Cardinal voting


Cardinal voting refers to any electoral system which allows the voter to give each candidate an independent rating or grade.
These are also referred to as "rated", "evaluative", "graded", or "absolute" voting systems.
Cardinal methods and ordinal methods 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:
Ratings ballots can be converted to ranked/preferential ballots. For example:
Rating Preference order
Candidate A99First
Candidate B20Third
Candidate C20Third
Candidate D55Second

This requires the voting system to accommodate a voter's indifference between two candidates.
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 cardinal voting methods may solve a very difficult problem:
A foundational result in social choice theory 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 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".
Psychological research has shown that cardinal ratings are more valid and convey more information than ordinal rankings in measuring human opinion.