I have been taking a course on Choice/Voting theory, Arrow's theory, etc. and ran into this book,

Gaming the Vote, discussing the benefits of Range Voting, e.g. each Voter gives each, or some of the, candidate{s} a "value", say from 0 to 5, and the winning candidate is the one with the largest total . The author indicates that this is a better voting system (at least statistically) than the others, though it does require that each voter be able to not only rank, e.g. a > b > c... the candidates, but also given them relative ratings.e.g. a = 5, b= 4, c=0

- Note: as is pointed out, this does not disprove Arrow's theorem, and of course in some cases may be worse than others, but the author suggests that this system generates choices that minimize the "Bayes Dissatisfaction" and is relatively resistant to strategic voting manipulation.

This system was, the author says, discussed by:

Warren D, Smith, during the 1990's, and his papers are at Temple University in

{Works} the following are the ones that I think may be most interesting to me :

My edit of the Wikipedia article is as follows

Range voting (also called ratings summation, average voting, cardinal ratings, score voting, 0–99 voting, the score system, or the point system) is a voting sym for one-seat elections under which voters score, e.g 1-5, 0-99, etc. each candidate, the scores are added up, and the candidate with the highest score wins. “Gaming the Vote” suggests that **Range voting** leads to the minimum Bayes dissatisfaction of all the voting systems analyzed. Range voting satisfies:
- monotonicity criterion,
- favorite betrayal criterion,
- participation criterion,
- consistency criterion
- independence of irrelevant alternatives,
*(See WIKI IIA)*
- Note: Range Voting does NOT satisfy the IIA condition as expressed by Arrow, who specifically rejects Cardinal ordering in this criteria, but it does satisfy the other condition
*"I**f A is preferred to B out of the choice set {A,B}, then introducing a third alternative X, thus expanding the choice set to {A,B,X}, must not make B preferable to A."*

- resolvability criterion,
- reversal symmetry.
- It is immune to cloning, except for the obvious specific case in which a candidate with clones ties, instead of achieving a unique win.

It dies not satisfy:
- not satisfy either the Condorcet criterion (i.e. is not a Condorcet method) or the Condorcet loser criterion, although with all-strategic voters and perfect information the Condorcet winner is a Nash equilibrium.[7]
- not satisfy the majority criterion, but it satisfies a weakened form of it: a majority can force their choice to win, although they might not exercise that capability.
- not satisfy the later-no-harm criterion, meaning that giving a positive rating to a less preferred candidate can cause a more preferred candidate to lose.
- not regarded as a counter-example to Arrow's theorem is that it is a cardinal voting system, while the "universality" criterion of Arrow's theorem effectively restricts that result to ordinal voting systems.

Note: I expect to add more links to Wikipedia discussions of various topics, but just wanted to point to the Smith papers now.

**Voting System evaluation**

A

**voting system** contains rules for valid voting, and how votes are counted and aggregated to yield a final result. The study of formally defined voting systems is called

**voting theory**,

With

**majority rule**, those who are unfamiliar with voting theory are often surprised that another voting system exists,

**each of which has some undesirable features**, or that "majority rule" systems can produce results not supported by a majority.