you're designing a website, ask them to list the things they hope the site will accomplish: sell a product? deepen a relationship? instill a sense of trust? get the user to call us? Once you have the laundry list, iteratively distill them into higher and higher level concepts until you arrive at a single idea (e.g. "This website should engage our users in a way that we become trusted advisors before they pick up the phone to call us."). Once you've established a central guiding principal, it can serve as a sort of Occam's Razor when faced with design choices that, at first, seem to be on equal footing.
In the other direction, it's important to communicate to the stakeholders any unintended consequences of their preference-based choices. Often, people will make design decisions based on associations with other examples they've seen without taking into account that that design decision was made to satisfy a very different goal. While the stakeholder may think the Old Spice Guy ads are cool, it may not be the best way to communicate your firms commitment to financial stability. Your warnings may fall on deaf ears, however... Even armed with rock-solid evidence. On one project, an early design presented some text as standard blue hyperlinks (#0000FF) on top of a pure red (#FF0000) background. We said we thought it would prove too difficult to read, but the stakeholders said, "We like red and blue." So, the next meeting, we showed up with printouts of studies that showed that the human eye is incapable of focusing on two frequencies of light so different in wavelength. The glanced at the reports, looked back at the mockups and said, "We like blue on red." It was only changed after it was put into production and users complained about it in testing.
The greatest risks to managing a design effort are ambiguity and lack of information. Taking steps to establish traceability and finding ways to open bilateral lines of communication will reduce those risks. You may still find yourself in a debate between Wedgewood and Cornflower, but it will hopefully be a more informed debate. When all else fails, the CEO is always right.