Score voting

Example

Suppose Tennessee is holding an election on the location of its capital. The population is split between four cities, and all the voters want the capital to be as close to them as possible. The options are:

• Memphis, large but far to the west
• Nashville, medium, near the center
• Chattanooga, small and in the east
• Knoxville, small and isolated

Suppose that 100 voters each decided to grant from 0 to 10 points to each city such that their most liked choice got 10 points, and least liked choice got 0 points, with the intermediate choices getting an amount proportional to their relative distance.

Nashville, the capital in real life, likewise wins in the example.

For comparison, note that traditional first-past-the-post would elect Memphis, even though most citizens consider it the worst choice, because 42% is larger than any other single city. Instant-runoff voting would elect the 2nd-worst choice (Knoxville), because the central candidates would be eliminated early (and Chattanooga voters preferring Knoxville above Nashville). In approval voting, with each voter selecting their top two cities, Nashville would win because of the significant boost from Memphis residents.

Properties

Score voting allows voters to express preferences of varying strengths, making it a rated voting system.

Score voting is not vulnerable to the less-is-more paradox, i.e. raising a candidate's rating can never hurt their chances of winning. Score also satisfies the participation criterion, i.e. a candidate can never lose as a result of voters turning out to support them. Score voting satisfies independence of irrelevant alternatives, and does not tend to exhibit spoiler effects.

It does not satisfy the Condorcet criterion, i.e. the method does not always agree with the majority rule. However, when voters all vote strategically, basing their votes on polling or past election results, the majority-preferred candidate will win.

Strategy

Ideal score voting strategy for well-informed voters is generally identical to their optimal approval voting strategy; voters will want to give their least and most favorite candidates a minimum and a maximum score, respectively. The game-theoretical analysis shows that this claim is not fully general, but holds in most cases. Another strategic voting tactic is given by the weighted mean utility theorem, maximum score for all candidates preferred compared to the expected winners weighted with winning probability and minimum score for all others.

Papers have found that "experimental results support the concept of bias toward unselfish outcomes in large elections." The authors observed what they termed ethical considerations dominating voter behavior as pivot probability decreased. This would imply that larger elections, or those perceived as having a wider margin of victory, would result in fewer tactical voters.

How voters precisely grade candidates is a topic that is not fully settled, although experiments show that their behavior depends on the grade scale, its length, and the possibility to give negative grades.

STAR voting (Score Then Automatic Runoff) is a variant proposed to address some concerns about strategic exaggeration in score voting. Under this system, each voter may assign a score (from 0 to the maximum) to any number of candidates. Of the two highest-scoring candidates, the winner is the one most voters ranked higher. The runoff step was introduced to mitigate the incentive to exaggerate ratings in ordinary score voting.

Advocacy

Albert Heckscher was one of the earliest proponents, advocating for a form of score voting he called the "immanent method" in his 1892 dissertation, in which voters assign any number between -1 and +1 to each alternative, simulating their individual deliberation.

Currently, approval voting is advocated by The Center for Election Science. Since 2014, the Equal Vote Coalition advocates a variant method (STAR) with an extra second evaluation step to address some of the criticisms of traditional score voting.