# Cardinal voting

(Redirected from Cardinal voting systems)

Cardinal voting is an electoral system which allows the voter to give each candidate an independent rating or grade from among at least two levels of approval. Along with ordinal voting systems (also called ranked voting), they are the two main branches of modern voting systems to compete with the venerable simple plurality voting. These are also referred to as "rated", "evaluative", "graded", or "absolute" voting systems.[1][2]

On a rated ballot, the voter may rate each choice independently.
An approval voting ballot does not require ranking or exclusivity.
A majority judgment ballot is based on grades like those used in schools.

The simplest possible cardinal method is Approval voting, which allows only the two grades: "approved" or "unapproved". Other cardinal methods include Score/Range voting, in which ratings are numerical and the candidate with the highest average (or total[3][4]) rating wins; and Majority Judgment, in which ratings are verbal grades and the candidate with the highest median grade wins.

Other variants include disapproval voting options such as negative assignment, but typically out of the same absolute number of votes. That is, a -2 and a +8 add up to ten points, not six, because the absolute value of a negative vote is the same as positive.

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.[5][6][7][8]

Others, however, argue that this is not true, for instance because interpersonal comparisons of cardinal measures are impossible.[9] If that is the case, then cardinal methods do indeed fail to escape Arrow's result.

Psychological research has shown that cardinal ratings are more valid and convey more information than ordinal rankings in measuring human opinion.[10][11][12][13]

In any case, cardinal methods do fall under the Gibbard–Satterthwaite theorem, and therefore any such method must be subject to strategic voting in some instances.[14][15][dubious ][16]

## References

1. ^ "Cardinal voting systems - Electowiki". wiki.electorama.com. Retrieved 2017-01-31.
2. ^ "Voting system - Electowiki". wiki.electorama.com. Retrieved 2017-01-31.
3. ^ "Social Choice and Beyond - Range Voting". www.socialchoiceandbeyond.com. Retrieved 2016-12-10. with the winner being the one with the largest point total. Or, alternatively, the average may be computed and the one with the highest average wins
4. ^ "Score Voting". The Center for Election Science. 2015-05-21. Retrieved 2016-12-10. Simplified forms of score voting automatically give skipped candidates the lowest possible score for the ballot they were skipped. Other forms have those ballots not affect the candidate’s rating at all. Those forms not affecting the candidates rating frequently make use of quotas. Quotas demand a minimum proportion of voters rate that candidate in some way before that candidate is eligible to win.
5. ^ Vasiljev, Sergei (2008-04-01). "Cardinal Voting: The Way to Escape the Social Choice Impossibility". Rochester, NY: Social Science Research Network. SSRN .
6. ^ "Interview with Dr. Kenneth Arrow". The Center for Election Science. October 6, 2012. CES: you mention that your theorem applies to preferential systems or ranking systems. ... But the system that you're just referring to, Approval Voting, falls within a class called cardinal systems. ... Dr. Arrow: And as I said, that in effect implies more information. ... I’m a little inclined to think that score systems where you categorize in maybe three or four classes probably (in spite of what I said about manipulation) is probably the best.
7. ^ "RangeVoting.org - Arrow's theorem". rangevoting.org. Retrieved 2016-12-10. according to Arrow's definition, range voting is "not" a voting system at all
8. ^ "How I Came to Care About Voting Systems". The Center for Election Science. 2011-12-21. Retrieved 2016-12-10. But Arrow only intended his criteria to apply to ranking systems.
9. ^ "Why Not Ranking?". The Center for Election Science. 2016-05-31. Retrieved 2017-01-22. Many voting theorists have resisted asking for more than a ranking, with economics-based reasoning: utilities are not comparable between people. ... But no economist would bat an eye at asking one of the A voters above whether they'd prefer a coin flip between A and B winning or C winning outright...
10. ^ Conklin, E. S.; Sutherland, J. W. (1923-02-01). "A Comparison of the Scale of Values Method with the Order-of-Merit Method.". Journal of Experimental Psychology. 6 (1): 44–57. ISSN 0022-1015. doi:10.1037/h0074763. the scale-of-values method can be used for approximately the same purposes as the order-of-merit method, but that the scale-of-values method is a better means of obtaining a record of judgments
11. ^ Moore, Michael (1975-07-01). "Rating versus ranking in the Rokeach Value Survey: An Israeli comparison". European Journal of Social Psychology. 5 (3): 405–408. ISSN 1099-0992. doi:10.1002/ejsp.2420050313. The extremely high degree of correspondence found between ranking and rating averages ... does not leave any doubt about the preferability of the rating method for group description purposes. The obvious advantage of rating is that while its results are virtually identical to what is obtained by ranking, it supplies more information than ranking does.
12. ^ Maio, Gregory R.; Roese, Neal J.; Seligman, Clive; Katz, Albert (1996-06-01). "Rankings, Ratings, and the Measurement of Values: Evidence for the Superior Validity of Ratings". Basic and Applied Social Psychology. 18 (2): 171–181. ISSN 0197-3533. doi:10.1207/s15324834basp1802_4. Many value researchers have assumed that rankings of values are more valid than ratings of values because rankings force participants to differentiate more incisively between similarly regarded values ... Results indicated that ratings tended to evidence greater validity than rankings within moderate and low-differentiating participants. In addition, the validity of ratings was greater than rankings overall.
13. ^ Johnson, Marilyn F.; Sallis, James F.; Hovell, Melbourne F. (1999-09-01). "Comparison of Rated and Ranked Health and Lifestyle Values". American Journal of Health Behavior. 23 (5): 356–367. doi:10.5993/AJHB.23.5.5. the test-retest reliabilities of the ranking items were slightly higher than were those of the rating items, but construct validities were lower. Because validity is the most important consideration ... the findings of the present research support the use of the rating format in assessing health values. ... added benefit of item independence, which allows for greater flexibility in statistical analyses. ... also easier than ranking items for respondents to complete.
14. ^ Quinn, Jameson (2014-10-22). "Answer to 'What is the significance of the Gibbard-Satterthwaite theorem?'". quora.com. Retrieved 2017-01-22. rated voting systems ... give voters more "expressivity" ... than ranked systems ... Though the G-S theorem still applies, at least there is always a "semi-honest" strategy — one that does not involve giving more support to a candidate you like less than to one you like more.
15. ^ Durand, François (2017-01-06). "Answer to 'Does Gibbard–Satterthwaite theorem apply to all voting systems?'". politics.stackexchange.com. Retrieved 2017-01-22. Whereas Satterthwaite's version only applies to ordinal voting methods, Gibbard's version applies to all deterministic voting methods, including non-ordinal ones.
16. ^ "The Gibbard-Satterthwaite theorem about honest & strategic voting". rangevoting.org. Retrieved 2017-01-22. In range voting elections with 3-or-fewer candidates, it never pays to submit a dishonest vote claiming A>B when you really feel B≥A. ... The Gibbard-Satterthwaite theorem only applies to rank-order-ballot voting systems.