In order to best represent the views of an individual where the individual might support more than one alternative, a ranking of the those alternatives by the individual captures preferences such that his or her vote counts fully if any of the supported alternatives is considered with respect to any other alternative without penalty for supporting multiple alternatives and that degree of potential consensus may be ascertained.
The important idea is that the individual should never have to compromise what they believe to be the best alternative in the fear that their vote will not count because it is a minority view. The effect of this is to give individuals power over political powers such as political parties. It enables a true democracy.
Automated voting can, by a process of elimination of losing alternatives, narrow down the alternatives such that simulated run off elections can be used to decide among the top alternatives.
Example: Consider the following rank orderings of supported alternatives A, B, C, D
joe: A, B, C
mary: D, B, A
john: B, A, D
We can first eliminate C and D as having the least support. We then have 2 votes for B over A and one for A over B. B wins despite the fact that both A and B had the same number of supporters. The majority supported B over A.
Note that mary is not penalized for putting an unpopular choice, D, first. She still gets a full vote for B when D is eliminated. note also that while joe indicated support for B, his full vote goes to A in favor of B, in the simulated runoff between A and B.