Cardinal voting systems: Difference between revisions

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Cardinal voting is when each voter can assign a numerical score to each candidate. Strictly speaking, cardinal voting can pass more information than the ordinal (rank) voting. This can clearly be seen by the fact that a rank can be derived from a set of numbers provided there are more possible numbers than candidates. A distinction should be made between the "pure" cardinal methods Approval Voting and Score Voting, and "semi-cardinal" methods, such as STAR Voting and all other cardinal methods. Most of this article discusses the properties that pure cardinal methods pass. Unlike ordinal voting, [[W:Arrow's Impossibility Theorem|Arrow's Impossibility Theorem]] does not apply to pure cardinal methods. Furthermore, all pure cardinal methods satisfy the participation criterion.

In pure Cardinal voting, if any set of voters increase a candidate's score, it obviously can help him, but cannot hurt him. That is a restatement of monotonicity. It is a stricter requirement than Independence of Irrelevant Alternatives so it is satisfied as well. As such, a ~~voter’s~~ score for candidate C in no way affects the battle between A vs. B. Hence, a voter can give their honest opinion of C without fear of a wasted vote or hurting A. There is never incentive for favorite betrayal by giving a higher score to a candidate who is liked less.

In pure Cardinal voting, if any set of voters increase a candidate's score, it obviously can help him, but cannot hurt him. That is a restatement of monotonicity. It is a stricter requirement than Independence of Irrelevant Alternatives so it is satisfied as well. As such, a voter's score for candidate C in no way affects the battle between A vs. B. Hence, a voter can give their honest opinion of C without fear of a wasted vote or hurting A. There is never incentive for favorite betrayal by giving a higher score to a candidate who is liked less.

While in all systems all votes are actually counted, there is a psychological effect to the feeling that the vote “does not count” in a wasted vote situation. Pure cardinal voting is likely to maximize the number of people who vote for a candidate to become the representative. This is expected to have a knock-on effect of better acceptance of results and higher voter turnout.

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! Method !! Aggregation !! Gradation

|-

| [[Score Voting]]|| [[Utilitarian winner | Sum]] || > 2

| [[Score Voting]]|| [[Utilitarian winner|Sum]] || > 2

|-

| [[Approval Voting]] || [[Utilitarian winner | Sum]] || [[Approval Voting | Binary]]

| [[Approval Voting]] || [[Utilitarian winner|Sum]] || [[Approval Voting|Binary]]

|-

| [[STAR voting]] || [[STAR voting | Sum, then top two run-off]] || > 2

| [[STAR voting]] || [[STAR voting|Sum, then top two run-off]] || > 2

|-

| [[Median Ratings]]|| Median || > 2

|-

| [[Majority Choice Approval]]|| Median || [[Approval Voting | Binary]]

| [[Majority Choice Approval]]|| Median || [[Approval Voting|Binary]]

|-

| [[Majority Approval Voting]]|| Median || [[Approval Voting | Binary]]

| [[Majority Approval Voting]]|| Median || [[Approval Voting|Binary]]

|}

== [[Multi-Member Systems|Multi-Member Methods]]==

===[[Block voting | Bloc Methods]] ===

===[[Block voting|Bloc Methods]] ===

Bloc Methods find the candidate set with the most support or the most votes overall. The number of seats up for election is determined and the top candidates are elected to fill those seats.

* '''Bloc Approval Voting''': Each voter chooses (no ranking) as many candidates as desired. Only one vote is allowed per candidate. Voters may not vote more than once for any one candidate. Add all the votes. Elect the candidates with the most votes until all positions are filled.

* '''Bloc Score Voting''': Each voter scores all the candidates on a scale with three or more units. Starting the scale at zero is preferable. Add all the scores. Elect the candidates with the highest total score until all positions are filled.

* '''Bloc STAR Voting''': Each voter scores all the candidates on a scale from ~~0-5~~. All the scores are added and the two highest scoring candidates advance to an automatic runoff. The finalist who was preferred by (scored higher by) more voters wins the first seat. The next two highest scoring candidates then runoff, with the finalist preferred by more voters winning the next seat. This process continues until all positions are filled.

