Voting algorithms

This paper presents efficient n-way plurality and threshold voting algorithms based on the type of voting (exact, inexact, or approval), rule for output selection (plurality or threshold) and properties of the input object space (size and structure). Exact voting is the most common voting method and is the easiest to implement. Inexact voting algorithms are more complicated due to intransitivity of approximate equality. In approval voting, each input to the voting process consists of a finite or infinite set of values that have been “approved” by the corresponding computation channel and the value, or set of values, with the highest approval voting must emerge as output. Multiple approved values can result from a nonunique answer to a given problem or from uncertainties in the solution process. For exact voting, the complexity of an n-way voting algorithm depends on the structure of the input object space. Threshold voting often requires less time and space, except when the threshold is very small. The author extends the techniques for designing efficient exact voting algorithms to inexact and approval voting schemes. Results show that optimal linear-time (in n) voting algorithms are available when the input object space is small. Next in the time-complexity hierarchy is the case of a totally-ordered object space that supports worst-case order-[n·log(n)]-time algorithms for both exact and inexact voting as well as for certain approval-voting schemes