Cardinal voting
Cardinal voting refers to any electoral system which allows the voter to give each candidate an independent evaluation, typically a rating or grade. These are also referred to as "rated" (ratings ballot), "evaluative", "graded", or "absolute" voting systems. "Cardinal" methods (based on cardinal utility) and "ordinal methods" (based on "ordinal utility") are two main categories of modern voting systems, along with plurality voting. Variants. There are several voting systems that allow independent ratings of each candidate. For example: Additionally, several cardinal systems have variants for multi-winner elections, typically meant to produce proportional representation, such as: Relationship to  rankings. Ratings ballots can be converted to ranked/preferential ballots. For example: This requires the voting system to accommodate a voter's indifference between two candidates (as in Ranked Pairs or Schulze method). The opposite is not true: Rankings cannot be converted to ratings, since ratings carry more information about strength of preference, which is destroyed when converting to rankings. Analysis. By avoiding ranking (and its implication of a monotonic approval reduction from most- to least-preferred candidate) cardinal voting methods may solve a very difficult problem: A foundational result in social choice theory (the study of voting methods ) is Arrow's impossibility theorem, which states that no method can comply with all of a simple set of desirable criteria. However, since one of these criteria (called "universality") implicitly requires that a method be ordinal, not cardinal, Arrow's theorem does not apply to cardinal methods. Others, however, argue that ratings are fundamentally invalid, because meaningful interpersonal comparisons of utility are impossible. This was Arrow's original justification for only considering ranked systems, but later in life he stated that cardinal methods are "probably the best". Cardinal methods inherently impose a tactical concern that any voter has regarding their  second-favorite candidate, in the case that there are 3 or more candidates. Score too high (or Approve) and the voter harms their favorite candidate's chance to win. Score too low (or not Approve) and the voter helps the candidate they least desire to beat their second-favorite and perhaps win. Psychological research has shown that cardinal ratings (on a numerical or Likert scale, for instance) are more valid and convey more information than ordinal rankings in measuring human opinion.