* '''Bloc STAR Voting''': Each voter scores all the candidates on a scale from 0–5. All the scores are added and the two highest scoring candidates advance to an automatic runoff. The finalist who was preferred by (scored higher by) more voters wins the first seat. The next two highest scoring candidates then runoff, with the finalist preferred by more voters winning the next seat. This process continues until all positions are filled.

===Sequential [[Proportional representation | Proportional]] Methods===

===Sequential [[Proportional representation|Proportional]] Methods===

Sequential Cardinal Systems elect winners one at a time in sequence using a candidate selection method and a reweighting mechanism. The single-winner version of the selection is applied to find the first winner, then a reweighting is applied before the selection of the next and subsequent winners. A reweighting is applied to either the ballot or the scores for the ballot itself. The purpose of the reweighting phase is to ensure that the [[Proportional representation| Hare Quota Criterion]] is met to ensure proportional election outcomes.

Sequential Cardinal Systems elect winners one at a time in sequence using a candidate selection method and a reweighting mechanism. The single-winner version of the selection is applied to find the first winner, then a reweighting is applied before the selection of the next and subsequent winners. A reweighting is applied to either the ballot or the scores for the ballot itself. The purpose of the reweighting phase is to ensure that the [[Proportional representation|Hare Quota Criterion]] is met to ensure proportional election outcomes.

{| class="wikitable"

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! System !! Gradation !! Selection !! Reweight

|-

| [[Reweighted Range Voting]] || > 2 || [[Utilitarian winner | Sum]] || [[Jefferson method]]

| [[Reweighted Range Voting]] || > 2 || [[Utilitarian winner|Sum]] || [[Jefferson method]]

|-

| [[w:Sequential proportional approval voting|Sequential proportional approval voting]] || [[Approval Voting | Binary]] || [[Utilitarian winner | Sum]] || [[Jefferson method]]

| [[w:Sequential proportional approval voting|Sequential proportional approval voting]] || [[Approval Voting|Binary]] || [[Utilitarian winner|Sum]] || [[Jefferson method]]

|-

| [[Sequentially Spent Score]] || > 2|| [[Utilitarian winner | Sum]] || [[Vote Unitarity]]

| [[Sequentially Spent Score]] || > 2|| [[Utilitarian winner|Sum]] || [[Vote Unitarity]]

|-

| [[Allocated Score]] || > 2|| [[Utilitarian winner | Sum]] || [[Allocated Score | Allocate]]

| [[Allocated Score]] || > 2|| [[Utilitarian winner|Sum]] || [[Allocated Score|Allocate]]

|-

| [[Sequential Monroe]] || > 2|| Highest Sum in a Hare Quota || [[Allocated Score | Allocate]]

| [[Sequential Monroe]] || > 2|| Highest Sum in a Hare Quota || [[Allocated Score|Allocate]]

|-

| [[Sequential Ebert]] || [[Approval Voting | Binary]] || [[Utilitarian winner | Sum]] || [[Ebert's Method]]

| [[Sequential Ebert]] || [[Approval Voting|Binary]] || [[Utilitarian winner|Sum]] || [[Ebert's Method]]

|}

===[https://rangevoting.org/QualityMulti.html Optimal] [[Proportional representation | Proportional]] Methods ===

===[https://rangevoting.org/QualityMulti.html Optimal] [[Proportional representation|Proportional]] Methods ===

Optimal Systems select all winners at once by optimizing a specific desirable metric for proportionality. First a "quality function" or desired outcome is determined, and then an algorithm is used to determine the winner set that best maximizes that outcome. In most systems this is done by permuting to all possible winner sets not a [[W: Mathematical optimization | maximization algorithm]]. This makes such systems computationally expensive.

Optimal Systems select all winners at once by optimizing a specific desirable metric for proportionality. First a "quality function" or desired outcome is determined, and then an algorithm is used to determine the winner set that best maximizes that outcome. In most systems this is done by permuting to all possible winner sets not a [[W: Mathematical optimization|maximization algorithm]]. This makes such systems computationally expensive.

* [https://rangevoting.org/QualityMulti.html Harmonic Voting]